numpypy

Name	numpypy JSON
Version	1.17.2 JSON
	download
home_page	https://github.com/PythonSJL/PyPyNum
Summary	(It is an alias for PyPyNum) PyPyNum is a multifunctional Python math lib. It includes modules for math, data analysis, array ops, crypto, physics, randomness, data prep, stats, solving eqns, image processing, interp, matrix calc, and high-precision math. Designed for scientific computing, data science, and machine learning, PyPyNum provides efficient and versatile tools.
upload_time	2024-12-08 23:26:38
maintainer	None
docs_url	None
author	Shen Jiayi
requires_python	>=3.4
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keywords	math 数学 mathematics 数学计算 numerical 数值 computation 计算 scientific 科学 algebra 代数 calculus 微积分 statistics 统计 linear-algebra 线性代数 optimization 优化 numerical-analysis 数值分析 matrix 矩阵 vector 向量 tensor 张量 numerics 数值计算 library 库 tools 工具 utils 实用程序 algorithms 算法 software 软件 package 包 methods 方法 data-science 数据科学 machine-learning 机器学习 computational 计算的 operations 操作 functions 函数 processing 处理 programming 编程 simulation 仿真 visualization 可视化 physics 物理
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            # PyPyNum

PyPyNum is a multifunctional Python math lib. It includes modules for math, data analysis, array ops, crypto, physics,
randomness, data prep, stats, solving eqns, image processing, interp, matrix calc, and high-precision math. Designed for
scientific computing, data science, and machine learning, PyPyNum provides efficient and versatile tools.

```
 ________   ___    ___  ________   ___    ___  ________    ___  ___   _____ ______
|\   __  \ |\  \  /  /||\   __  \ |\  \  /  /||\   ___  \ |\  \|\  \ |\   _ \  _   \
\ \  \|\  \\ \  \/  / /\ \  \|\  \\ \  \/  / /\ \  \\ \  \\ \  \\\  \\ \  \\\__\ \  \
 \ \   ____\\ \    / /  \ \   ____\\ \    / /  \ \  \\ \  \\ \  \\\  \\ \  \\|__| \  \
  \ \  \___| \/  /  /    \ \  \___| \/  /  /    \ \  \\ \  \\ \  \\\  \\ \  \    \ \  \
   \ \__\  __/  / /       \ \__\  __/  / /       \ \__\\ \__\\ \_______\\ \__\    \ \__\
    \|__| |\___/ /         \|__| |\___/ /         \|__| \|__| \|_______| \|__|     \|__|
          \|___|/                \|___|/
```

[![Downloads](https://static.pepy.tech/badge/pypynum)](https://pepy.tech/project/pypynum)
[![Downloads](https://static.pepy.tech/badge/pypynum/month)](https://pepy.tech/project/pypynum)
[![Downloads](https://static.pepy.tech/badge/pypynum/week)](https://pepy.tech/project/pypynum)

## Version -> 1.17.2 | PyPI -> https://pypi.org/project/PyPyNum/ | Gitee -> https://www.gitee.com/PythonSJL/PyPyNum | GitHub -> https://github.com/PythonSJL/PyPyNum

![LOGO](PyPyNum.png)

The logo cannot be displayed on PyPI, it can be viewed in Gitee or GitHub.

### Introduction

+ Multi functional math library, similar to numpy, scipy, etc., designed specifically for PyPy interpreters and also
  supports other types of Python interpreters
+ Update versions periodically to add more practical features
+ If you need to contact, please add QQ number 2261748025 (Py𝙿𝚢𝚝𝚑𝚘𝚗-水晶兰), or through my email 2261748025@qq.com

```
+++++++++++++++++++++++++++++++++++++++++
+ Tip:                                  +
+ Have suggestions or feature requests? +
+ Feel free to share them with us.      +
+ Your feedback is highly appreciated!  +
+++++++++++++++++++++++++++++++++++++++++
```

### Copyright and License

This Python library is licensed under the GNU Affero General Public License version 3 (AGPLv3).

The license is designed to ensure that network server software is made available to the community, allowing users to
access the source code of modified versions when the software is used to provide network services.

**Key Terms and Conditions:**

- Source Code: The library must be provided with its source code, and any modifications must also be distributed under
  the AGPLv3.
- Free Redistribution: The library can be distributed in source and binary forms without any restrictions.
- No Discrimination: The license does not restrict the use of the software by individuals or organizations, nor does it
  discriminate against fields of use.
- No Discrimination Against Persons or Groups: The license does not restrict anyone from receiving the software.
- Patent License: The patent holder must grant a patent license to anyone who uses the software.
- No Surrender of Others' Freedom: The license does not allow any conditions that contradict the AGPLv3.
- Remote Network Interaction: If the software can interact with users remotely, the source code must be made available
  at no charge.
- Revised Versions of this License: The Free Software Foundation may publish revised versions of the AGPLv3, and users
  have the option to follow the terms of any version.
- Disclaimer of Warranty: There is no warranty for the software, to the extent permitted by applicable law.
- Limitation of Liability: The copyright holder and any other party who modifies and conveys the software are not liable
  for damages arising from the use or inability to use the software.

**Full License Text:**

[GNU Affero General Public License](https://www.gnu.org/licenses/agpl-3.0.en.html)

### Name and Function Introduction of Submodules

|   Submodule Name    |                       Function Introduction                        |
|:-------------------:|:------------------------------------------------------------------:|
|  `pypynum.arrays`   | Provides operations and calculations for multi-dimensional arrays. |
|   `pypynum.chars`   |       Contains a variety of special mathematical characters.       |
|  `pypynum.ciphers`  |      Implements various encryption and decryption algorithms.      |
|  `pypynum.consts`   |           Contains mathematical and physical constants.            |
|  `pypynum.crandom`  |                 Generates random complex numbers.                  |
| `pypynum.dataproc`  |          Tools for data preprocessing and transformation.          |
|   `pypynum.dists`   |    Statistical distribution functions and related calculations.    |
| `pypynum.equations` |         Solves equations and performs symbolic operations.         |
|    `pypynum.fft`    |  Implements Fast Fourier Transforms and related functionalities.   |
|   `pypynum.files`   |                  File reading and writing tools.                   |
|   `pypynum.geoms`   |             Geometric shapes and calculation methods.              |
|  `pypynum.graphs`   |           Graph theory algorithms and network analysis.            |
|  `pypynum.groups`   |         Group theory calculations and structural analysis.         |
| `pypynum.hypcmpnms` |        Hypercomplex number operations and transformations.         |
|  `pypynum.images`   |              Image processing and manipulation tools.              |
|  `pypynum.interp`   |         Interpolation methods and function approximation.          |
|  `pypynum.kernels`  |          Implementation of kernel functions and methods.           |
|  `pypynum.logics`   |                    Simulates logical circuits.                     |
|   `pypynum.maths`   |     Basic mathematical operations and commonly used functions.     |
| `pypynum.matrices`  |         Matrix operations and linear algebra calculations.         |
| `pypynum.multiprec` |               High-precision numerical computations.               |
| `pypynum.networks`  |                   Network models and algorithms.                   |
|  `pypynum.numbers`  |           Operations on numerical types and properties.            |
| `pypynum.plotting`  |                     Data visualization tools.                      |
|   `pypynum.polys`   |              Polynomial operations and calculations.               |
| `pypynum.pprinters` |              Advanced printing and formatting output.              |
|  `pypynum.random`   |                Generates arrays of random numbers.                 |
|   `pypynum.regs`    |               Regression analysis and model fitting.               |
|   `pypynum.seqs`    |              Computes various mathematical sequences.              |
|  `pypynum.special`  | Provides advanced special functions for mathematical computations. |
| `pypynum.stattest`  |                Statistical tests and data analysis.                |
|  `pypynum.symbols`  |         Symbolic computation and expression manipulation.          |
|  `pypynum.tensors`  |                Tensor operations and calculations.                 |
|   `pypynum.test`    |                Simple code testing for the library.                |
|   `pypynum.this`    |     The Zen of the library, expressing its guiding principles.     |
|   `pypynum.tools`   |                General tools and helper functions.                 |
|   `pypynum.trees`   |           Tree structures and algorithm implementations.           |
|   `pypynum.types`   |      Contains various types, exceptions, and configurations.       |
|  `pypynum.ufuncs`   |           Universal functions and vectorized operations.           |
|   `pypynum.utils`   |             Utility programs and auxiliary functions.              |
|  `pypynum.vectors`  |                Vector operations and calculations.                 |
|   `pypynum.zh_cn`   | Provides Chinese language interfaces for various functionalities.  |

### The Zen of PyPyNum (Preview)

```
                The Zen of PyPyNum, by Shen Jiayi

In this mathematical sanctuary, we weave our algorithms with pure Python threads.

Precision outweighs approximation.
Elegance in mathematics transcends the bulky algorithms.
Clarity in logic illuminates the darkest problems.
Simplicity in form is the pinnacle of sophistication.
Flat hierarchies in our code mirror the linear nature of functions.
Sparse code, like a minimal polynomial, retains essence without redundancy.
```

```
...

Do you want to view all the content?

Enter "from pypynum import this" in your

Python interpreter and run it!
```

```
                                                                September 5, 2024
```

### Functional Changes Compared to the Previous Version

```
!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=

Fixed some known issues.

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=

The pypynum.utils module has recently introduced a new class
called RadixInt. This class is designed to facilitate the
representation and manipulation of integers in various bases,
ranging from base 2 to base 36.

The RadixInt class within the pypynum.utils module provides a
robust way to work with integers in custom bases. It allows
users to initialize instances with either a decimal number or a
string representation of a number in the desired base. The class
supports conversion between different bases, as well as basic
arithmetic operations that can be performed on integers
represented in various bases.


<<< The following are some usage examples >>>


from pypynum import RadixInt

# Base-2 and base-10 numbers
binary_num = RadixInt("1010", 2)
decimal_num = RadixInt(10, 10)
print(binary_num)  # Output: (1010)_{2}
print(decimal_num)  # Output: (10)_{10}
binary_to_octal = RadixInt("1010", 2).to_base(8)
print(binary_to_octal)  # Output: (12)_{8}
# Addition
result_add = binary_num + decimal_num
print(result_add)  # Output: (20)_{10}
# Base-8 and base-10 numbers
octal_num = RadixInt("123", 8)
decimal_num = RadixInt(5, 10)
# Subtraction
result_sub = octal_num - decimal_num
print(result_sub)  # Output: (78)_{10}
# Base-16 and base-2 numbers
hex_num = RadixInt("1A", 16)
binary_num = RadixInt("11", 2)
# Multiplication
result_mul = hex_num * binary_num
print(result_mul)  # Output: (78)_{10}

!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=
```

### Run Time Test

Python interpreter version

+ CPython 3.8.10

+ PyPy 3.10.12

| Matrix Time Test                               | NumPy+CPython (seconds)                                                                                                                                                            | Ranking | PyPyNum+PyPy (seconds)                                                                                                                                                             | Ranking | Mpmath_+_PyPy_ (seconds)                                                                                                                                                         | Ranking | SymPy_+_PyPy_ (seconds)                                                                                                                                                                                                                    | Ranking |
|------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|
| Create a hundred order random number matrix    | 0.000083                                                                                                                                                                           | 1       | 0.005374                                                                                                                                                                           | 2       | 0.075253                                                                                                                                                                         | 3       | 0.230530                                                                                                                                                                                                                                   | 4       |
| Create a thousand order random number matrix   | 0.006740                                                                                                                                                                           | 1       | 0.035666                                                                                                                                                                           | 2       | 1.200950                                                                                                                                                                         | 3       | 4.370265                                                                                                                                                                                                                                   | 4       |
| Addition of matrices of order one hundred      | 0.000029                                                                                                                                                                           | 1       | 0.002163                                                                                                                                                                           | 2       | 0.045641                                                                                                                                                                         | 4       | 0.035700                                                                                                                                                                                                                                   | 3       |
| Adding matrices of order one thousand          | 0.002647                                                                                                                                                                           | 1       | 0.019111                                                                                                                                                                           | 2       | 1.746957                                                                                                                                                                         | 4       | 0.771542                                                                                                                                                                                                                                   | 3       |
| Determinant of a hundred order matrix          | 0.087209                                                                                                                                                                           | 2       | 0.016331                                                                                                                                                                           | 1       | 4.354507                                                                                                                                                                         | 3       | 5.157206                                                                                                                                                                                                                                   | 4       |
| Determinant of a thousand order matrix         | 0.616113                                                                                                                                                                           | 1       | 3.509747                                                                                                                                                                           | 2       | It takes a long time                                                                                                                                                             | 3       | It takes a long time                                                                                                                                                                                                                       | 4       |
| Finding the inverse of a hundred order matrix  | 0.162770                                                                                                                                                                           | 2       | 0.015768                                                                                                                                                                           | 1       | 8.162948                                                                                                                                                                         | 3       | 21.437424                                                                                                                                                                                                                                  | 4       |
| Finding the inverse of a thousand order matrix | 0.598905                                                                                                                                                                           | 1       | 17.072552                                                                                                                                                                          | 2       | It takes a long time                                                                                                                                                             | 3       | It takes a long time                                                                                                                                                                                                                       | 4       |
| Array output effect                            | ```[[[[ -7 -67]```<br>```[-78  29]]```<br><br>```[[-86 -97]```<br>```[ 68  -3]]]```<br><br><br>```[[[ 11  42]```<br>```[ 24 -65]]```<br><br>```[[-60  72]```<br>```[ 73   2]]]]``` | /       | ```[[[[ 37  83]```<br>```[ 40   2]]```<br><br>```[[ -5 -34]```<br>```[ -7  72]]]```<br><br><br>```[[[ 13 -64]```<br>```[  6  90]]```<br><br>```[[ 68  57]```<br>```[ 78  11]]]]``` | /       | ```[-80.0   -8.0  80.0  -88.0]```<br>```[-99.0  -43.0  87.0   81.0]```<br>```[ 20.0  -55.0  98.0    8.0]```<br>```[  8.0   44.0  64.0  -35.0]```<br><br>(Only supports matrices) | /       | ```⎡⎡16   -56⎤  ⎡ 8   -28⎤⎤```<br>```⎢⎢        ⎥  ⎢        ⎥⎥```<br>```⎢⎣-56  56 ⎦  ⎣-28  28 ⎦⎥```<br>```⎢                      ⎥```<br>```⎢ ⎡-2  7 ⎤   ⎡-18  63 ⎤⎥```<br>```⎢ ⎢      ⎥   ⎢        ⎥⎥```<br>```⎣ ⎣7   -7⎦   ⎣63   -63⎦⎦``` | /       |

### Basic Structure

```
PyPyNum
├── arrays
│   ├── CLASS
│   │   ├── Array(object)/__init__(self: Any, data: Any, check: Any) -> Any
│   │   └── BoolArray(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── array(data: Any) -> Any
│       ├── asarray(data: Any) -> Any
│       ├── aslist(data: Any) -> Any
│       ├── boolarray(data: Any) -> Any
│       ├── fill(shape: typing.Union[list, tuple], sequence: typing.Union[list, tuple, str], repeat: bool, pad: typing.Any, rtype: typing.Callable) -> typing.Any
│       ├── full(shape: typing.Union[list, tuple], fill_value: typing.Any, rtype: typing.Callable) -> typing.Any
│       ├── full_like(a: typing.Any, fill_value: typing.Any, rtype: typing.Callable) -> typing.Any
│       ├── get_shape(data: Any) -> Any
│       ├── is_valid_array(_array: Any, _shape: Any) -> Any
│       ├── ones(shape: typing.Union[list, tuple], rtype: typing.Callable) -> typing.Any
│       ├── ones_like(a: typing.Any, rtype: typing.Callable) -> typing.Any
│       ├── tensorproduct(tensors: pypynum.arrays.Array) -> pypynum.arrays.Array
│       ├── zeros(shape: typing.Union[list, tuple], rtype: typing.Callable) -> typing.Any
│       └── zeros_like(a: typing.Any, rtype: typing.Callable) -> typing.Any
├── chars
│   ├── CLASS
│   └── FUNCTION
│       ├── int2subscript(standard_str: str) -> str
│       ├── int2superscript(standard_str: str) -> str
│       ├── subscript2int(subscript_str: str) -> str
│       └── superscript2int(superscript_str: str) -> str
├── ciphers
│   ├── CLASS
│   └── FUNCTION
│       ├── atbash(text: str) -> str
│       ├── base_64(text: str, decrypt: bool) -> str
│       ├── caesar(text: str, shift: int, decrypt: bool) -> str
│       ├── hill256(text: bytes, key: list, decrypt: bool) -> bytes
│       ├── ksa(key: bytes) -> list
│       ├── morse(text: str, decrypt: bool) -> str
│       ├── playfair(text: str, key: str, decrypt: bool) -> str
│       ├── prga(s: list) -> Any
│       ├── rc4(text: bytes, key: bytes) -> bytes
│       ├── rot13(text: str) -> str
│       ├── substitution(text: str, sub_map: dict, decrypt: bool) -> str
│       └── vigenere(text: str, key: str, decrypt: bool) -> str
├── consts
│   ├── CLASS
│   └── FUNCTION
├── crandom
│   ├── CLASS
│   └── FUNCTION
│       ├── randint_polar(left: int, right: int, mod: typing.Union[int, float], angle: typing.Union[int, float]) -> complex
│       ├── randint_rect(left: int, right: int, real: typing.Union[int, float], imag: typing.Union[int, float]) -> complex
│       ├── random_polar(mod: typing.Union[int, float], angle: typing.Union[int, float]) -> complex
│       ├── random_rect(real: typing.Union[int, float], imag: typing.Union[int, float]) -> complex
│       ├── uniform_polar(left: typing.Union[int, float], right: typing.Union[int, float], mod: typing.Union[int, float], angle: typing.Union[int, float]) -> complex
│       └── uniform_rect(left: typing.Union[int, float], right: typing.Union[int, float], real: typing.Union[int, float], imag: typing.Union[int, float]) -> complex
├── dataproc
│   ├── CLASS
│   │   └── Series(object)/__init__(self: Any, data: typing.Any, index: typing.Any) -> None
│   └── FUNCTION
├── dists
│   ├── CLASS
│   └── FUNCTION
│       ├── beta_pdf(x: Any, a: Any, b: Any) -> Any
│       ├── binom_pmf(k: Any, n: Any, p: Any) -> Any
│       ├── cauchy_cdf(x: Any, x0: Any, gamma: Any) -> Any
│       ├── cauchy_pdf(x: Any, x0: Any, gamma: Any) -> Any
│       ├── chi2_cdf(x: Any, df: Any) -> Any
│       ├── chi2_pdf(x: Any, df: Any) -> Any
│       ├── expon_cdf(x: Any, scale: Any) -> Any
│       ├── expon_pdf(x: Any, scale: Any) -> Any
│       ├── f_pdf(x: Any, dfnum: Any, dfden: Any) -> Any
│       ├── gamma_pdf(x: Any, shape: Any, scale: Any) -> Any
│       ├── geometric_pmf(k: Any, p: Any) -> Any
│       ├── hypergeom_pmf(k: Any, mg: Any, n: Any, nt: Any) -> Any
│       ├── invgauss_pdf(x: Any, mu: Any, lambda_: Any, alpha: Any) -> Any
│       ├── levy_pdf(x: Any, c: Any) -> Any
│       ├── log_logistic_cdf(x: Any, alpha: Any, beta: Any) -> Any
│       ├── log_logistic_pdf(x: Any, alpha: Any, beta: Any) -> Any
│       ├── logistic_cdf(x: Any, mu: Any, s: Any) -> Any
│       ├── logistic_pdf(x: Any, mu: Any, s: Any) -> Any
│       ├── lognorm_cdf(x: Any, mu: Any, sigma: Any) -> Any
│       ├── lognorm_pdf(x: Any, s: Any, scale: Any) -> Any
│       ├── logser_pmf(k: Any, p: Any) -> Any
│       ├── multinomial_pmf(k: Any, n: Any, p: Any) -> Any
│       ├── nbinom_pmf(k: Any, n: Any, p: Any) -> Any
│       ├── nhypergeom_pmf(k: Any, m: Any, n: Any, r: Any) -> Any
│       ├── normal_cdf(x: Any, mu: Any, sigma: Any) -> Any
│       ├── normal_pdf(x: Any, mu: Any, sigma: Any) -> Any
│       ├── pareto_pdf(x: Any, k: Any, m: Any) -> Any
│       ├── poisson_pmf(k: Any, mu: Any) -> Any
│       ├── rayleigh_pdf(x: Any, sigma: Any) -> Any
│       ├── t_pdf(x: Any, df: Any) -> Any
│       ├── uniform_cdf(x: Any, loc: Any, scale: Any) -> Any
│       ├── uniform_pdf(x: Any, loc: Any, scale: Any) -> Any
│       ├── vonmises_pdf(x: Any, mu: Any, kappa: Any) -> Any
│       ├── weibull_max_pdf(x: Any, c: Any, scale: Any, loc: Any) -> Any
│       ├── weibull_min_pdf(x: Any, c: Any, scale: Any, loc: Any) -> Any
│       └── zipf_pmf(k: Any, s: Any, n: Any) -> Any
├── equations
│   ├── CLASS
│   └── FUNCTION
│       ├── lin_eq(left: list, right: list) -> list
│       └── poly_eq(coefficients: list) -> list
├── fft
│   ├── CLASS
│   │   └── FT1D(object)/__init__(self: Any, data: Any) -> Any
│   └── FUNCTION
├── files
│   ├── CLASS
│   └── FUNCTION
│       ├── read(file: str) -> list
│       └── write(file: str, cls: object) -> Any
├── geoms
│   ├── CLASS
│   │   ├── Circle(object)/__init__(self: Any, center: typing.Union[list, tuple], radius: typing.Union[int, float]) -> Any
│   │   ├── Line(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> Any
│   │   ├── Point(object)/__init__(self: Any, p: typing.Union[list, tuple]) -> Any
│   │   ├── Polygon(object)/__init__(self: Any, p: typing.Union[list, tuple]) -> Any
│   │   ├── Quadrilateral(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple], c: typing.Union[list, tuple], d: typing.Union[list, tuple]) -> Any
│   │   └── Triangle(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple], c: typing.Union[list, tuple]) -> Any
│   └── FUNCTION
│       └── distance(g1: Any, g2: Any, error: typing.Union[int, float]) -> float
├── graphs
│   ├── CLASS
│   │   ├── BaseGraph(object)/__init__(self: Any) -> Any
│   │   ├── BaseWeGraph(pypynum.graphs.BaseGraph)/__init__(self: Any) -> Any
│   │   ├── DiGraph(pypynum.graphs.BaseGraph)/__init__(self: Any) -> Any
│   │   ├── UnGraph(pypynum.graphs.BaseGraph)/__init__(self: Any) -> Any
│   │   ├── WeDiGraph(pypynum.graphs.BaseWeGraph)/__init__(self: Any) -> Any
│   │   └── WeUnGraph(pypynum.graphs.BaseWeGraph)/__init__(self: Any) -> Any
│   └── FUNCTION
├── groups
│   ├── CLASS
│   │   └── Group(object)/__init__(self: Any, data: Any, operation: Any) -> Any
│   └── FUNCTION
│       └── group(data: Any) -> Any
├── hypcmpnms
│   ├── CLASS
│   │   ├── Euler(object)/__init__(self: Any, y: typing.Union[int, float], p: typing.Union[int, float], r: typing.Union[int, float]) -> Any
│   │   ├── Octonion(object)/__init__(self: Any, s: typing.Union[int, float], t: typing.Union[int, float], u: typing.Union[int, float], v: typing.Union[int, float], w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> Any
│   │   └── Quaternion(object)/__init__(self: Any, w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> Any
│   └── FUNCTION
│       ├── convert(data: typing.Union[pypynum.hypcmpnms.Quaternion, pypynum.matrices.Matrix, pypynum.hypcmpnms.Euler], to: str) -> typing.Union[pypynum.hypcmpnms.Quaternion, pypynum.matrices.Matrix, pypynum.hypcmpnms.Euler]
│       ├── euler(yaw: typing.Union[int, float], pitch: typing.Union[int, float], roll: typing.Union[int, float]) -> pypynum.hypcmpnms.Euler
│       ├── octo(s: typing.Union[int, float], t: typing.Union[int, float], u: typing.Union[int, float], v: typing.Union[int, float], w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> pypynum.hypcmpnms.Octonion
│       └── quat(w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> pypynum.hypcmpnms.Quaternion
├── images
│   ├── CLASS
│   │   ├── BMP(pypynum.images.BaseImage)/__init__(self: Any) -> None
│   │   ├── BaseImage(object)/__init__(self: Any) -> None
│   │   └── PNG(pypynum.images.BaseImage)/__init__(self: Any) -> None
│   └── FUNCTION
│       └── crc(data: Any, length: Any, init: Any, xor: Any) -> Any
├── interp
│   ├── CLASS
│   └── FUNCTION
│       ├── bicubic(x: Any) -> Any
│       ├── contribute(src: Any, x: Any, y: Any, channels: Any) -> Any
│       ├── interp1d(data: typing.Union[list, tuple], length: int) -> list
│       └── interp2d(src: Any, new_height: Any, new_width: Any, channels: Any, round_res: Any, min_val: Any, max_val: Any) -> Any
├── kernels
│   ├── CLASS
│   └── FUNCTION
│       ├── det2x2kernel(a: typing.Union[list, tuple]) -> float
│       ├── det3x3kernel(a: typing.Union[list, tuple]) -> float
│       ├── det4x4kernel(a: typing.Union[list, tuple]) -> float
│       ├── eigen2x2kernel(a: typing.Union[list, tuple]) -> tuple
│       ├── inv2x2kernel(a: typing.Union[list, tuple]) -> list
│       ├── inv3x3kernel(a: typing.Union[list, tuple]) -> list
│       ├── inv4x4kernel(a: typing.Union[list, tuple]) -> list
│       ├── lu2x2kernel(a: typing.Union[list, tuple]) -> tuple
│       ├── lu3x3kernel(a: typing.Union[list, tuple]) -> tuple
│       ├── lu4x4kernel(a: typing.Union[list, tuple]) -> tuple
│       ├── matexp2x2kernel(a: typing.Union[list, tuple]) -> list
│       ├── matmul2x2kernel(a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> list
│       ├── matmul3x3kernel(a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> list
│       ├── matmul4x4kernel(a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> list
│       └── matpow2x2kernel(a: typing.Union[list, tuple], n: typing.Union[int, float, complex]) -> list
├── logics
│   ├── CLASS
│   │   ├── AND(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── Basic(object)/__init__(self: Any, label: Any) -> Any
│   │   ├── Binary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── COMP(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── DFF(pypynum.logics.Unary)/__init__(self: Any, label: Any, pin0: Any, state: Any) -> Any
│   │   ├── FullAdder(pypynum.logics.Ternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any
│   │   ├── FullSuber(pypynum.logics.Ternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any
│   │   ├── HalfAdder(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── HalfSuber(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── JKFF(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, state: Any) -> Any
│   │   ├── NAND(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── NOR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── NOT(pypynum.logics.Unary)/__init__(self: Any, label: Any, pin0: Any) -> Any
│   │   ├── OR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   ├── Quaternary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any
│   │   ├── TFF(pypynum.logics.Unary)/__init__(self: Any, label: Any, pin0: Any, state: Any) -> Any
│   │   ├── Ternary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any
│   │   ├── TwoBDiver(pypynum.logics.Quaternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any
│   │   ├── TwoBMuler(pypynum.logics.Quaternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any
│   │   ├── Unary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any) -> Any
│   │   ├── XNOR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   │   └── XOR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any
│   └── FUNCTION
│       └── connector(previous: Any, latter: Any) -> Any
├── maths
│   ├── CLASS
│   └── FUNCTION
│       ├── arrangement(n: int, r: int) -> int
│       ├── combination(n: int, r: int) -> int
│       ├── acos(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acosh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acot(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acoth(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acsc(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── acsch(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── arrangement(n: int, r: int) -> int
│       ├── asec(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── asech(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── asin(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── asinh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── atan(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── atanh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── average(data: typing.Union[list, tuple], weights: typing.Union[list, tuple]) -> float
│       ├── beta(p: typing.Union[int, float], q: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── central_moment(data: typing.Union[list, tuple], order: int) -> float
│       ├── coeff_det(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── combination(n: int, r: int) -> int
│       ├── corr_coeff(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── cos(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cosh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cot(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── coth(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cov(x: typing.Union[list, tuple], y: typing.Union[list, tuple], ddof: int) -> typing.Union[int, float, complex]
│       ├── crt(n: typing.Union[list, tuple], a: typing.Union[list, tuple]) -> int
│       ├── csc(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── csch(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── cumprod(lst: typing.Union[list, tuple]) -> list
│       ├── cumsum(lst: typing.Union[list, tuple]) -> list
│       ├── deriv(f: Any, x: float, h: float, method: str, args: Any, kwargs: Any) -> Any
│       ├── erf(x: typing.Union[int, float]) -> float
│       ├── exgcd(a: int, b: int) -> tuple
│       ├── exp(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── factorial(n: int) -> int
│       ├── freq(data: typing.Union[list, tuple]) -> dict
│       ├── gamma(alpha: typing.Union[int, float]) -> float
│       ├── gcd(args: int) -> int
│       ├── geom_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── harm_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── integ(f: Any, x_start: typing.Union[int, float], x_end: typing.Union[int, float], n: int, args: Any, kwargs: Any) -> float
│       ├── iroot(y: int, n: int) -> int
│       ├── is_possibly_square(n: int) -> bool
│       ├── is_square(n: int) -> bool
│       ├── isqrt(x: int) -> int
│       ├── kurt(data: typing.Union[list, tuple], fisher: bool) -> float
│       ├── lcm(args: int) -> int
│       ├── ln(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── lowergamma(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── median(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── mod_order(a: int, n: int, b: int) -> int
│       ├── mode(data: typing.Union[list, tuple]) -> Any
│       ├── normalize(data: typing.Union[list, tuple], target: typing.Union[int, float, complex]) -> typing.Union[list, tuple]
│       ├── parity(x: int) -> int
│       ├── pi(i: int, n: int, f: Any) -> typing.Union[int, float, complex]
│       ├── power_mean(numbers: typing.Union[list, tuple], p: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── primitive_root(a: int, single: bool) -> typing.Union[int, list]
│       ├── product(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── ptp(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── quantile(data: list, q: float, interpolation: str, ordered: bool) -> float
│       ├── raw_moment(data: typing.Union[list, tuple], order: int) -> float
│       ├── roll(seq: typing.Union[list, tuple, str], shift: int) -> typing.Union[list, tuple, str]
│       ├── root(x: typing.Union[int, float, complex], y: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── sec(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── sech(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── sigma(i: int, n: int, f: Any) -> typing.Union[int, float, complex]
│       ├── sigmoid(x: typing.Union[int, float]) -> float
│       ├── sign(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── sin(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── sinh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── skew(data: typing.Union[list, tuple]) -> float
│       ├── square_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── std(numbers: typing.Union[list, tuple], ddof: int) -> typing.Union[int, float, complex]
│       ├── sumprod(arrays: typing.Union[list, tuple]) -> typing.Union[int, float, complex]
│       ├── tan(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── tanh(x: typing.Union[int, float]) -> typing.Union[int, float]
│       ├── totient(n: int) -> int
│       ├── uppergamma(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── var(numbers: typing.Union[list, tuple], ddof: int) -> typing.Union[int, float, complex]
│       ├── xlogy(x: typing.Union[int, float, complex], y: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       └── zeta(alpha: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
├── matrices
│   ├── CLASS
│   │   └── Matrix(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── cholesky(matrix: pypynum.matrices.Matrix, hermitian: bool) -> pypynum.matrices.Matrix
│       ├── diag(v: typing.Any, k: int, n: int, m: int) -> typing.Any
│       ├── diag_indices(n: int, k: int, m: int) -> tuple
│       ├── eigen(matrix: pypynum.matrices.Matrix) -> tuple
│       ├── hessenberg(matrix: pypynum.matrices.Matrix) -> tuple
│       ├── identity(n: int, m: int) -> pypynum.matrices.Matrix
│       ├── lu(matrix: pypynum.matrices.Matrix) -> tuple
│       ├── mat(data: Any) -> Any
│       ├── perm_mat(num_rows: int, num_cols: int, row_swaps: typing.Union[list, tuple], col_swaps: typing.Union[list, tuple], rtype: typing.Callable) -> typing.Any
│       ├── perm_mat_indices(num_rows: int, num_cols: int, row_swaps: typing.Union[list, tuple], col_swaps: typing.Union[list, tuple]) -> tuple
│       ├── qr(matrix: pypynum.matrices.Matrix, reduce: bool) -> tuple
│       ├── rank_decomp(matrix: pypynum.matrices.Matrix) -> tuple
│       ├── rotate90(matrix: pypynum.matrices.Matrix, times: int) -> pypynum.matrices.Matrix
│       ├── svd(matrix: pypynum.matrices.Matrix, full: bool, calc_uv: bool) -> tuple
│       ├── tril_indices(n: int, k: int, m: int) -> tuple
│       └── triu_indices(n: int, k: int, m: int) -> tuple
├── multiprec
│   ├── CLASS
│   │   └── MPComplex(object)/__init__(self: Any, real: Any, imag: Any, sigfigs: Any) -> Any
│   └── FUNCTION
│       ├── _remove_trailing_zeros(value: typing.Any) -> str
│       ├── _setprec(sigfigs: int) -> Any
│       ├── asmpc(real: typing.Union[int, float, str, decimal.Decimal, complex, pypynum.multiprec.MPComplex], imag: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> pypynum.multiprec.MPComplex
│       ├── frac2dec(frac: fractions.Fraction, sigfigs: int) -> decimal.Decimal
│       ├── mp_acos(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_asin(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_atan(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_atan2(y: typing.Union[int, float, str, decimal.Decimal], x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_catalan(sigfigs: int) -> decimal.Decimal
│       ├── mp_cos(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_cosh(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_e(sigfigs: int, method: str) -> decimal.Decimal
│       ├── mp_euler_gamma(sigfigs: int) -> decimal.Decimal
│       ├── mp_exp(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int, builtin: bool) -> decimal.Decimal
│       ├── mp_fresnel_c(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_fresnel_s(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       ├── mp_ln(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int, builtin: bool) -> decimal.Decimal
│       ├── mp_log(x: typing.Union[int, float, str, decimal.Decimal], base: typing.Union[int, float, str, decimal.Decimal], sigfigs: int, builtin: bool) -> decimal.Decimal
│       ├── mp_phi(sigfigs: int, method: str) -> decimal.Decimal
│       ├── mp_pi(sigfigs: int, method: str) -> decimal.Decimal
│       ├── mp_sin(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
│       └── mp_sinh(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal
├── networks
│   ├── CLASS
│   │   └── NeuralNetwork(object)/__init__(self: Any, _input: Any, _hidden: Any, _output: Any) -> Any
│   └── FUNCTION
│       └── neuraln(_input: Any, _hidden: Any, _output: Any) -> Any
├── numbers
│   ├── CLASS
│   └── FUNCTION
│       ├── float2fraction(number: float, mixed: bool, error: float) -> tuple
│       ├── int2roman(integer: int, overline: bool) -> str
│       ├── int2words(integer: int) -> str
│       ├── parse_float(s: str) -> tuple
│       ├── roman2int(roman_num: str) -> int
│       ├── split_float(s: str) -> tuple
│       └── str2int(string: str) -> int
├── plotting
│   ├── CLASS
│   └── FUNCTION
│       ├── background(right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool) -> typing.Union[list, str]
│       ├── binary(function: Any, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], error: Any, compare: Any, string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]
│       ├── c_unary(function: Any, projection: str, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]
│       ├── change(data: typing.Union[list, str]) -> typing.Union[list, str]
│       ├── color(text: str, rgb: typing.Union[list, tuple]) -> str
│       └── unary(function: Any, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]
├── polys
│   ├── CLASS
│   │   └── Polynomial(object)/__init__(self: Any, terms: Any) -> Any
│   └── FUNCTION
│       ├── chebgauss(n: Any) -> Any
│       ├── chebpoly(n: Any, single: Any) -> Any
│       ├── from_coeffs(coeffs: Any) -> Any
│       ├── from_coords(coords: Any) -> Any
│       ├── laggauss(n: Any) -> Any
│       ├── lagpoly(n: Any, single: Any) -> Any
│       ├── leggauss(n: Any) -> Any
│       ├── legpoly(n: Any, single: Any) -> Any
│       └── poly(terms: Any) -> Any
├── pprinters
│   ├── CLASS
│   └── FUNCTION
│       └── pprint_matrix(matrix: Any, style: Any, output: Any) -> Any
├── random
│   ├── CLASS
│   └── FUNCTION
│       ├── __create_nested_list(dimensions: Any, func: Any) -> Any
│       ├── __validate_shape(shape: Any) -> Any
│       ├── choice(seq: typing.Union[list, tuple, str], shape: typing.Union[list, tuple]) -> Any
│       ├── gauss(mu: typing.Union[int, float], sigma: typing.Union[int, float], shape: typing.Union[list, tuple]) -> typing.Union[float, list]
│       ├── rand(shape: typing.Union[list, tuple]) -> typing.Union[float, list]
│       ├── randint(a: int, b: int, shape: typing.Union[list, tuple]) -> typing.Union[int, list]
│       └── uniform(a: typing.Union[int, float], b: typing.Union[int, float], shape: typing.Union[list, tuple]) -> typing.Union[float, list]
├── regs
│   ├── CLASS
│   └── FUNCTION
│       ├── lin_reg(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> list
│       ├── par_reg(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> list
│       └── poly_reg(x: typing.Union[list, tuple], y: typing.Union[list, tuple], n: int) -> list
├── seqs
│   ├── CLASS
│   └── FUNCTION
│       ├── arithmetic_sequence(a1: typing.Union[int, float], an: typing.Union[int, float], d: typing.Union[int, float], n: typing.Union[int, float], s: typing.Union[int, float]) -> dict
│       ├── bell(n: int) -> list
│       ├── bernoulli(n: int, single: bool) -> typing.Union[list, tuple]
│       ├── catalan(n: int, single: bool) -> typing.Union[int, list]
│       ├── farey(n: int) -> list
│       ├── fibonacci(n: int, single: bool) -> typing.Union[int, list]
│       ├── geometric_sequence(a1: typing.Union[int, float], an: typing.Union[int, float], r: typing.Union[int, float], n: typing.Union[int, float], s: typing.Union[int, float]) -> dict
│       ├── lucas(n: int, single: bool) -> typing.Union[int, list]
│       ├── padovan(n: int, single: bool) -> typing.Union[int, list]
│       ├── pascal(n: int) -> list
│       ├── pell(n: int, single: bool) -> typing.Union[int, list]
│       ├── pelllucas(n: int, single: bool) -> typing.Union[int, list]
│       ├── perrin(n: int, single: bool) -> typing.Union[int, list]
│       ├── recaman(n: int, single: bool) -> typing.Union[int, list]
│       ├── stirling1(n: int) -> list
│       ├── stirling2(n: int) -> list
│       ├── sylvester(n: int, single: bool) -> typing.Union[int, list]
│       ├── tetranacci(n: int, single: bool) -> typing.Union[int, list]
│       └── tribonacci(n: int, single: bool) -> typing.Union[int, list]
├── special
│   ├── CLASS
│   └── FUNCTION
│       ├── besseli0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── besseli1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── besseliv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── besselj0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── besselj1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── besseljv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── hyp0f1(b0: typing.Union[int, float, complex], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── hyp1f1(a0: typing.Union[int, float, complex], b0: typing.Union[int, float, complex], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── hyp2f1(a0: typing.Union[int, float, complex], a1: typing.Union[int, float, complex], b0: typing.Union[int, float, complex], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── hyppfq(a: typing.Union[list, tuple], b: typing.Union[list, tuple], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qbeta(a: typing.Union[int, float, complex], b: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qbinomial(n: typing.Union[int, float, complex], m: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qcos_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qcos_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qcosh_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qcosh_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qexp_large(z: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qexp_small(z: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qfactorial(n: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qgamma(n: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qpi(q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qpochhammer(a: typing.Union[int, float, complex], q: typing.Union[int, float, complex], n: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qsin_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qsin_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       ├── qsinh_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
│       └── qsinh_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
├── stattest
│   ├── CLASS
│   └── FUNCTION
│       ├── chi2_cont(contingency: list, lambda_: float, calc_p: bool, corr: bool) -> tuple
│       ├── chisquare(observed: list, expected: list) -> tuple
│       ├── kurttest(data: list, two_tailed: bool) -> tuple
│       ├── mediantest(samples: Any, ties: Any, lambda_: Any, corr: Any) -> Any
│       ├── normaltest(data: list) -> tuple
│       └── skewtest(data: list, two_tailed: bool) -> tuple
├── symbols
│   ├── CLASS
│   └── FUNCTION
│       └── parse_expr(expr: str) -> list
├── tensors
│   ├── CLASS
│   │   └── Tensor(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       ├── ten(data: list) -> pypynum.tensors.Tensor
│       └── tensor_and_number(tensor: Any, operator: Any, number: Any) -> Any
├── test
│   ├── CLASS
│   └── FUNCTION
├── this
│   ├── CLASS
│   └── FUNCTION
├── tools
│   ├── CLASS
│   └── FUNCTION
│       ├── classify(array: typing.Union[list, tuple]) -> dict
│       ├── cos_sim(seq1: typing.Union[list, tuple, str], seq2: typing.Union[list, tuple, str], is_vector: bool) -> float
│       ├── damerau(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> int
│       ├── dedup(iterable: typing.Union[list, tuple, str]) -> typing.Union[list, tuple, str]
│       ├── fast_pow(a: typing.Any, n: int, init: typing.Any, mul: typing.Callable) -> typing.Any
│       ├── findall(seq: typing.Union[list, tuple, str], pat: typing.Union[list, tuple, str]) -> list
│       ├── frange(start: typing.Union[int, float], stop: typing.Union[int, float], step: float) -> list
│       ├── geomspace(start: typing.Union[int, float], stop: typing.Union[int, float], number: int) -> list
│       ├── kmp_table(pattern: typing.Union[list, tuple, str]) -> list
│       ├── lcsubseq(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> list
│       ├── lcsubstr(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> list
│       ├── levenshtein(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> int
│       ├── linspace(start: typing.Union[int, float], stop: typing.Union[int, float], number: int) -> list
│       ├── lstrip(sequence: typing.Any, keys: typing.Any) -> typing.Any
│       ├── magic_square(n: int) -> list
│       ├── primality(n: int, iter_num: int) -> bool
│       ├── prime_factors(integer: int, dictionary: bool, pollard_rho: bool) -> typing.Union[list, dict]
│       ├── primes(limit: int) -> list
│       ├── replace(seq: typing.Union[list, tuple], old: typing.Union[list, tuple], new: typing.Union[list, tuple], count: int) -> typing.Union[list, tuple]
│       ├── rstrip(sequence: typing.Any, keys: typing.Any) -> typing.Any
│       ├── semiprimes(limit: int) -> list
│       ├── split(iterable: typing.Union[list, tuple, str], key: typing.Union[list, tuple], retain: bool) -> list
│       ├── strip(sequence: typing.Any, keys: typing.Any) -> typing.Any
│       ├── strip_helper(sequence: typing.Any, keys_set: set, strip_start: bool, strip_end: bool) -> typing.Any
│       └── twinprimes(limit: int) -> list
├── trees
│   ├── CLASS
│   │   ├── BTNode(object)/__init__(self: Any, data: Any) -> Any
│   │   ├── BinaryTree(object)/__init__(self: Any, root: Any) -> Any
│   │   ├── MTNode(object)/__init__(self: Any, data: Any) -> Any
│   │   ├── MultiTree(object)/__init__(self: Any, root: Any) -> Any
│   │   ├── RBTNode(object)/__init__(self: Any, data: Any, color: Any) -> Any
│   │   └── RedBlackTree(object)/__init__(self: Any) -> Any
│   └── FUNCTION
├── types
│   ├── CLASS
│   └── FUNCTION
├── ufuncs
│   ├── CLASS
│   └── FUNCTION
│       ├── add(x: Any, y: Any) -> Any
│       ├── apply(a: Any, func: Any, rtype: Any) -> Any
│       ├── base_ufunc(arrays: Any, func: Any, args: Any, rtype: Any) -> Any
│       ├── divide(x: Any, y: Any) -> Any
│       ├── eq(x: Any, y: Any) -> Any
│       ├── floor_divide(x: Any, y: Any) -> Any
│       ├── ge(x: Any, y: Any) -> Any
│       ├── gt(x: Any, y: Any) -> Any
│       ├── le(x: Any, y: Any) -> Any
│       ├── lt(x: Any, y: Any) -> Any
│       ├── modulo(x: Any, y: Any) -> Any
│       ├── multiply(x: Any, y: Any) -> Any
│       ├── ne(x: Any, y: Any) -> Any
│       ├── power(x: Any, y: Any, m: Any) -> Any
│       ├── subtract(x: Any, y: Any) -> Any
│       └── ufunc_helper(x: Any, y: Any, func: Any) -> Any
├── utils
│   ├── CLASS
│   │   ├── InfIterator(object)/__init__(self: Any, start: typing.Union[int, float, complex], mode: str, common: typing.Union[int, float, complex]) -> Any
│   │   ├── IntervalSet(object)/__init__(self: Any, intervals: Any) -> Any
│   │   ├── LinkedList(object)/__init__(self: Any) -> Any
│   │   ├── LinkedListNode(object)/__init__(self: Any, value: Any, next_node: Any) -> Any
│   │   └── OrderedSet(object)/__init__(self: Any, sequence: Any) -> Any
│   └── FUNCTION
├── vectors
│   ├── CLASS
│   │   └── Vector(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any
│   └── FUNCTION
│       └── vec(data: Any) -> Any
└── zh_cn
    ├── CLASS
    └── FUNCTION
        ├── Fraction转为Decimal(分数对象: fractions.Fraction, 有效位数: int) -> decimal.Decimal
        ├── RC4伪随机生成算法(密钥序列: list) -> Any
        ├── RC4初始化密钥调度算法(密钥: bytes) -> list
        ├── RC4密码(文本: bytes, 密钥: bytes) -> bytes
        ├── ROT13密码(文本: str) -> str
        ├── S型函数(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── base64密码(文本: str, 解密: bool) -> str
        ├── x对数y乘积(x: float, y: float) -> float
        ├── y次方根(被开方数: typing.Union[int, float, complex], 开方数: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 一维傅里叶变换(数据: Any) -> pypynum.fft.FT1D
        ├── 上伽玛(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 上标转整数(上标字符串: str) -> str
        ├── 下伽玛(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 下标转整数(下标字符串: str) -> str
        ├── 中位数(数据: typing.List[float]) -> float
        ├── 中国剩余定理(n: typing.List[int], a: typing.List[int]) -> int
        ├── 中心矩(数据: typing.List[float], 阶数: int) -> float
        ├── 乘积和(多个数组: typing.List[typing.Any]) -> float
        ├── 代替密码(文本: str, 替换映射: dict, 解密: bool) -> str
        ├── 众数(数据: typing.List[typing.Any]) -> Any
        ├── 伽玛函数(alpha: float) -> float
        ├── 余切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 余割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 余弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 偏度(数据: typing.List[float]) -> float
        ├── 全一(形状: Any, 返回类型: Any) -> Any
        ├── 全部填充(形状: Any, 填充值: Any, 返回类型: Any) -> Any
        ├── 全零(形状: Any, 返回类型: Any) -> Any
        ├── 写入(文件: str, 对象: object) -> Any
        ├── 几何平均数(数据: typing.List[float]) -> float
        ├── 凯撒密码(文本: str, 移位: int, 解密: bool) -> str
        ├── 分位数(数据: list, 分位值: float, 插值方法: str, 已排序: bool) -> float
        ├── 判定系数(x: typing.List[float], y: typing.List[float]) -> float
        ├── 判断平方数(n: int) -> bool
        ├── 加权平均(数据: typing.List[float], 权重: typing.List[float]) -> float
        ├── 协方差(x: typing.List[float], y: typing.List[float], 自由度: int) -> float
        ├── 原根(a: int, 单个: bool) -> typing.Union[int, typing.List[int]]
        ├── 原点矩(数据: typing.List[float], 阶数: int) -> float
        ├── 双曲余切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 双曲余割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 双曲余弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 双曲正切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 双曲正割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 双曲正弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反余切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反余割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反余弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反双曲余切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反双曲余割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反双曲余弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反双曲正切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反双曲正割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反双曲正弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反正切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反正割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 反正弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 可能是平方数(n: int) -> bool
        ├── 填充序列(形状: Any, 序列: Any, 重复: Any, 填充: Any, 返回类型: Any) -> Any
        ├── 多次方根取整(被开方数: int, 开方数: int) -> int
        ├── 多精度余弦(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度双曲余弦(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度双曲正弦(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度反余弦(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度反正切(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度反正弦(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度圆周率(有效位数: int, 方法: str) -> decimal.Decimal
        ├── 多精度复数(实部: typing.Union[int, float, str, decimal.Decimal], 虚部: typing.Union[int, float, str, decimal.Decimal], 有效位数: int) -> pypynum.multiprec.MPComplex
        ├── 多精度对数(真数: typing.Union[int, float], 底数: typing.Union[int, float], 有效位数: int, 使用内置方法: bool) -> decimal.Decimal
        ├── 多精度方位角(y: typing.Union[int, float], x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度欧拉伽马(有效位数: int) -> decimal.Decimal
        ├── 多精度正弦(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度自然对数(真数: typing.Union[int, float], 有效位数: int, 使用内置方法: bool) -> decimal.Decimal
        ├── 多精度自然常数(有效位数: int, 方法: str) -> decimal.Decimal
        ├── 多精度自然指数(指数: typing.Union[int, float], 有效位数: int, 使用内置方法: bool) -> decimal.Decimal
        ├── 多精度菲涅耳余弦积分(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度菲涅耳正弦积分(x: typing.Union[int, float], 有效位数: int) -> decimal.Decimal
        ├── 多精度黄金分割率(有效位数: int, 方法: str) -> decimal.Decimal
        ├── 多项式方程(系数: list) -> list
        ├── 字符串转整数(字符串: str) -> int
        ├── 导数(函数: Any, 参数: float, 步长: float, 额外参数: Any, 额外关键字参数: Any) -> float
        ├── 峰度(数据: typing.List[float], 费希尔: bool) -> float
        ├── 希尔256密码(文本: bytes, 密钥: list, 解密: bool) -> bytes
        ├── 平均数(数据: typing.List[float]) -> float
        ├── 平方平均数(数据: typing.List[float]) -> float
        ├── 平方根取整(被开方数: int) -> int
        ├── 序列滚动(序列: typing.Iterator[typing.Any], 偏移: int) -> typing.Iterator[typing.Any]
        ├── 归一化(数据: typing.List[float], 目标: float) -> typing.List[float]
        ├── 扩展欧几里得算法(a: int, b: int) -> typing.Tuple[int, int, int]
        ├── 拆分浮点数字符串(字符串: str) -> tuple
        ├── 排列数(总数: int, 选取数: int) -> int
        ├── 数组(数据: list, 检查: bool) -> pypynum.arrays.Array
        ├── 整数转上标(标准字符串: str) -> str
        ├── 整数转下标(标准字符串: str) -> str
        ├── 整数转单词(整数: int) -> str
        ├── 整数转罗马数(整数: int, 上划线: bool) -> str
        ├── 方差(数据: typing.List[float], 自由度: int) -> float
        ├── 普莱费尔密码(文本: str, 密钥: str, 解密: bool) -> str
        ├── 最大公约数(args: int) -> int
        ├── 最小公倍数(args: int) -> int
        ├── 极差(数据: typing.List[float]) -> float
        ├── 标准差(数据: typing.List[float], 自由度: int) -> float
        ├── 模运算阶(a: int, n: int, b: int) -> int
        ├── 欧拉函数(n: int) -> int
        ├── 正切(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 正割(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 正弦(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 浮点数转分数(数值: float, 是否带分数: bool, 误差: float) -> tuple
        ├── 相关系数(x: typing.List[float], y: typing.List[float]) -> float
        ├── 积分(函数: Any, 积分开始: float, 积分结束: float, 积分点数: int, 额外参数: Any, 额外关键字参数: Any) -> float
        ├── 积累乘积(数据: typing.List[float]) -> float
        ├── 符号函数(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 类似形状全一(数组A: Any, 返回类型: Any) -> Any
        ├── 类似形状全零(数组A: Any, 返回类型: Any) -> Any
        ├── 类似形状填充(数组A: Any, 填充值: Any, 返回类型: Any) -> Any
        ├── 累乘积(序列: typing.List[float]) -> typing.List[float]
        ├── 累加和(序列: typing.List[float]) -> typing.List[float]
        ├── 线性方程组(左边: list, 右边: list) -> list
        ├── 组合数(总数: int, 选取数: int) -> int
        ├── 维吉尼亚密码(文本: str, 密钥: str, 解密: bool) -> str
        ├── 罗马数转整数(罗马数: str) -> int
        ├── 自然对数(真数: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 自然指数(指数: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 莫尔斯密码(文本: str, 解密: bool) -> str
        ├── 解析浮点数字符串(字符串: str) -> tuple
        ├── 误差函数(x: typing.Union[int, float]) -> typing.Union[int, float]
        ├── 读取(文件: str) -> list
        ├── 调和平均数(数据: typing.List[float]) -> float
        ├── 贝塔函数(p: float, q: float) -> float
        ├── 贝塞尔函数I0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 贝塞尔函数I1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 贝塞尔函数Iv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 贝塞尔函数J0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 贝塞尔函数J1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 贝塞尔函数Jv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]
        ├── 负一整数次幂(指数: int) -> int
        ├── 转为多精度复数(实部: typing.Union[int, float, str, decimal.Decimal, complex, pypynum.multiprec.MPComplex], 虚部: typing.Union[int, float, str, decimal.Decimal], 有效位数: int) -> pypynum.multiprec.MPComplex
        ├── 转换为列表(数据: Any) -> list
        ├── 转换为数组(数据: Any) -> pypynum.arrays.Array
        ├── 连续乘积(下界: int, 上界: int, 函数: typing.Callable) -> float
        ├── 连续加和(下界: int, 上界: int, 函数: typing.Callable) -> float
        ├── 阶乘函数(n: int) -> int
        ├── 阿特巴什密码(文本: str) -> str
        ├── 频率统计(数据: typing.List[typing.Any]) -> typing.Dict[typing.Any, int]
        └── 黎曼函数(alpha: float) -> float
```

### Code Testing

```python
from pypynum import (arrays, geoms, hypcmpnms, logics, matrices, multiprec, special, vectors,
                     ciphers, consts, equations, maths, plotting, random, regs, tools)

...

print(arrays.array())
print(arrays.array([1, 2, 3, 4, 5, 6, 7, 8]))
print(arrays.array([[1, 2, 3, 4], [5, 6, 7, 8]]))
print(arrays.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]))

"""
[]
[1 2 3 4 5 6 7 8]
[[1 2 3 4]
 [5 6 7 8]]
[[[1 2]
  [3 4]]

 [[5 6]
  [7 8]]]
"""

triangle = geoms.Triangle((0, 0), (2, 2), (3, 0))
print(triangle.perimeter())
print(triangle.area())
print(triangle.centroid())

"""
8.06449510224598
3.0
(1.6666666666666667, 0.6666666666666666)
"""

q0 = hypcmpnms.quat(1, 2, 3, 4)
q1 = hypcmpnms.quat(5, 6, 7, 8)
print(q0)
print(q1)
print(q0 + q1)
print(q0 * q1)
print(q0.inverse())
print(q1.conjugate())

"""
(1+2i+3j+4k)
(5+6i+7j+8k)
(6+8i+10j+12k)
(-60+12i+30j+24k)
(0.03333333333333333-0.06666666666666667i-0.1j-0.13333333333333333k)
(5-6i-7j-8k)
"""

a, b, c = 1, 1, 1
adder0, adder1 = logics.HalfAdder("alpha", a, b), logics.HalfAdder("beta", c, None)
xor0 = logics.XOR("alpha")
ff0, ff1 = logics.DFF("alpha"), logics.DFF("beta")
xor0.set_order0(1)
xor0.set_order1(1)
logics.connector(adder0, adder1)
logics.connector(adder0, xor0)
logics.connector(adder1, xor0)
logics.connector(adder1, ff0)
logics.connector(xor0, ff1)
print("sum: {}, carry: {}".format(ff0.out(), ff1.out()))

"""
sum: [1], carry: [1]
"""

m0 = matrices.mat([[1, 2], [3, 4]])
m1 = matrices.mat([[5, 6], [7, 8]])
print(m0)
print(m1)
print(m0 + m1)
print(m0 @ m1)
print(m0.inv())
print(m1.rank())

"""
[[1 2]
 [3 4]]
[[5 6]
 [7 8]]
[[ 6  8]
 [10 12]]
[[19 22]
 [43 50]]
[[ -1.9999999999999996   0.9999999999999998]
 [  1.4999999999999998 -0.49999999999999994]]
2
"""

mp_complex1 = multiprec.MPComplex("1.4142135623730950488016887242096980785696718753769",
                                  "2.7182818284590452353602874713527", sigfigs=30)
mp_complex2 = multiprec.MPComplex("1.7320508075688772935274463415059",
                                  "3.141592653589793238462643383279502884197169399375105820974944", sigfigs=40)
modulus = mp_complex1.modulus(sigfigs=25)
print("Modulus of the complex1:", modulus)
sqrt_complex = mp_complex2.sqrt()
print("Square root of the complex2:", sqrt_complex)
power_result = mp_complex1 ** mp_complex2
print("Power of complex1 raised to complex2:", power_result)
euler_gamma = multiprec.mp_euler_gamma(sigfigs=45)
print("Value of Euler's gamma constant:", euler_gamma)
log_2 = multiprec.mp_log(2, 10, sigfigs=50)
print("Logarithm of 2 (base 10):", log_2)
exp_e_squared = multiprec.mp_exp(multiprec.mp_e() ** 2, sigfigs=20)
print("Value of exp(e^2):", exp_e_squared)

"""
Modulus of the complex1: 3.064156670102011971734464
Square root of the complex2: 1.630869996965458756791024890326755654659+0.9631646481434200567938527724670041364524i
Power of complex1 raised to complex2: 0.144632311554759549910373681031-0.17337039786352194417298867399i
Value of Euler's gamma constant: 0.577215664901532860606512090082402431042159336
Logarithm of 2 (base 10): 0.30102999566398119521373889472449302676818988146211
Value of exp(e^2): 1618.1779919126535017
"""

print("Bessel Function of the first kind, order 0 at x=1:", special.besselj0(1))
print("Modified Bessel function of the first kind, order 1 at x=1:", special.besseli1(1))
print("Hypergeometric function 0F1 at z=0.5 with b0=1:", special.hyp0f1(1, 0.5))
print("Hypergeometric function 1F1 at z=1 with a0=1, b0=1:", special.hyp1f1(1, 1, 1))
print("q-Pochhammer Symbol with a=2+1j, q=0.5+0.1j, n=2+1j:", special.qpochhammer(2 + 1j, 0.5 + 0.1j, 2 + 1j))
print("q-Gamma Function at n=2 with q=0.5+0.1j:", special.qgamma(2, 0.5 + 0.1j))

"""
Bessel Function of the first kind, order 0 at x=1: 0.7651976865579666
Modified Bessel function of the first kind, order 1 at x=1: 0.565159103992485
Hypergeometric function 0F1 at z=0.5 with b0=1: 1.5660829297563503
Hypergeometric function 1F1 at z=1 with a0=1, b0=1: 2.7182818284590455
q-Pochhammer Symbol with a=2+1j, q=0.5+0.1j, n=2+1j: (-0.33353429405776575+1.8573191887407854j)
q-Gamma Function at n=2 with q=0.5+0.1j: (0.9999999999999989-4.953510875709033e-16j)
"""

string = "PyPyNum"
encrypted = ciphers.caesar(string, 10)
print(string)
print(encrypted)
print(ciphers.caesar(encrypted, 10, decrypt=True))
encrypted = ciphers.vigenere(string, "ciphers")
print(string)
print(encrypted)
print(ciphers.vigenere(encrypted, "ciphers", decrypt=True))
encrypted = ciphers.morse(string)
print(string)
print(encrypted)
print(ciphers.morse(encrypted, decrypt=True))

"""
PyPyNum
ZiZiXew
PyPyNum
PyPyNum
RgEfRle
PyPyNum
PyPyNum
.--. -.-- .--. -.-- -. ..- --
PYPYNUM
"""

v0 = vectors.vec([1, 2, 3, 4])
v1 = vectors.vec([5, 6, 7, 8])
print(v0)
print(v1)
print(v0 + v1)
print(v0 @ v1)
print(v0.normalize())
print(v1.angles())

"""
[1 2 3 4]
[5 6 7 8]
[ 5 12 21 32]
70
[0.18257418583505536  0.3651483716701107  0.5477225575051661  0.7302967433402214]
[1.1820279130506308, 1.0985826410133916, 1.0114070854293842, 0.9191723423169716]
"""

print(consts.TB)
print(consts.e)
print(consts.h)
print(consts.phi)
print(consts.pi)
print(consts.tera)

"""
1099511627776
2.718281828459045
6.62607015e-34
1.618033988749895
3.141592653589793
1000000000000
"""

p = [1, -2, -3, 4]
m = [
    [
        [1, 2, 3],
        [6, 10, 12],
        [7, 16, 9]
    ],
    [-1, -2, -3]
]
print(equations.poly_eq(p))
print(equations.lin_eq(*m))

"""
[(-1.5615528128088307-6.5209667308287455e-24j), (1.0000000000000007+3.241554513744382e-25j), (2.5615528128088294+4.456233626665941e-24j)]
[1.6666666666666665, -0.6666666666666666, -0.4444444444444444]
"""

print(maths.cot(consts.pi / 3))
print(maths.gamma(1.5))
print(maths.pi(1, 10, lambda x: x ** 2))
print(maths.product([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))
print(maths.sigma(1, 10, lambda x: x ** 2))
print(maths.var([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))

"""
0.577350269189626
0.886226925452758
13168189440000
6469693230
385
73.29
"""

plt = plotting.unary(lambda x: x ** 2, top=10, bottom=0, character="+")
print(plt)
print(plotting.binary(lambda x, y: x ** 2 + y ** 2 - 10, right=10, left=0, compare="<=", basic=plotting.change(plt)))
print(plotting.c_unary(lambda x: x ** x, right=2, left=-2, top=2, bottom=-2, complexity=20, character="-"))

"""
  1.00e+01|         +                               +         
          |                                                   
          |          +                             +          
          |                                                   
          |           +                           +           
          |            +                         +            
          |                                                   
          |             +                       +             
  5.00e+00|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
          |              +                     +              
          |               +                   +               
          |                +                 +                
          |                 +               +                 
          |                  +             +                  
          |                   +           +                   
          |                    +         +                    
          |                     +++   +++                     
  0.00e+00|________________________+++________________________
           -5.00e+00             0.00e+00             5.00e+00
  1.00e+01|         +                               +         
          |                                                   
          |          +                             +          
          |                                                   
          |.........  +                           +           
          |.............                         +            
          |..............                                     
          |................                     +             
  5.00e+00|................_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
          |................                    +              
          |................                   +               
          |..............  +                 +                
          |.............    +               +                 
          |.........         +             +                  
          |                   +           +                   
          |                    +         +                    
          |                     +++   +++                     
  0.00e+00|________________________+++________________________
           -5.00e+00             0.00e+00             5.00e+00
  2.00e+00|           -                 -           -          -          -            -    
          |               -  -            -          -         -         -           -      
          |                     -           -         -        -        -          -        
          |-                       -          -       -       -        -         -          
          |     -   -                - -       --      -      -       -        -            
          |            -  -              -       -      -     -      -       -             -
          |                  -  - -       - --  - ---  -- -  --     -     - -         - -   
          |                         - -   -  --    --    -   -  - --     -       - -        
          |  -   -  - - -  -          - -- -   ---  ---  -   -   ---   --     - -           
          |             -    -  - - - --    ----- -- -- --- --  --  ---    --           -  -
          |               - -      -     ------------ ----  - --  -- - ---       - - -      
          |    -  -  -  - -  ----- - -- ----------------------- -- ----  - -- --            
          |   -  -   - -         - ---- ---------------------------------      - - - - -  - 
  0.00e+00|_ _ _ _ _ _ _ _-_-_-_-_---- ------------------------------------_-- _ _ _ _ _ _ _
          |            -  -   - - ----------------------------------------- -- - - - -      
          |   -  --  -  -       -- -  -  --------------------------------- -           -  - 
          |    -          - ---- - - -- --------------------- ----- ----    - -- -          
          |               -         - -- --------- -- -- -  -----  ---  -- -       - -  -   
          |             -  - -  - - - -    ---- --- --- --- --  --  ---     - -            -
          |  -   -  - -               - --     --   --   -   -    --   --       --          
          |                       - -     -  --    -    --   -- -  -     --        -  -     
          |                  -  -         - -   - - -  -- -   -     --      -           -   
          |            -  -            - -      --     --     -      -       - -           -
          |     -   -                -         -       -      -       -          -          
          |-                    -  -          -       -        -       -           -        
          |                  -              -         -        -        -            -      
          |               -               -          -         -         -                  
 -2.00e+00|___________-_________________-___________-_____________________-____________-____
           -2.00e+00                            0.00e+00                            2.00e+00
"""

print(random.gauss(0, 1, [2, 3, 4]))
print(random.rand([2, 3, 4]))
print(random.randint(0, 9, [2, 3, 4]))
print(random.uniform(0, 9, [2, 3, 4]))

"""
[[[0.19564108603837504, 1.01920370166293, -0.0432622197313817, 1.8767392228517594], [-0.9372140720220945, 0.6455939848661518, 0.06219926062283103, -0.03646501719525719], [-0.6575861228704779, -1.627831653990843, 1.4669927522358261, -2.1082184047042944]], [[-0.4550416369776341, 0.5921202822490813, 0.1393176939653395, -0.1994214479986489], [-0.559257919413219, -1.629764620332396, 0.04658277611512766, 0.20529751771180757], [0.492656546311569, 0.9731757491363898, -0.3281597719355017, -0.6855996837842998]]]
[[[0.9897608447208633, 0.9091539554606014, 0.839742901348473, 0.7483640950392159], [0.1271954637618754, 0.23914774960655272, 0.6603167703557995, 0.09706202212722614], [0.1020987366479954, 0.16628877700140854, 0.9844464087410161, 0.8213963537473721]], [[0.268434775377716, 0.8021623176316018, 0.48319517625501174, 0.30410149780944096], [0.8970313978138931, 0.9980790184879383, 0.1185467392465952, 0.19570961919567464], [0.08626090792820118, 0.5790211560246683, 0.7475290741004703, 0.8048613204213184]]]
[[[9, 0, 7, 5], [2, 7, 3, 5], [7, 6, 4, 2]], [[3, 4, 2, 0], [4, 2, 2, 1], [4, 5, 4, 9]]]
[[[8.067902792666303, 3.1398970785364244, 7.875028237778611, 7.766921948037462], [3.337337214716076, 2.852783099370506, 1.028257336777862, 7.822605535085232], [7.111199916783942, 5.890725764603359, 3.038605829888671, 6.272148674191553]], [[1.076715403659712, 6.806086377982102, 5.699002266942416, 1.1654651363361368], [1.3920577362733448, 8.527352563852686, 2.359964996027981, 5.183071574749471], [7.8250627862940725, 1.6259461468536924, 8.333173856724002, 5.068032713313034]]]
"""

print(regs.lin_reg(list(range(5)), [2, 4, 6, 7, 8]))
print(regs.par_reg(list(range(5)), [2, 4, 6, 7, 8]))
print(regs.poly_reg(list(range(5)), [2, 4, 6, 7, 8], 4))

"""
[1.5, 2.4000000000000004]
[-0.21428571428571563, 2.3571428571428625, 1.971428571428569]
[0.08333333333320592, -0.666666666666571, 1.4166666666628345, 1.1666666666688208, 1.9999999999999258]
"""

print(tools.classify([1, 2.3, 4 + 5j, "string", list, True, 3.14, False, tuple, tools]))
print(tools.dedup(["Python", 6, "NumPy", int, "PyPyNum", 9, "pypynum", "NumPy", 6, True]))
print(tools.frange(0, 3, 0.4))
print(tools.linspace(0, 2.8, 8))

"""
{<class 'int'>: [1], <class 'float'>: [2.3, 3.14], <class 'complex'>: [(4+5j)], <class 'str'>: ['string'], <class 'type'>: [<class 'list'>, <class 'tuple'>], <class 'bool'>: [True, False], <class 'module'>: [<module 'pypynum.tools' from 'C:\\Users\\Administrator\\PycharmProjects\\pythonProject\\pypynum\\tools.py'>]}
['Python', 6, 'NumPy', <class 'int'>, 'PyPyNum', 9, 'pypynum', True]
[0.0, 0.4, 0.8, 1.2000000000000002, 1.6, 2.0, 2.4000000000000004, 2.8000000000000003, 3.2]
[0.0, 0.39999999999999997, 0.7999999999999999, 1.2, 1.5999999999999999, 1.9999999999999998, 2.4, 2.8]
"""

# Tip:
# The test has been successfully passed and ended.
# These tests are only part of the functionality of this package.
# More features need to be explored and tried by yourself!
```

            

Raw data

            {
    "_id": null,
    "home_page": "https://github.com/PythonSJL/PyPyNum",
    "name": "numpypy",
    "maintainer": null,
    "docs_url": null,
    "requires_python": ">=3.4",
    "maintainer_email": null,
    "keywords": "math, \u6570\u5b66, mathematics, \u6570\u5b66\u8ba1\u7b97, numerical, \u6570\u503c, computation, \u8ba1\u7b97, scientific, \u79d1\u5b66, algebra, \u4ee3\u6570, calculus, \u5fae\u79ef\u5206, statistics, \u7edf\u8ba1, linear-algebra, \u7ebf\u6027\u4ee3\u6570, optimization, \u4f18\u5316, numerical-analysis, \u6570\u503c\u5206\u6790, matrix, \u77e9\u9635, vector, \u5411\u91cf, tensor, \u5f20\u91cf, numerics, \u6570\u503c\u8ba1\u7b97, library, \u5e93, tools, \u5de5\u5177, utils, \u5b9e\u7528\u7a0b\u5e8f, algorithms, \u7b97\u6cd5, software, \u8f6f\u4ef6, package, \u5305, methods, \u65b9\u6cd5, data-science, \u6570\u636e\u79d1\u5b66, machine-learning, \u673a\u5668\u5b66\u4e60, computational, \u8ba1\u7b97\u7684, operations, \u64cd\u4f5c, functions, \u51fd\u6570, processing, \u5904\u7406, programming, \u7f16\u7a0b, simulation, \u4eff\u771f, visualization, \u53ef\u89c6\u5316, physics, \u7269\u7406",
    "author": "Shen Jiayi",
    "author_email": "2261748025@qq.com",
    "download_url": "https://files.pythonhosted.org/packages/54/f8/c561889b1a6380fd2cd3004cad68185f4a579d00ddaa02a11ced89b57519/numpypy-1.17.2.tar.gz",
    "platform": null,
    "description": "\ufeff# PyPyNum\r\n\r\nPyPyNum is a multifunctional Python math lib. It includes modules for math, data analysis, array ops, crypto, physics,\r\nrandomness, data prep, stats, solving eqns, image processing, interp, matrix calc, and high-precision math. Designed for\r\nscientific computing, data science, and machine learning, PyPyNum provides efficient and versatile tools.\r\n\r\n```\r\n ________   ___    ___  ________   ___    ___  ________    ___  ___   _____ ______\r\n|\\   __  \\ |\\  \\  /  /||\\   __  \\ |\\  \\  /  /||\\   ___  \\ |\\  \\|\\  \\ |\\   _ \\  _   \\\r\n\\ \\  \\|\\  \\\\ \\  \\/  / /\\ \\  \\|\\  \\\\ \\  \\/  / /\\ \\  \\\\ \\  \\\\ \\  \\\\\\  \\\\ \\  \\\\\\__\\ \\  \\\r\n \\ \\   ____\\\\ \\    / /  \\ \\   ____\\\\ \\    / /  \\ \\  \\\\ \\  \\\\ \\  \\\\\\  \\\\ \\  \\\\|__| \\  \\\r\n  \\ \\  \\___| \\/  /  /    \\ \\  \\___| \\/  /  /    \\ \\  \\\\ \\  \\\\ \\  \\\\\\  \\\\ \\  \\    \\ \\  \\\r\n   \\ \\__\\  __/  / /       \\ \\__\\  __/  / /       \\ \\__\\\\ \\__\\\\ \\_______\\\\ \\__\\    \\ \\__\\\r\n    \\|__| |\\___/ /         \\|__| |\\___/ /         \\|__| \\|__| \\|_______| \\|__|     \\|__|\r\n          \\|___|/                \\|___|/\r\n```\r\n\r\n[![Downloads](https://static.pepy.tech/badge/pypynum)](https://pepy.tech/project/pypynum)\r\n[![Downloads](https://static.pepy.tech/badge/pypynum/month)](https://pepy.tech/project/pypynum)\r\n[![Downloads](https://static.pepy.tech/badge/pypynum/week)](https://pepy.tech/project/pypynum)\r\n\r\n## Version -> 1.17.2 | PyPI -> https://pypi.org/project/PyPyNum/ | Gitee -> https://www.gitee.com/PythonSJL/PyPyNum | GitHub -> https://github.com/PythonSJL/PyPyNum\r\n\r\n![LOGO](PyPyNum.png)\r\n\r\nThe logo cannot be displayed on PyPI, it can be viewed in Gitee or GitHub.\r\n\r\n### Introduction\r\n\r\n+ Multi functional math library, similar to numpy, scipy, etc., designed specifically for PyPy interpreters and also\r\n  supports other types of Python interpreters\r\n+ Update versions periodically to add more practical features\r\n+ If you need to contact, please add QQ number 2261748025 (Py\ud835\ude7f\ud835\udea2\ud835\ude9d\ud835\ude91\ud835\ude98\ud835\ude97-\u6c34\u6676\u5170), or through my email 2261748025@qq.com\r\n\r\n```\r\n+++++++++++++++++++++++++++++++++++++++++\r\n+ Tip:                                  +\r\n+ Have suggestions or feature requests? +\r\n+ Feel free to share them with us.      +\r\n+ Your feedback is highly appreciated!  +\r\n+++++++++++++++++++++++++++++++++++++++++\r\n```\r\n\r\n### Copyright and License\r\n\r\nThis Python library is licensed under the GNU Affero General Public License version 3 (AGPLv3).\r\n\r\nThe license is designed to ensure that network server software is made available to the community, allowing users to\r\naccess the source code of modified versions when the software is used to provide network services.\r\n\r\n**Key Terms and Conditions:**\r\n\r\n- Source Code: The library must be provided with its source code, and any modifications must also be distributed under\r\n  the AGPLv3.\r\n- Free Redistribution: The library can be distributed in source and binary forms without any restrictions.\r\n- No Discrimination: The license does not restrict the use of the software by individuals or organizations, nor does it\r\n  discriminate against fields of use.\r\n- No Discrimination Against Persons or Groups: The license does not restrict anyone from receiving the software.\r\n- Patent License: The patent holder must grant a patent license to anyone who uses the software.\r\n- No Surrender of Others' Freedom: The license does not allow any conditions that contradict the AGPLv3.\r\n- Remote Network Interaction: If the software can interact with users remotely, the source code must be made available\r\n  at no charge.\r\n- Revised Versions of this License: The Free Software Foundation may publish revised versions of the AGPLv3, and users\r\n  have the option to follow the terms of any version.\r\n- Disclaimer of Warranty: There is no warranty for the software, to the extent permitted by applicable law.\r\n- Limitation of Liability: The copyright holder and any other party who modifies and conveys the software are not liable\r\n  for damages arising from the use or inability to use the software.\r\n\r\n**Full License Text:**\r\n\r\n[GNU Affero General Public License](https://www.gnu.org/licenses/agpl-3.0.en.html)\r\n\r\n### Name and Function Introduction of Submodules\r\n\r\n|   Submodule Name    |                       Function Introduction                        |\r\n|:-------------------:|:------------------------------------------------------------------:|\r\n|  `pypynum.arrays`   | Provides operations and calculations for multi-dimensional arrays. |\r\n|   `pypynum.chars`   |       Contains a variety of special mathematical characters.       |\r\n|  `pypynum.ciphers`  |      Implements various encryption and decryption algorithms.      |\r\n|  `pypynum.consts`   |           Contains mathematical and physical constants.            |\r\n|  `pypynum.crandom`  |                 Generates random complex numbers.                  |\r\n| `pypynum.dataproc`  |          Tools for data preprocessing and transformation.          |\r\n|   `pypynum.dists`   |    Statistical distribution functions and related calculations.    |\r\n| `pypynum.equations` |         Solves equations and performs symbolic operations.         |\r\n|    `pypynum.fft`    |  Implements Fast Fourier Transforms and related functionalities.   |\r\n|   `pypynum.files`   |                  File reading and writing tools.                   |\r\n|   `pypynum.geoms`   |             Geometric shapes and calculation methods.              |\r\n|  `pypynum.graphs`   |           Graph theory algorithms and network analysis.            |\r\n|  `pypynum.groups`   |         Group theory calculations and structural analysis.         |\r\n| `pypynum.hypcmpnms` |        Hypercomplex number operations and transformations.         |\r\n|  `pypynum.images`   |              Image processing and manipulation tools.              |\r\n|  `pypynum.interp`   |         Interpolation methods and function approximation.          |\r\n|  `pypynum.kernels`  |          Implementation of kernel functions and methods.           |\r\n|  `pypynum.logics`   |                    Simulates logical circuits.                     |\r\n|   `pypynum.maths`   |     Basic mathematical operations and commonly used functions.     |\r\n| `pypynum.matrices`  |         Matrix operations and linear algebra calculations.         |\r\n| `pypynum.multiprec` |               High-precision numerical computations.               |\r\n| `pypynum.networks`  |                   Network models and algorithms.                   |\r\n|  `pypynum.numbers`  |           Operations on numerical types and properties.            |\r\n| `pypynum.plotting`  |                     Data visualization tools.                      |\r\n|   `pypynum.polys`   |              Polynomial operations and calculations.               |\r\n| `pypynum.pprinters` |              Advanced printing and formatting output.              |\r\n|  `pypynum.random`   |                Generates arrays of random numbers.                 |\r\n|   `pypynum.regs`    |               Regression analysis and model fitting.               |\r\n|   `pypynum.seqs`    |              Computes various mathematical sequences.              |\r\n|  `pypynum.special`  | Provides advanced special functions for mathematical computations. |\r\n| `pypynum.stattest`  |                Statistical tests and data analysis.                |\r\n|  `pypynum.symbols`  |         Symbolic computation and expression manipulation.          |\r\n|  `pypynum.tensors`  |                Tensor operations and calculations.                 |\r\n|   `pypynum.test`    |                Simple code testing for the library.                |\r\n|   `pypynum.this`    |     The Zen of the library, expressing its guiding principles.     |\r\n|   `pypynum.tools`   |                General tools and helper functions.                 |\r\n|   `pypynum.trees`   |           Tree structures and algorithm implementations.           |\r\n|   `pypynum.types`   |      Contains various types, exceptions, and configurations.       |\r\n|  `pypynum.ufuncs`   |           Universal functions and vectorized operations.           |\r\n|   `pypynum.utils`   |             Utility programs and auxiliary functions.              |\r\n|  `pypynum.vectors`  |                Vector operations and calculations.                 |\r\n|   `pypynum.zh_cn`   | Provides Chinese language interfaces for various functionalities.  |\r\n\r\n### The Zen of PyPyNum (Preview)\r\n\r\n```\r\n                The Zen of PyPyNum, by Shen Jiayi\r\n\r\nIn this mathematical sanctuary, we weave our algorithms with pure Python threads.\r\n\r\nPrecision outweighs approximation.\r\nElegance in mathematics transcends the bulky algorithms.\r\nClarity in logic illuminates the darkest problems.\r\nSimplicity in form is the pinnacle of sophistication.\r\nFlat hierarchies in our code mirror the linear nature of functions.\r\nSparse code, like a minimal polynomial, retains essence without redundancy.\r\n```\r\n\r\n```\r\n...\r\n\r\nDo you want to view all the content?\r\n\r\nEnter \"from pypynum import this\" in your\r\n\r\nPython interpreter and run it!\r\n```\r\n\r\n```\r\n                                                                September 5, 2024\r\n```\r\n\r\n### Functional Changes Compared to the Previous Version\r\n\r\n```\r\n!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=\r\n\r\nFixed some known issues.\r\n\r\n!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=\r\n\r\nThe pypynum.utils module has recently introduced a new class\r\ncalled RadixInt. This class is designed to facilitate the\r\nrepresentation and manipulation of integers in various bases,\r\nranging from base 2 to base 36.\r\n\r\nThe RadixInt class within the pypynum.utils module provides a\r\nrobust way to work with integers in custom bases. It allows\r\nusers to initialize instances with either a decimal number or a\r\nstring representation of a number in the desired base. The class\r\nsupports conversion between different bases, as well as basic\r\narithmetic operations that can be performed on integers\r\nrepresented in various bases.\r\n\r\n\r\n<<< The following are some usage examples >>>\r\n\r\n\r\nfrom pypynum import RadixInt\r\n\r\n# Base-2 and base-10 numbers\r\nbinary_num = RadixInt(\"1010\", 2)\r\ndecimal_num = RadixInt(10, 10)\r\nprint(binary_num)  # Output: (1010)_{2}\r\nprint(decimal_num)  # Output: (10)_{10}\r\nbinary_to_octal = RadixInt(\"1010\", 2).to_base(8)\r\nprint(binary_to_octal)  # Output: (12)_{8}\r\n# Addition\r\nresult_add = binary_num + decimal_num\r\nprint(result_add)  # Output: (20)_{10}\r\n# Base-8 and base-10 numbers\r\noctal_num = RadixInt(\"123\", 8)\r\ndecimal_num = RadixInt(5, 10)\r\n# Subtraction\r\nresult_sub = octal_num - decimal_num\r\nprint(result_sub)  # Output: (78)_{10}\r\n# Base-16 and base-2 numbers\r\nhex_num = RadixInt(\"1A\", 16)\r\nbinary_num = RadixInt(\"11\", 2)\r\n# Multiplication\r\nresult_mul = hex_num * binary_num\r\nprint(result_mul)  # Output: (78)_{10}\r\n\r\n!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=!=\r\n```\r\n\r\n### Run Time Test\r\n\r\nPython interpreter version\r\n\r\n+ CPython 3.8.10\r\n\r\n+ PyPy 3.10.12\r\n\r\n| Matrix Time Test                               | NumPy+CPython (seconds)                                                                                                                                                            | Ranking | PyPyNum+PyPy (seconds)                                                                                                                                                             | Ranking | Mpmath_+_PyPy_ (seconds)                                                                                                                                                         | Ranking | SymPy_+_PyPy_ (seconds)                                                                                                                                                                                                                    | Ranking |\r\n|------------------------------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------|\r\n| Create a hundred order random number matrix    | 0.000083                                                                                                                                                                           | 1       | 0.005374                                                                                                                                                                           | 2       | 0.075253                                                                                                                                                                         | 3       | 0.230530                                                                                                                                                                                                                                   | 4       |\r\n| Create a thousand order random number matrix   | 0.006740                                                                                                                                                                           | 1       | 0.035666                                                                                                                                                                           | 2       | 1.200950                                                                                                                                                                         | 3       | 4.370265                                                                                                                                                                                                                                   | 4       |\r\n| Addition of matrices of order one hundred      | 0.000029                                                                                                                                                                           | 1       | 0.002163                                                                                                                                                                           | 2       | 0.045641                                                                                                                                                                         | 4       | 0.035700                                                                                                                                                                                                                                   | 3       |\r\n| Adding matrices of order one thousand          | 0.002647                                                                                                                                                                           | 1       | 0.019111                                                                                                                                                                           | 2       | 1.746957                                                                                                                                                                         | 4       | 0.771542                                                                                                                                                                                                                                   | 3       |\r\n| Determinant of a hundred order matrix          | 0.087209                                                                                                                                                                           | 2       | 0.016331                                                                                                                                                                           | 1       | 4.354507                                                                                                                                                                         | 3       | 5.157206                                                                                                                                                                                                                                   | 4       |\r\n| Determinant of a thousand order matrix         | 0.616113                                                                                                                                                                           | 1       | 3.509747                                                                                                                                                                           | 2       | It takes a long time                                                                                                                                                             | 3       | It takes a long time                                                                                                                                                                                                                       | 4       |\r\n| Finding the inverse of a hundred order matrix  | 0.162770                                                                                                                                                                           | 2       | 0.015768                                                                                                                                                                           | 1       | 8.162948                                                                                                                                                                         | 3       | 21.437424                                                                                                                                                                                                                                  | 4       |\r\n| Finding the inverse of a thousand order matrix | 0.598905                                                                                                                                                                           | 1       | 17.072552                                                                                                                                                                          | 2       | It takes a long time                                                                                                                                                             | 3       | It takes a long time                                                                                                                                                                                                                       | 4       |\r\n| Array output effect                            | ```[[[[\u2002-7\u2002-67]```<br>```[-78\u2002\u200229]]```<br><br>```[[-86\u2002-97]```<br>```[\u200268\u2002\u2002-3]]]```<br><br><br>```[[[\u200211\u2002\u200242]```<br>```[\u200224\u2002-65]]```<br><br>```[[-60\u2002\u200272]```<br>```[\u200273\u2002\u2002\u20022]]]]``` | /       | ```[[[[\u200237\u2002\u200283]```<br>```[\u200240\u2002\u2002\u20022]]```<br><br>```[[\u2002-5\u2002-34]```<br>```[\u2002-7\u2002\u200272]]]```<br><br><br>```[[[\u200213\u2002-64]```<br>```[\u2002\u20026\u2002\u200290]]```<br><br>```[[\u200268\u2002\u200257]```<br>```[\u200278\u2002\u200211]]]]``` | /       | ```[-80.0\u2002\u2002\u2002-8.0\u2002\u200280.0\u2002\u2002-88.0]```<br>```[-99.0\u2002\u2002-43.0\u2002\u200287.0\u2002\u2002\u200281.0]```<br>```[\u200220.0\u2002\u2002-55.0\u2002\u200298.0\u2002\u2002\u2002\u20028.0]```<br>```[\u2002\u20028.0\u2002\u2002\u200244.0\u2002\u200264.0\u2002\u2002-35.0]```<br><br>(Only supports matrices) | /       | ```\u23a1\u23a116\u2002\u2002\u2002-56\u23a4\u2002\u2002\u23a1\u20028\u2002\u2002\u2002-28\u23a4\u23a4```<br>```\u23a2\u23a2\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u23a5\u2002\u2002\u23a2\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u23a5\u23a5```<br>```\u23a2\u23a3-56\u2002\u200256\u2002\u23a6\u2002\u2002\u23a3-28\u2002\u200228\u2002\u23a6\u23a5```<br>```\u23a2\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u23a5```<br>```\u23a2\u2002\u23a1-2\u2002\u20027\u2002\u23a4\u2002\u2002\u2002\u23a1-18\u2002\u200263\u2002\u23a4\u23a5```<br>```\u23a2\u2002\u23a2\u2002\u2002\u2002\u2002\u2002\u2002\u23a5\u2002\u2002\u2002\u23a2\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u2002\u23a5\u23a5```<br>```\u23a3\u2002\u23a37\u2002\u2002\u2002-7\u23a6\u2002\u2002\u2002\u23a363\u2002\u2002\u2002-63\u23a6\u23a6``` | /       |\r\n\r\n### Basic Structure\r\n\r\n```\r\nPyPyNum\r\n\u251c\u2500\u2500 arrays\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 Array(object)/__init__(self: Any, data: Any, check: Any) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 BoolArray(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 array(data: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 asarray(data: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 aslist(data: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 boolarray(data: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 fill(shape: typing.Union[list, tuple], sequence: typing.Union[list, tuple, str], repeat: bool, pad: typing.Any, rtype: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 full(shape: typing.Union[list, tuple], fill_value: typing.Any, rtype: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 full_like(a: typing.Any, fill_value: typing.Any, rtype: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 get_shape(data: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 is_valid_array(_array: Any, _shape: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 ones(shape: typing.Union[list, tuple], rtype: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 ones_like(a: typing.Any, rtype: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 tensorproduct(tensors: pypynum.arrays.Array) -> pypynum.arrays.Array\r\n\u2502       \u251c\u2500\u2500 zeros(shape: typing.Union[list, tuple], rtype: typing.Callable) -> typing.Any\r\n\u2502       \u2514\u2500\u2500 zeros_like(a: typing.Any, rtype: typing.Callable) -> typing.Any\r\n\u251c\u2500\u2500 chars\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 int2subscript(standard_str: str) -> str\r\n\u2502       \u251c\u2500\u2500 int2superscript(standard_str: str) -> str\r\n\u2502       \u251c\u2500\u2500 subscript2int(subscript_str: str) -> str\r\n\u2502       \u2514\u2500\u2500 superscript2int(superscript_str: str) -> str\r\n\u251c\u2500\u2500 ciphers\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 atbash(text: str) -> str\r\n\u2502       \u251c\u2500\u2500 base_64(text: str, decrypt: bool) -> str\r\n\u2502       \u251c\u2500\u2500 caesar(text: str, shift: int, decrypt: bool) -> str\r\n\u2502       \u251c\u2500\u2500 hill256(text: bytes, key: list, decrypt: bool) -> bytes\r\n\u2502       \u251c\u2500\u2500 ksa(key: bytes) -> list\r\n\u2502       \u251c\u2500\u2500 morse(text: str, decrypt: bool) -> str\r\n\u2502       \u251c\u2500\u2500 playfair(text: str, key: str, decrypt: bool) -> str\r\n\u2502       \u251c\u2500\u2500 prga(s: list) -> Any\r\n\u2502       \u251c\u2500\u2500 rc4(text: bytes, key: bytes) -> bytes\r\n\u2502       \u251c\u2500\u2500 rot13(text: str) -> str\r\n\u2502       \u251c\u2500\u2500 substitution(text: str, sub_map: dict, decrypt: bool) -> str\r\n\u2502       \u2514\u2500\u2500 vigenere(text: str, key: str, decrypt: bool) -> str\r\n\u251c\u2500\u2500 consts\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 crandom\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 randint_polar(left: int, right: int, mod: typing.Union[int, float], angle: typing.Union[int, float]) -> complex\r\n\u2502       \u251c\u2500\u2500 randint_rect(left: int, right: int, real: typing.Union[int, float], imag: typing.Union[int, float]) -> complex\r\n\u2502       \u251c\u2500\u2500 random_polar(mod: typing.Union[int, float], angle: typing.Union[int, float]) -> complex\r\n\u2502       \u251c\u2500\u2500 random_rect(real: typing.Union[int, float], imag: typing.Union[int, float]) -> complex\r\n\u2502       \u251c\u2500\u2500 uniform_polar(left: typing.Union[int, float], right: typing.Union[int, float], mod: typing.Union[int, float], angle: typing.Union[int, float]) -> complex\r\n\u2502       \u2514\u2500\u2500 uniform_rect(left: typing.Union[int, float], right: typing.Union[int, float], real: typing.Union[int, float], imag: typing.Union[int, float]) -> complex\r\n\u251c\u2500\u2500 dataproc\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 Series(object)/__init__(self: Any, data: typing.Any, index: typing.Any) -> None\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 dists\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 beta_pdf(x: Any, a: Any, b: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 binom_pmf(k: Any, n: Any, p: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 cauchy_cdf(x: Any, x0: Any, gamma: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 cauchy_pdf(x: Any, x0: Any, gamma: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 chi2_cdf(x: Any, df: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 chi2_pdf(x: Any, df: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 expon_cdf(x: Any, scale: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 expon_pdf(x: Any, scale: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 f_pdf(x: Any, dfnum: Any, dfden: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 gamma_pdf(x: Any, shape: Any, scale: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 geometric_pmf(k: Any, p: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 hypergeom_pmf(k: Any, mg: Any, n: Any, nt: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 invgauss_pdf(x: Any, mu: Any, lambda_: Any, alpha: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 levy_pdf(x: Any, c: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 log_logistic_cdf(x: Any, alpha: Any, beta: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 log_logistic_pdf(x: Any, alpha: Any, beta: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 logistic_cdf(x: Any, mu: Any, s: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 logistic_pdf(x: Any, mu: Any, s: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 lognorm_cdf(x: Any, mu: Any, sigma: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 lognorm_pdf(x: Any, s: Any, scale: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 logser_pmf(k: Any, p: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 multinomial_pmf(k: Any, n: Any, p: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 nbinom_pmf(k: Any, n: Any, p: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 nhypergeom_pmf(k: Any, m: Any, n: Any, r: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 normal_cdf(x: Any, mu: Any, sigma: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 normal_pdf(x: Any, mu: Any, sigma: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 pareto_pdf(x: Any, k: Any, m: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 poisson_pmf(k: Any, mu: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 rayleigh_pdf(x: Any, sigma: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 t_pdf(x: Any, df: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 uniform_cdf(x: Any, loc: Any, scale: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 uniform_pdf(x: Any, loc: Any, scale: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 vonmises_pdf(x: Any, mu: Any, kappa: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 weibull_max_pdf(x: Any, c: Any, scale: Any, loc: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 weibull_min_pdf(x: Any, c: Any, scale: Any, loc: Any) -> Any\r\n\u2502       \u2514\u2500\u2500 zipf_pmf(k: Any, s: Any, n: Any) -> Any\r\n\u251c\u2500\u2500 equations\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 lin_eq(left: list, right: list) -> list\r\n\u2502       \u2514\u2500\u2500 poly_eq(coefficients: list) -> list\r\n\u251c\u2500\u2500 fft\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 FT1D(object)/__init__(self: Any, data: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 files\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 read(file: str) -> list\r\n\u2502       \u2514\u2500\u2500 write(file: str, cls: object) -> Any\r\n\u251c\u2500\u2500 geoms\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 Circle(object)/__init__(self: Any, center: typing.Union[list, tuple], radius: typing.Union[int, float]) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Line(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Point(object)/__init__(self: Any, p: typing.Union[list, tuple]) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Polygon(object)/__init__(self: Any, p: typing.Union[list, tuple]) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Quadrilateral(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple], c: typing.Union[list, tuple], d: typing.Union[list, tuple]) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 Triangle(object)/__init__(self: Any, a: typing.Union[list, tuple], b: typing.Union[list, tuple], c: typing.Union[list, tuple]) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 distance(g1: Any, g2: Any, error: typing.Union[int, float]) -> float\r\n\u251c\u2500\u2500 graphs\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 BaseGraph(object)/__init__(self: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 BaseWeGraph(pypynum.graphs.BaseGraph)/__init__(self: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 DiGraph(pypynum.graphs.BaseGraph)/__init__(self: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 UnGraph(pypynum.graphs.BaseGraph)/__init__(self: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 WeDiGraph(pypynum.graphs.BaseWeGraph)/__init__(self: Any) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 WeUnGraph(pypynum.graphs.BaseWeGraph)/__init__(self: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 groups\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 Group(object)/__init__(self: Any, data: Any, operation: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 group(data: Any) -> Any\r\n\u251c\u2500\u2500 hypcmpnms\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 Euler(object)/__init__(self: Any, y: typing.Union[int, float], p: typing.Union[int, float], r: typing.Union[int, float]) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Octonion(object)/__init__(self: Any, s: typing.Union[int, float], t: typing.Union[int, float], u: typing.Union[int, float], v: typing.Union[int, float], w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 Quaternion(object)/__init__(self: Any, w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 convert(data: typing.Union[pypynum.hypcmpnms.Quaternion, pypynum.matrices.Matrix, pypynum.hypcmpnms.Euler], to: str) -> typing.Union[pypynum.hypcmpnms.Quaternion, pypynum.matrices.Matrix, pypynum.hypcmpnms.Euler]\r\n\u2502       \u251c\u2500\u2500 euler(yaw: typing.Union[int, float], pitch: typing.Union[int, float], roll: typing.Union[int, float]) -> pypynum.hypcmpnms.Euler\r\n\u2502       \u251c\u2500\u2500 octo(s: typing.Union[int, float], t: typing.Union[int, float], u: typing.Union[int, float], v: typing.Union[int, float], w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> pypynum.hypcmpnms.Octonion\r\n\u2502       \u2514\u2500\u2500 quat(w: typing.Union[int, float], x: typing.Union[int, float], y: typing.Union[int, float], z: typing.Union[int, float]) -> pypynum.hypcmpnms.Quaternion\r\n\u251c\u2500\u2500 images\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 BMP(pypynum.images.BaseImage)/__init__(self: Any) -> None\r\n\u2502   \u2502   \u251c\u2500\u2500 BaseImage(object)/__init__(self: Any) -> None\r\n\u2502   \u2502   \u2514\u2500\u2500 PNG(pypynum.images.BaseImage)/__init__(self: Any) -> None\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 crc(data: Any, length: Any, init: Any, xor: Any) -> Any\r\n\u251c\u2500\u2500 interp\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 bicubic(x: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 contribute(src: Any, x: Any, y: Any, channels: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 interp1d(data: typing.Union[list, tuple], length: int) -> list\r\n\u2502       \u2514\u2500\u2500 interp2d(src: Any, new_height: Any, new_width: Any, channels: Any, round_res: Any, min_val: Any, max_val: Any) -> Any\r\n\u251c\u2500\u2500 kernels\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 det2x2kernel(a: typing.Union[list, tuple]) -> float\r\n\u2502       \u251c\u2500\u2500 det3x3kernel(a: typing.Union[list, tuple]) -> float\r\n\u2502       \u251c\u2500\u2500 det4x4kernel(a: typing.Union[list, tuple]) -> float\r\n\u2502       \u251c\u2500\u2500 eigen2x2kernel(a: typing.Union[list, tuple]) -> tuple\r\n\u2502       \u251c\u2500\u2500 inv2x2kernel(a: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 inv3x3kernel(a: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 inv4x4kernel(a: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 lu2x2kernel(a: typing.Union[list, tuple]) -> tuple\r\n\u2502       \u251c\u2500\u2500 lu3x3kernel(a: typing.Union[list, tuple]) -> tuple\r\n\u2502       \u251c\u2500\u2500 lu4x4kernel(a: typing.Union[list, tuple]) -> tuple\r\n\u2502       \u251c\u2500\u2500 matexp2x2kernel(a: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 matmul2x2kernel(a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 matmul3x3kernel(a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 matmul4x4kernel(a: typing.Union[list, tuple], b: typing.Union[list, tuple]) -> list\r\n\u2502       \u2514\u2500\u2500 matpow2x2kernel(a: typing.Union[list, tuple], n: typing.Union[int, float, complex]) -> list\r\n\u251c\u2500\u2500 logics\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 AND(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Basic(object)/__init__(self: Any, label: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Binary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 COMP(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 DFF(pypynum.logics.Unary)/__init__(self: Any, label: Any, pin0: Any, state: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 FullAdder(pypynum.logics.Ternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 FullSuber(pypynum.logics.Ternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 HalfAdder(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 HalfSuber(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 JKFF(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, state: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 NAND(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 NOR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 NOT(pypynum.logics.Unary)/__init__(self: Any, label: Any, pin0: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 OR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Quaternary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 TFF(pypynum.logics.Unary)/__init__(self: Any, label: Any, pin0: Any, state: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Ternary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 TwoBDiver(pypynum.logics.Quaternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 TwoBMuler(pypynum.logics.Quaternary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any, pin2: Any, pin3: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 Unary(pypynum.logics.Basic)/__init__(self: Any, label: Any, pin0: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 XNOR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 XOR(pypynum.logics.Binary)/__init__(self: Any, label: Any, pin0: Any, pin1: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 connector(previous: Any, latter: Any) -> Any\r\n\u251c\u2500\u2500 maths\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 arrangement(n: int, r: int) -> int\r\n\u2502       \u251c\u2500\u2500 combination(n: int, r: int) -> int\r\n\u2502       \u251c\u2500\u2500 acos(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 acosh(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 acot(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 acoth(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 acsc(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 acsch(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 arrangement(n: int, r: int) -> int\r\n\u2502       \u251c\u2500\u2500 asec(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 asech(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 asin(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 asinh(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 atan(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 atanh(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 average(data: typing.Union[list, tuple], weights: typing.Union[list, tuple]) -> float\r\n\u2502       \u251c\u2500\u2500 beta(p: typing.Union[int, float], q: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 central_moment(data: typing.Union[list, tuple], order: int) -> float\r\n\u2502       \u251c\u2500\u2500 coeff_det(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 combination(n: int, r: int) -> int\r\n\u2502       \u251c\u2500\u2500 corr_coeff(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 cos(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 cosh(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 cot(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 coth(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 cov(x: typing.Union[list, tuple], y: typing.Union[list, tuple], ddof: int) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 crt(n: typing.Union[list, tuple], a: typing.Union[list, tuple]) -> int\r\n\u2502       \u251c\u2500\u2500 csc(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 csch(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 cumprod(lst: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 cumsum(lst: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 deriv(f: Any, x: float, h: float, method: str, args: Any, kwargs: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 erf(x: typing.Union[int, float]) -> float\r\n\u2502       \u251c\u2500\u2500 exgcd(a: int, b: int) -> tuple\r\n\u2502       \u251c\u2500\u2500 exp(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 factorial(n: int) -> int\r\n\u2502       \u251c\u2500\u2500 freq(data: typing.Union[list, tuple]) -> dict\r\n\u2502       \u251c\u2500\u2500 gamma(alpha: typing.Union[int, float]) -> float\r\n\u2502       \u251c\u2500\u2500 gcd(args: int) -> int\r\n\u2502       \u251c\u2500\u2500 geom_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 harm_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 integ(f: Any, x_start: typing.Union[int, float], x_end: typing.Union[int, float], n: int, args: Any, kwargs: Any) -> float\r\n\u2502       \u251c\u2500\u2500 iroot(y: int, n: int) -> int\r\n\u2502       \u251c\u2500\u2500 is_possibly_square(n: int) -> bool\r\n\u2502       \u251c\u2500\u2500 is_square(n: int) -> bool\r\n\u2502       \u251c\u2500\u2500 isqrt(x: int) -> int\r\n\u2502       \u251c\u2500\u2500 kurt(data: typing.Union[list, tuple], fisher: bool) -> float\r\n\u2502       \u251c\u2500\u2500 lcm(args: int) -> int\r\n\u2502       \u251c\u2500\u2500 ln(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 lowergamma(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 median(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 mod_order(a: int, n: int, b: int) -> int\r\n\u2502       \u251c\u2500\u2500 mode(data: typing.Union[list, tuple]) -> Any\r\n\u2502       \u251c\u2500\u2500 normalize(data: typing.Union[list, tuple], target: typing.Union[int, float, complex]) -> typing.Union[list, tuple]\r\n\u2502       \u251c\u2500\u2500 parity(x: int) -> int\r\n\u2502       \u251c\u2500\u2500 pi(i: int, n: int, f: Any) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 power_mean(numbers: typing.Union[list, tuple], p: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 primitive_root(a: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 product(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 ptp(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 quantile(data: list, q: float, interpolation: str, ordered: bool) -> float\r\n\u2502       \u251c\u2500\u2500 raw_moment(data: typing.Union[list, tuple], order: int) -> float\r\n\u2502       \u251c\u2500\u2500 roll(seq: typing.Union[list, tuple, str], shift: int) -> typing.Union[list, tuple, str]\r\n\u2502       \u251c\u2500\u2500 root(x: typing.Union[int, float, complex], y: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 sec(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 sech(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 sigma(i: int, n: int, f: Any) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 sigmoid(x: typing.Union[int, float]) -> float\r\n\u2502       \u251c\u2500\u2500 sign(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 sin(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 sinh(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 skew(data: typing.Union[list, tuple]) -> float\r\n\u2502       \u251c\u2500\u2500 square_mean(numbers: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 std(numbers: typing.Union[list, tuple], ddof: int) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 sumprod(arrays: typing.Union[list, tuple]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 tan(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 tanh(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n\u2502       \u251c\u2500\u2500 totient(n: int) -> int\r\n\u2502       \u251c\u2500\u2500 uppergamma(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 var(numbers: typing.Union[list, tuple], ddof: int) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 xlogy(x: typing.Union[int, float, complex], y: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u2514\u2500\u2500 zeta(alpha: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u251c\u2500\u2500 matrices\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 Matrix(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 cholesky(matrix: pypynum.matrices.Matrix, hermitian: bool) -> pypynum.matrices.Matrix\r\n\u2502       \u251c\u2500\u2500 diag(v: typing.Any, k: int, n: int, m: int) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 diag_indices(n: int, k: int, m: int) -> tuple\r\n\u2502       \u251c\u2500\u2500 eigen(matrix: pypynum.matrices.Matrix) -> tuple\r\n\u2502       \u251c\u2500\u2500 hessenberg(matrix: pypynum.matrices.Matrix) -> tuple\r\n\u2502       \u251c\u2500\u2500 identity(n: int, m: int) -> pypynum.matrices.Matrix\r\n\u2502       \u251c\u2500\u2500 lu(matrix: pypynum.matrices.Matrix) -> tuple\r\n\u2502       \u251c\u2500\u2500 mat(data: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 perm_mat(num_rows: int, num_cols: int, row_swaps: typing.Union[list, tuple], col_swaps: typing.Union[list, tuple], rtype: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 perm_mat_indices(num_rows: int, num_cols: int, row_swaps: typing.Union[list, tuple], col_swaps: typing.Union[list, tuple]) -> tuple\r\n\u2502       \u251c\u2500\u2500 qr(matrix: pypynum.matrices.Matrix, reduce: bool) -> tuple\r\n\u2502       \u251c\u2500\u2500 rank_decomp(matrix: pypynum.matrices.Matrix) -> tuple\r\n\u2502       \u251c\u2500\u2500 rotate90(matrix: pypynum.matrices.Matrix, times: int) -> pypynum.matrices.Matrix\r\n\u2502       \u251c\u2500\u2500 svd(matrix: pypynum.matrices.Matrix, full: bool, calc_uv: bool) -> tuple\r\n\u2502       \u251c\u2500\u2500 tril_indices(n: int, k: int, m: int) -> tuple\r\n\u2502       \u2514\u2500\u2500 triu_indices(n: int, k: int, m: int) -> tuple\r\n\u251c\u2500\u2500 multiprec\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 MPComplex(object)/__init__(self: Any, real: Any, imag: Any, sigfigs: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 _remove_trailing_zeros(value: typing.Any) -> str\r\n\u2502       \u251c\u2500\u2500 _setprec(sigfigs: int) -> Any\r\n\u2502       \u251c\u2500\u2500 asmpc(real: typing.Union[int, float, str, decimal.Decimal, complex, pypynum.multiprec.MPComplex], imag: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> pypynum.multiprec.MPComplex\r\n\u2502       \u251c\u2500\u2500 frac2dec(frac: fractions.Fraction, sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_acos(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_asin(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_atan(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_atan2(y: typing.Union[int, float, str, decimal.Decimal], x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_catalan(sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_cos(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_cosh(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_e(sigfigs: int, method: str) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_euler_gamma(sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_exp(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int, builtin: bool) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_fresnel_c(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_fresnel_s(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_ln(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int, builtin: bool) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_log(x: typing.Union[int, float, str, decimal.Decimal], base: typing.Union[int, float, str, decimal.Decimal], sigfigs: int, builtin: bool) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_phi(sigfigs: int, method: str) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_pi(sigfigs: int, method: str) -> decimal.Decimal\r\n\u2502       \u251c\u2500\u2500 mp_sin(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u2502       \u2514\u2500\u2500 mp_sinh(x: typing.Union[int, float, str, decimal.Decimal], sigfigs: int) -> decimal.Decimal\r\n\u251c\u2500\u2500 networks\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 NeuralNetwork(object)/__init__(self: Any, _input: Any, _hidden: Any, _output: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 neuraln(_input: Any, _hidden: Any, _output: Any) -> Any\r\n\u251c\u2500\u2500 numbers\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 float2fraction(number: float, mixed: bool, error: float) -> tuple\r\n\u2502       \u251c\u2500\u2500 int2roman(integer: int, overline: bool) -> str\r\n\u2502       \u251c\u2500\u2500 int2words(integer: int) -> str\r\n\u2502       \u251c\u2500\u2500 parse_float(s: str) -> tuple\r\n\u2502       \u251c\u2500\u2500 roman2int(roman_num: str) -> int\r\n\u2502       \u251c\u2500\u2500 split_float(s: str) -> tuple\r\n\u2502       \u2514\u2500\u2500 str2int(string: str) -> int\r\n\u251c\u2500\u2500 plotting\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 background(right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool) -> typing.Union[list, str]\r\n\u2502       \u251c\u2500\u2500 binary(function: Any, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], error: Any, compare: Any, string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]\r\n\u2502       \u251c\u2500\u2500 c_unary(function: Any, projection: str, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]\r\n\u2502       \u251c\u2500\u2500 change(data: typing.Union[list, str]) -> typing.Union[list, str]\r\n\u2502       \u251c\u2500\u2500 color(text: str, rgb: typing.Union[list, tuple]) -> str\r\n\u2502       \u2514\u2500\u2500 unary(function: Any, right: typing.Union[int, float], left: typing.Union[int, float], top: typing.Union[int, float], bottom: typing.Union[int, float], complexity: typing.Union[int, float], ratio: typing.Union[int, float], string: bool, basic: list, character: str, data: bool, coloration: Any) -> typing.Union[list, str]\r\n\u251c\u2500\u2500 polys\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 Polynomial(object)/__init__(self: Any, terms: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 chebgauss(n: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 chebpoly(n: Any, single: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 from_coeffs(coeffs: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 from_coords(coords: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 laggauss(n: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 lagpoly(n: Any, single: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 leggauss(n: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 legpoly(n: Any, single: Any) -> Any\r\n\u2502       \u2514\u2500\u2500 poly(terms: Any) -> Any\r\n\u251c\u2500\u2500 pprinters\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 pprint_matrix(matrix: Any, style: Any, output: Any) -> Any\r\n\u251c\u2500\u2500 random\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 __create_nested_list(dimensions: Any, func: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 __validate_shape(shape: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 choice(seq: typing.Union[list, tuple, str], shape: typing.Union[list, tuple]) -> Any\r\n\u2502       \u251c\u2500\u2500 gauss(mu: typing.Union[int, float], sigma: typing.Union[int, float], shape: typing.Union[list, tuple]) -> typing.Union[float, list]\r\n\u2502       \u251c\u2500\u2500 rand(shape: typing.Union[list, tuple]) -> typing.Union[float, list]\r\n\u2502       \u251c\u2500\u2500 randint(a: int, b: int, shape: typing.Union[list, tuple]) -> typing.Union[int, list]\r\n\u2502       \u2514\u2500\u2500 uniform(a: typing.Union[int, float], b: typing.Union[int, float], shape: typing.Union[list, tuple]) -> typing.Union[float, list]\r\n\u251c\u2500\u2500 regs\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 lin_reg(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> list\r\n\u2502       \u251c\u2500\u2500 par_reg(x: typing.Union[list, tuple], y: typing.Union[list, tuple]) -> list\r\n\u2502       \u2514\u2500\u2500 poly_reg(x: typing.Union[list, tuple], y: typing.Union[list, tuple], n: int) -> list\r\n\u251c\u2500\u2500 seqs\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 arithmetic_sequence(a1: typing.Union[int, float], an: typing.Union[int, float], d: typing.Union[int, float], n: typing.Union[int, float], s: typing.Union[int, float]) -> dict\r\n\u2502       \u251c\u2500\u2500 bell(n: int) -> list\r\n\u2502       \u251c\u2500\u2500 bernoulli(n: int, single: bool) -> typing.Union[list, tuple]\r\n\u2502       \u251c\u2500\u2500 catalan(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 farey(n: int) -> list\r\n\u2502       \u251c\u2500\u2500 fibonacci(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 geometric_sequence(a1: typing.Union[int, float], an: typing.Union[int, float], r: typing.Union[int, float], n: typing.Union[int, float], s: typing.Union[int, float]) -> dict\r\n\u2502       \u251c\u2500\u2500 lucas(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 padovan(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 pascal(n: int) -> list\r\n\u2502       \u251c\u2500\u2500 pell(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 pelllucas(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 perrin(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 recaman(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 stirling1(n: int) -> list\r\n\u2502       \u251c\u2500\u2500 stirling2(n: int) -> list\r\n\u2502       \u251c\u2500\u2500 sylvester(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u251c\u2500\u2500 tetranacci(n: int, single: bool) -> typing.Union[int, list]\r\n\u2502       \u2514\u2500\u2500 tribonacci(n: int, single: bool) -> typing.Union[int, list]\r\n\u251c\u2500\u2500 special\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 besseli0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 besseli1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 besseliv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 besselj0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 besselj1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 besseljv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 hyp0f1(b0: typing.Union[int, float, complex], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 hyp1f1(a0: typing.Union[int, float, complex], b0: typing.Union[int, float, complex], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 hyp2f1(a0: typing.Union[int, float, complex], a1: typing.Union[int, float, complex], b0: typing.Union[int, float, complex], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 hyppfq(a: typing.Union[list, tuple], b: typing.Union[list, tuple], z: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qbeta(a: typing.Union[int, float, complex], b: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qbinomial(n: typing.Union[int, float, complex], m: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qcos_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qcos_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qcosh_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qcosh_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qexp_large(z: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qexp_small(z: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qfactorial(n: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qgamma(n: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qpi(q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qpochhammer(a: typing.Union[int, float, complex], q: typing.Union[int, float, complex], n: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qsin_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qsin_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u251c\u2500\u2500 qsinh_large(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u2502       \u2514\u2500\u2500 qsinh_small(x: typing.Union[int, float, complex], q: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n\u251c\u2500\u2500 stattest\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 chi2_cont(contingency: list, lambda_: float, calc_p: bool, corr: bool) -> tuple\r\n\u2502       \u251c\u2500\u2500 chisquare(observed: list, expected: list) -> tuple\r\n\u2502       \u251c\u2500\u2500 kurttest(data: list, two_tailed: bool) -> tuple\r\n\u2502       \u251c\u2500\u2500 mediantest(samples: Any, ties: Any, lambda_: Any, corr: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 normaltest(data: list) -> tuple\r\n\u2502       \u2514\u2500\u2500 skewtest(data: list, two_tailed: bool) -> tuple\r\n\u251c\u2500\u2500 symbols\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 parse_expr(expr: str) -> list\r\n\u251c\u2500\u2500 tensors\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 Tensor(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 ten(data: list) -> pypynum.tensors.Tensor\r\n\u2502       \u2514\u2500\u2500 tensor_and_number(tensor: Any, operator: Any, number: Any) -> Any\r\n\u251c\u2500\u2500 test\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 this\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 tools\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 classify(array: typing.Union[list, tuple]) -> dict\r\n\u2502       \u251c\u2500\u2500 cos_sim(seq1: typing.Union[list, tuple, str], seq2: typing.Union[list, tuple, str], is_vector: bool) -> float\r\n\u2502       \u251c\u2500\u2500 damerau(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> int\r\n\u2502       \u251c\u2500\u2500 dedup(iterable: typing.Union[list, tuple, str]) -> typing.Union[list, tuple, str]\r\n\u2502       \u251c\u2500\u2500 fast_pow(a: typing.Any, n: int, init: typing.Any, mul: typing.Callable) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 findall(seq: typing.Union[list, tuple, str], pat: typing.Union[list, tuple, str]) -> list\r\n\u2502       \u251c\u2500\u2500 frange(start: typing.Union[int, float], stop: typing.Union[int, float], step: float) -> list\r\n\u2502       \u251c\u2500\u2500 geomspace(start: typing.Union[int, float], stop: typing.Union[int, float], number: int) -> list\r\n\u2502       \u251c\u2500\u2500 kmp_table(pattern: typing.Union[list, tuple, str]) -> list\r\n\u2502       \u251c\u2500\u2500 lcsubseq(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> list\r\n\u2502       \u251c\u2500\u2500 lcsubstr(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> list\r\n\u2502       \u251c\u2500\u2500 levenshtein(x: typing.Union[list, tuple, str], y: typing.Union[list, tuple, str]) -> int\r\n\u2502       \u251c\u2500\u2500 linspace(start: typing.Union[int, float], stop: typing.Union[int, float], number: int) -> list\r\n\u2502       \u251c\u2500\u2500 lstrip(sequence: typing.Any, keys: typing.Any) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 magic_square(n: int) -> list\r\n\u2502       \u251c\u2500\u2500 primality(n: int, iter_num: int) -> bool\r\n\u2502       \u251c\u2500\u2500 prime_factors(integer: int, dictionary: bool, pollard_rho: bool) -> typing.Union[list, dict]\r\n\u2502       \u251c\u2500\u2500 primes(limit: int) -> list\r\n\u2502       \u251c\u2500\u2500 replace(seq: typing.Union[list, tuple], old: typing.Union[list, tuple], new: typing.Union[list, tuple], count: int) -> typing.Union[list, tuple]\r\n\u2502       \u251c\u2500\u2500 rstrip(sequence: typing.Any, keys: typing.Any) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 semiprimes(limit: int) -> list\r\n\u2502       \u251c\u2500\u2500 split(iterable: typing.Union[list, tuple, str], key: typing.Union[list, tuple], retain: bool) -> list\r\n\u2502       \u251c\u2500\u2500 strip(sequence: typing.Any, keys: typing.Any) -> typing.Any\r\n\u2502       \u251c\u2500\u2500 strip_helper(sequence: typing.Any, keys_set: set, strip_start: bool, strip_end: bool) -> typing.Any\r\n\u2502       \u2514\u2500\u2500 twinprimes(limit: int) -> list\r\n\u251c\u2500\u2500 trees\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 BTNode(object)/__init__(self: Any, data: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 BinaryTree(object)/__init__(self: Any, root: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 MTNode(object)/__init__(self: Any, data: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 MultiTree(object)/__init__(self: Any, root: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 RBTNode(object)/__init__(self: Any, data: Any, color: Any) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 RedBlackTree(object)/__init__(self: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 types\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 ufuncs\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u251c\u2500\u2500 add(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 apply(a: Any, func: Any, rtype: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 base_ufunc(arrays: Any, func: Any, args: Any, rtype: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 divide(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 eq(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 floor_divide(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 ge(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 gt(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 le(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 lt(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 modulo(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 multiply(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 ne(x: Any, y: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 power(x: Any, y: Any, m: Any) -> Any\r\n\u2502       \u251c\u2500\u2500 subtract(x: Any, y: Any) -> Any\r\n\u2502       \u2514\u2500\u2500 ufunc_helper(x: Any, y: Any, func: Any) -> Any\r\n\u251c\u2500\u2500 utils\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u251c\u2500\u2500 InfIterator(object)/__init__(self: Any, start: typing.Union[int, float, complex], mode: str, common: typing.Union[int, float, complex]) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 IntervalSet(object)/__init__(self: Any, intervals: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 LinkedList(object)/__init__(self: Any) -> Any\r\n\u2502   \u2502   \u251c\u2500\u2500 LinkedListNode(object)/__init__(self: Any, value: Any, next_node: Any) -> Any\r\n\u2502   \u2502   \u2514\u2500\u2500 OrderedSet(object)/__init__(self: Any, sequence: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u251c\u2500\u2500 vectors\r\n\u2502   \u251c\u2500\u2500 CLASS\r\n\u2502   \u2502   \u2514\u2500\u2500 Vector(pypynum.arrays.Array)/__init__(self: Any, data: Any, check: Any) -> Any\r\n\u2502   \u2514\u2500\u2500 FUNCTION\r\n\u2502       \u2514\u2500\u2500 vec(data: Any) -> Any\r\n\u2514\u2500\u2500 zh_cn\r\n    \u251c\u2500\u2500 CLASS\r\n    \u2514\u2500\u2500 FUNCTION\r\n        \u251c\u2500\u2500 Fraction\u8f6c\u4e3aDecimal(\u5206\u6570\u5bf9\u8c61: fractions.Fraction, \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 RC4\u4f2a\u968f\u673a\u751f\u6210\u7b97\u6cd5(\u5bc6\u94a5\u5e8f\u5217: list) -> Any\r\n        \u251c\u2500\u2500 RC4\u521d\u59cb\u5316\u5bc6\u94a5\u8c03\u5ea6\u7b97\u6cd5(\u5bc6\u94a5: bytes) -> list\r\n        \u251c\u2500\u2500 RC4\u5bc6\u7801(\u6587\u672c: bytes, \u5bc6\u94a5: bytes) -> bytes\r\n        \u251c\u2500\u2500 ROT13\u5bc6\u7801(\u6587\u672c: str) -> str\r\n        \u251c\u2500\u2500 S\u578b\u51fd\u6570(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 base64\u5bc6\u7801(\u6587\u672c: str, \u89e3\u5bc6: bool) -> str\r\n        \u251c\u2500\u2500 x\u5bf9\u6570y\u4e58\u79ef(x: float, y: float) -> float\r\n        \u251c\u2500\u2500 y\u6b21\u65b9\u6839(\u88ab\u5f00\u65b9\u6570: typing.Union[int, float, complex], \u5f00\u65b9\u6570: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u4e00\u7ef4\u5085\u91cc\u53f6\u53d8\u6362(\u6570\u636e: Any) -> pypynum.fft.FT1D\r\n        \u251c\u2500\u2500 \u4e0a\u4f3d\u739b(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u4e0a\u6807\u8f6c\u6574\u6570(\u4e0a\u6807\u5b57\u7b26\u4e32: str) -> str\r\n        \u251c\u2500\u2500 \u4e0b\u4f3d\u739b(s: typing.Union[int, float, complex], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u4e0b\u6807\u8f6c\u6574\u6570(\u4e0b\u6807\u5b57\u7b26\u4e32: str) -> str\r\n        \u251c\u2500\u2500 \u4e2d\u4f4d\u6570(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u4e2d\u56fd\u5269\u4f59\u5b9a\u7406(n: typing.List[int], a: typing.List[int]) -> int\r\n        \u251c\u2500\u2500 \u4e2d\u5fc3\u77e9(\u6570\u636e: typing.List[float], \u9636\u6570: int) -> float\r\n        \u251c\u2500\u2500 \u4e58\u79ef\u548c(\u591a\u4e2a\u6570\u7ec4: typing.List[typing.Any]) -> float\r\n        \u251c\u2500\u2500 \u4ee3\u66ff\u5bc6\u7801(\u6587\u672c: str, \u66ff\u6362\u6620\u5c04: dict, \u89e3\u5bc6: bool) -> str\r\n        \u251c\u2500\u2500 \u4f17\u6570(\u6570\u636e: typing.List[typing.Any]) -> Any\r\n        \u251c\u2500\u2500 \u4f3d\u739b\u51fd\u6570(alpha: float) -> float\r\n        \u251c\u2500\u2500 \u4f59\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u4f59\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u4f59\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u504f\u5ea6(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u5168\u4e00(\u5f62\u72b6: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u5168\u90e8\u586b\u5145(\u5f62\u72b6: Any, \u586b\u5145\u503c: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u5168\u96f6(\u5f62\u72b6: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u5199\u5165(\u6587\u4ef6: str, \u5bf9\u8c61: object) -> Any\r\n        \u251c\u2500\u2500 \u51e0\u4f55\u5e73\u5747\u6570(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u51ef\u6492\u5bc6\u7801(\u6587\u672c: str, \u79fb\u4f4d: int, \u89e3\u5bc6: bool) -> str\r\n        \u251c\u2500\u2500 \u5206\u4f4d\u6570(\u6570\u636e: list, \u5206\u4f4d\u503c: float, \u63d2\u503c\u65b9\u6cd5: str, \u5df2\u6392\u5e8f: bool) -> float\r\n        \u251c\u2500\u2500 \u5224\u5b9a\u7cfb\u6570(x: typing.List[float], y: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u5224\u65ad\u5e73\u65b9\u6570(n: int) -> bool\r\n        \u251c\u2500\u2500 \u52a0\u6743\u5e73\u5747(\u6570\u636e: typing.List[float], \u6743\u91cd: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u534f\u65b9\u5dee(x: typing.List[float], y: typing.List[float], \u81ea\u7531\u5ea6: int) -> float\r\n        \u251c\u2500\u2500 \u539f\u6839(a: int, \u5355\u4e2a: bool) -> typing.Union[int, typing.List[int]]\r\n        \u251c\u2500\u2500 \u539f\u70b9\u77e9(\u6570\u636e: typing.List[float], \u9636\u6570: int) -> float\r\n        \u251c\u2500\u2500 \u53cc\u66f2\u4f59\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cc\u66f2\u4f59\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cc\u66f2\u4f59\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cc\u66f2\u6b63\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cc\u66f2\u6b63\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cc\u66f2\u6b63\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u4f59\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u4f59\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u4f59\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u53cc\u66f2\u4f59\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u53cc\u66f2\u4f59\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u53cc\u66f2\u4f59\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u53cc\u66f2\u6b63\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u53cc\u66f2\u6b63\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u53cc\u66f2\u6b63\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u6b63\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u6b63\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53cd\u6b63\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u53ef\u80fd\u662f\u5e73\u65b9\u6570(n: int) -> bool\r\n        \u251c\u2500\u2500 \u586b\u5145\u5e8f\u5217(\u5f62\u72b6: Any, \u5e8f\u5217: Any, \u91cd\u590d: Any, \u586b\u5145: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u591a\u6b21\u65b9\u6839\u53d6\u6574(\u88ab\u5f00\u65b9\u6570: int, \u5f00\u65b9\u6570: int) -> int\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u4f59\u5f26(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u53cc\u66f2\u4f59\u5f26(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u53cc\u66f2\u6b63\u5f26(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u53cd\u4f59\u5f26(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u53cd\u6b63\u5207(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u53cd\u6b63\u5f26(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u5706\u5468\u7387(\u6709\u6548\u4f4d\u6570: int, \u65b9\u6cd5: str) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u590d\u6570(\u5b9e\u90e8: typing.Union[int, float, str, decimal.Decimal], \u865a\u90e8: typing.Union[int, float, str, decimal.Decimal], \u6709\u6548\u4f4d\u6570: int) -> pypynum.multiprec.MPComplex\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u5bf9\u6570(\u771f\u6570: typing.Union[int, float], \u5e95\u6570: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int, \u4f7f\u7528\u5185\u7f6e\u65b9\u6cd5: bool) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u65b9\u4f4d\u89d2(y: typing.Union[int, float], x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u6b27\u62c9\u4f3d\u9a6c(\u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u6b63\u5f26(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u81ea\u7136\u5bf9\u6570(\u771f\u6570: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int, \u4f7f\u7528\u5185\u7f6e\u65b9\u6cd5: bool) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u81ea\u7136\u5e38\u6570(\u6709\u6548\u4f4d\u6570: int, \u65b9\u6cd5: str) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u81ea\u7136\u6307\u6570(\u6307\u6570: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int, \u4f7f\u7528\u5185\u7f6e\u65b9\u6cd5: bool) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u83f2\u6d85\u8033\u4f59\u5f26\u79ef\u5206(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u83f2\u6d85\u8033\u6b63\u5f26\u79ef\u5206(x: typing.Union[int, float], \u6709\u6548\u4f4d\u6570: int) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u7cbe\u5ea6\u9ec4\u91d1\u5206\u5272\u7387(\u6709\u6548\u4f4d\u6570: int, \u65b9\u6cd5: str) -> decimal.Decimal\r\n        \u251c\u2500\u2500 \u591a\u9879\u5f0f\u65b9\u7a0b(\u7cfb\u6570: list) -> list\r\n        \u251c\u2500\u2500 \u5b57\u7b26\u4e32\u8f6c\u6574\u6570(\u5b57\u7b26\u4e32: str) -> int\r\n        \u251c\u2500\u2500 \u5bfc\u6570(\u51fd\u6570: Any, \u53c2\u6570: float, \u6b65\u957f: float, \u989d\u5916\u53c2\u6570: Any, \u989d\u5916\u5173\u952e\u5b57\u53c2\u6570: Any) -> float\r\n        \u251c\u2500\u2500 \u5cf0\u5ea6(\u6570\u636e: typing.List[float], \u8d39\u5e0c\u5c14: bool) -> float\r\n        \u251c\u2500\u2500 \u5e0c\u5c14256\u5bc6\u7801(\u6587\u672c: bytes, \u5bc6\u94a5: list, \u89e3\u5bc6: bool) -> bytes\r\n        \u251c\u2500\u2500 \u5e73\u5747\u6570(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u5e73\u65b9\u5e73\u5747\u6570(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u5e73\u65b9\u6839\u53d6\u6574(\u88ab\u5f00\u65b9\u6570: int) -> int\r\n        \u251c\u2500\u2500 \u5e8f\u5217\u6eda\u52a8(\u5e8f\u5217: typing.Iterator[typing.Any], \u504f\u79fb: int) -> typing.Iterator[typing.Any]\r\n        \u251c\u2500\u2500 \u5f52\u4e00\u5316(\u6570\u636e: typing.List[float], \u76ee\u6807: float) -> typing.List[float]\r\n        \u251c\u2500\u2500 \u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5(a: int, b: int) -> typing.Tuple[int, int, int]\r\n        \u251c\u2500\u2500 \u62c6\u5206\u6d6e\u70b9\u6570\u5b57\u7b26\u4e32(\u5b57\u7b26\u4e32: str) -> tuple\r\n        \u251c\u2500\u2500 \u6392\u5217\u6570(\u603b\u6570: int, \u9009\u53d6\u6570: int) -> int\r\n        \u251c\u2500\u2500 \u6570\u7ec4(\u6570\u636e: list, \u68c0\u67e5: bool) -> pypynum.arrays.Array\r\n        \u251c\u2500\u2500 \u6574\u6570\u8f6c\u4e0a\u6807(\u6807\u51c6\u5b57\u7b26\u4e32: str) -> str\r\n        \u251c\u2500\u2500 \u6574\u6570\u8f6c\u4e0b\u6807(\u6807\u51c6\u5b57\u7b26\u4e32: str) -> str\r\n        \u251c\u2500\u2500 \u6574\u6570\u8f6c\u5355\u8bcd(\u6574\u6570: int) -> str\r\n        \u251c\u2500\u2500 \u6574\u6570\u8f6c\u7f57\u9a6c\u6570(\u6574\u6570: int, \u4e0a\u5212\u7ebf: bool) -> str\r\n        \u251c\u2500\u2500 \u65b9\u5dee(\u6570\u636e: typing.List[float], \u81ea\u7531\u5ea6: int) -> float\r\n        \u251c\u2500\u2500 \u666e\u83b1\u8d39\u5c14\u5bc6\u7801(\u6587\u672c: str, \u5bc6\u94a5: str, \u89e3\u5bc6: bool) -> str\r\n        \u251c\u2500\u2500 \u6700\u5927\u516c\u7ea6\u6570(args: int) -> int\r\n        \u251c\u2500\u2500 \u6700\u5c0f\u516c\u500d\u6570(args: int) -> int\r\n        \u251c\u2500\u2500 \u6781\u5dee(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u6807\u51c6\u5dee(\u6570\u636e: typing.List[float], \u81ea\u7531\u5ea6: int) -> float\r\n        \u251c\u2500\u2500 \u6a21\u8fd0\u7b97\u9636(a: int, n: int, b: int) -> int\r\n        \u251c\u2500\u2500 \u6b27\u62c9\u51fd\u6570(n: int) -> int\r\n        \u251c\u2500\u2500 \u6b63\u5207(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u6b63\u5272(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u6b63\u5f26(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u6d6e\u70b9\u6570\u8f6c\u5206\u6570(\u6570\u503c: float, \u662f\u5426\u5e26\u5206\u6570: bool, \u8bef\u5dee: float) -> tuple\r\n        \u251c\u2500\u2500 \u76f8\u5173\u7cfb\u6570(x: typing.List[float], y: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u79ef\u5206(\u51fd\u6570: Any, \u79ef\u5206\u5f00\u59cb: float, \u79ef\u5206\u7ed3\u675f: float, \u79ef\u5206\u70b9\u6570: int, \u989d\u5916\u53c2\u6570: Any, \u989d\u5916\u5173\u952e\u5b57\u53c2\u6570: Any) -> float\r\n        \u251c\u2500\u2500 \u79ef\u7d2f\u4e58\u79ef(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u7b26\u53f7\u51fd\u6570(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u7c7b\u4f3c\u5f62\u72b6\u5168\u4e00(\u6570\u7ec4A: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u7c7b\u4f3c\u5f62\u72b6\u5168\u96f6(\u6570\u7ec4A: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u7c7b\u4f3c\u5f62\u72b6\u586b\u5145(\u6570\u7ec4A: Any, \u586b\u5145\u503c: Any, \u8fd4\u56de\u7c7b\u578b: Any) -> Any\r\n        \u251c\u2500\u2500 \u7d2f\u4e58\u79ef(\u5e8f\u5217: typing.List[float]) -> typing.List[float]\r\n        \u251c\u2500\u2500 \u7d2f\u52a0\u548c(\u5e8f\u5217: typing.List[float]) -> typing.List[float]\r\n        \u251c\u2500\u2500 \u7ebf\u6027\u65b9\u7a0b\u7ec4(\u5de6\u8fb9: list, \u53f3\u8fb9: list) -> list\r\n        \u251c\u2500\u2500 \u7ec4\u5408\u6570(\u603b\u6570: int, \u9009\u53d6\u6570: int) -> int\r\n        \u251c\u2500\u2500 \u7ef4\u5409\u5c3c\u4e9a\u5bc6\u7801(\u6587\u672c: str, \u5bc6\u94a5: str, \u89e3\u5bc6: bool) -> str\r\n        \u251c\u2500\u2500 \u7f57\u9a6c\u6570\u8f6c\u6574\u6570(\u7f57\u9a6c\u6570: str) -> int\r\n        \u251c\u2500\u2500 \u81ea\u7136\u5bf9\u6570(\u771f\u6570: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u81ea\u7136\u6307\u6570(\u6307\u6570: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u83ab\u5c14\u65af\u5bc6\u7801(\u6587\u672c: str, \u89e3\u5bc6: bool) -> str\r\n        \u251c\u2500\u2500 \u89e3\u6790\u6d6e\u70b9\u6570\u5b57\u7b26\u4e32(\u5b57\u7b26\u4e32: str) -> tuple\r\n        \u251c\u2500\u2500 \u8bef\u5dee\u51fd\u6570(x: typing.Union[int, float]) -> typing.Union[int, float]\r\n        \u251c\u2500\u2500 \u8bfb\u53d6(\u6587\u4ef6: str) -> list\r\n        \u251c\u2500\u2500 \u8c03\u548c\u5e73\u5747\u6570(\u6570\u636e: typing.List[float]) -> float\r\n        \u251c\u2500\u2500 \u8d1d\u5854\u51fd\u6570(p: float, q: float) -> float\r\n        \u251c\u2500\u2500 \u8d1d\u585e\u5c14\u51fd\u6570I0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u8d1d\u585e\u5c14\u51fd\u6570I1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u8d1d\u585e\u5c14\u51fd\u6570Iv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u8d1d\u585e\u5c14\u51fd\u6570J0(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u8d1d\u585e\u5c14\u51fd\u6570J1(x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u8d1d\u585e\u5c14\u51fd\u6570Jv(v: typing.Union[int, float], x: typing.Union[int, float, complex]) -> typing.Union[int, float, complex]\r\n        \u251c\u2500\u2500 \u8d1f\u4e00\u6574\u6570\u6b21\u5e42(\u6307\u6570: int) -> int\r\n        \u251c\u2500\u2500 \u8f6c\u4e3a\u591a\u7cbe\u5ea6\u590d\u6570(\u5b9e\u90e8: typing.Union[int, float, str, decimal.Decimal, complex, pypynum.multiprec.MPComplex], \u865a\u90e8: typing.Union[int, float, str, decimal.Decimal], \u6709\u6548\u4f4d\u6570: int) -> pypynum.multiprec.MPComplex\r\n        \u251c\u2500\u2500 \u8f6c\u6362\u4e3a\u5217\u8868(\u6570\u636e: Any) -> list\r\n        \u251c\u2500\u2500 \u8f6c\u6362\u4e3a\u6570\u7ec4(\u6570\u636e: Any) -> pypynum.arrays.Array\r\n        \u251c\u2500\u2500 \u8fde\u7eed\u4e58\u79ef(\u4e0b\u754c: int, \u4e0a\u754c: int, \u51fd\u6570: typing.Callable) -> float\r\n        \u251c\u2500\u2500 \u8fde\u7eed\u52a0\u548c(\u4e0b\u754c: int, \u4e0a\u754c: int, \u51fd\u6570: typing.Callable) -> float\r\n        \u251c\u2500\u2500 \u9636\u4e58\u51fd\u6570(n: int) -> int\r\n        \u251c\u2500\u2500 \u963f\u7279\u5df4\u4ec0\u5bc6\u7801(\u6587\u672c: str) -> str\r\n        \u251c\u2500\u2500 \u9891\u7387\u7edf\u8ba1(\u6570\u636e: typing.List[typing.Any]) -> typing.Dict[typing.Any, int]\r\n        \u2514\u2500\u2500 \u9ece\u66fc\u51fd\u6570(alpha: float) -> float\r\n```\r\n\r\n### Code Testing\r\n\r\n```python\r\nfrom pypynum import (arrays, geoms, hypcmpnms, logics, matrices, multiprec, special, vectors,\r\n                     ciphers, consts, equations, maths, plotting, random, regs, tools)\r\n\r\n...\r\n\r\nprint(arrays.array())\r\nprint(arrays.array([1, 2, 3, 4, 5, 6, 7, 8]))\r\nprint(arrays.array([[1, 2, 3, 4], [5, 6, 7, 8]]))\r\nprint(arrays.array([[[1, 2], [3, 4]], [[5, 6], [7, 8]]]))\r\n\r\n\"\"\"\r\n[]\r\n[1 2 3 4 5 6 7 8]\r\n[[1 2 3 4]\r\n [5 6 7 8]]\r\n[[[1 2]\r\n  [3 4]]\r\n\r\n [[5 6]\r\n  [7 8]]]\r\n\"\"\"\r\n\r\ntriangle = geoms.Triangle((0, 0), (2, 2), (3, 0))\r\nprint(triangle.perimeter())\r\nprint(triangle.area())\r\nprint(triangle.centroid())\r\n\r\n\"\"\"\r\n8.06449510224598\r\n3.0\r\n(1.6666666666666667, 0.6666666666666666)\r\n\"\"\"\r\n\r\nq0 = hypcmpnms.quat(1, 2, 3, 4)\r\nq1 = hypcmpnms.quat(5, 6, 7, 8)\r\nprint(q0)\r\nprint(q1)\r\nprint(q0 + q1)\r\nprint(q0 * q1)\r\nprint(q0.inverse())\r\nprint(q1.conjugate())\r\n\r\n\"\"\"\r\n(1+2i+3j+4k)\r\n(5+6i+7j+8k)\r\n(6+8i+10j+12k)\r\n(-60+12i+30j+24k)\r\n(0.03333333333333333-0.06666666666666667i-0.1j-0.13333333333333333k)\r\n(5-6i-7j-8k)\r\n\"\"\"\r\n\r\na, b, c = 1, 1, 1\r\nadder0, adder1 = logics.HalfAdder(\"alpha\", a, b), logics.HalfAdder(\"beta\", c, None)\r\nxor0 = logics.XOR(\"alpha\")\r\nff0, ff1 = logics.DFF(\"alpha\"), logics.DFF(\"beta\")\r\nxor0.set_order0(1)\r\nxor0.set_order1(1)\r\nlogics.connector(adder0, adder1)\r\nlogics.connector(adder0, xor0)\r\nlogics.connector(adder1, xor0)\r\nlogics.connector(adder1, ff0)\r\nlogics.connector(xor0, ff1)\r\nprint(\"sum: {}, carry: {}\".format(ff0.out(), ff1.out()))\r\n\r\n\"\"\"\r\nsum: [1], carry: [1]\r\n\"\"\"\r\n\r\nm0 = matrices.mat([[1, 2], [3, 4]])\r\nm1 = matrices.mat([[5, 6], [7, 8]])\r\nprint(m0)\r\nprint(m1)\r\nprint(m0 + m1)\r\nprint(m0 @ m1)\r\nprint(m0.inv())\r\nprint(m1.rank())\r\n\r\n\"\"\"\r\n[[1 2]\r\n [3 4]]\r\n[[5 6]\r\n [7 8]]\r\n[[ 6  8]\r\n [10 12]]\r\n[[19 22]\r\n [43 50]]\r\n[[ -1.9999999999999996   0.9999999999999998]\r\n [  1.4999999999999998 -0.49999999999999994]]\r\n2\r\n\"\"\"\r\n\r\nmp_complex1 = multiprec.MPComplex(\"1.4142135623730950488016887242096980785696718753769\",\r\n                                  \"2.7182818284590452353602874713527\", sigfigs=30)\r\nmp_complex2 = multiprec.MPComplex(\"1.7320508075688772935274463415059\",\r\n                                  \"3.141592653589793238462643383279502884197169399375105820974944\", sigfigs=40)\r\nmodulus = mp_complex1.modulus(sigfigs=25)\r\nprint(\"Modulus of the complex1:\", modulus)\r\nsqrt_complex = mp_complex2.sqrt()\r\nprint(\"Square root of the complex2:\", sqrt_complex)\r\npower_result = mp_complex1 ** mp_complex2\r\nprint(\"Power of complex1 raised to complex2:\", power_result)\r\neuler_gamma = multiprec.mp_euler_gamma(sigfigs=45)\r\nprint(\"Value of Euler's gamma constant:\", euler_gamma)\r\nlog_2 = multiprec.mp_log(2, 10, sigfigs=50)\r\nprint(\"Logarithm of 2 (base 10):\", log_2)\r\nexp_e_squared = multiprec.mp_exp(multiprec.mp_e() ** 2, sigfigs=20)\r\nprint(\"Value of exp(e^2):\", exp_e_squared)\r\n\r\n\"\"\"\r\nModulus of the complex1: 3.064156670102011971734464\r\nSquare root of the complex2: 1.630869996965458756791024890326755654659+0.9631646481434200567938527724670041364524i\r\nPower of complex1 raised to complex2: 0.144632311554759549910373681031-0.17337039786352194417298867399i\r\nValue of Euler's gamma constant: 0.577215664901532860606512090082402431042159336\r\nLogarithm of 2 (base 10): 0.30102999566398119521373889472449302676818988146211\r\nValue of exp(e^2): 1618.1779919126535017\r\n\"\"\"\r\n\r\nprint(\"Bessel Function of the first kind, order 0 at x=1:\", special.besselj0(1))\r\nprint(\"Modified Bessel function of the first kind, order 1 at x=1:\", special.besseli1(1))\r\nprint(\"Hypergeometric function 0F1 at z=0.5 with b0=1:\", special.hyp0f1(1, 0.5))\r\nprint(\"Hypergeometric function 1F1 at z=1 with a0=1, b0=1:\", special.hyp1f1(1, 1, 1))\r\nprint(\"q-Pochhammer Symbol with a=2+1j, q=0.5+0.1j, n=2+1j:\", special.qpochhammer(2 + 1j, 0.5 + 0.1j, 2 + 1j))\r\nprint(\"q-Gamma Function at n=2 with q=0.5+0.1j:\", special.qgamma(2, 0.5 + 0.1j))\r\n\r\n\"\"\"\r\nBessel Function of the first kind, order 0 at x=1: 0.7651976865579666\r\nModified Bessel function of the first kind, order 1 at x=1: 0.565159103992485\r\nHypergeometric function 0F1 at z=0.5 with b0=1: 1.5660829297563503\r\nHypergeometric function 1F1 at z=1 with a0=1, b0=1: 2.7182818284590455\r\nq-Pochhammer Symbol with a=2+1j, q=0.5+0.1j, n=2+1j: (-0.33353429405776575+1.8573191887407854j)\r\nq-Gamma Function at n=2 with q=0.5+0.1j: (0.9999999999999989-4.953510875709033e-16j)\r\n\"\"\"\r\n\r\nstring = \"PyPyNum\"\r\nencrypted = ciphers.caesar(string, 10)\r\nprint(string)\r\nprint(encrypted)\r\nprint(ciphers.caesar(encrypted, 10, decrypt=True))\r\nencrypted = ciphers.vigenere(string, \"ciphers\")\r\nprint(string)\r\nprint(encrypted)\r\nprint(ciphers.vigenere(encrypted, \"ciphers\", decrypt=True))\r\nencrypted = ciphers.morse(string)\r\nprint(string)\r\nprint(encrypted)\r\nprint(ciphers.morse(encrypted, decrypt=True))\r\n\r\n\"\"\"\r\nPyPyNum\r\nZiZiXew\r\nPyPyNum\r\nPyPyNum\r\nRgEfRle\r\nPyPyNum\r\nPyPyNum\r\n.--. -.-- .--. -.-- -. ..- --\r\nPYPYNUM\r\n\"\"\"\r\n\r\nv0 = vectors.vec([1, 2, 3, 4])\r\nv1 = vectors.vec([5, 6, 7, 8])\r\nprint(v0)\r\nprint(v1)\r\nprint(v0 + v1)\r\nprint(v0 @ v1)\r\nprint(v0.normalize())\r\nprint(v1.angles())\r\n\r\n\"\"\"\r\n[1 2 3 4]\r\n[5 6 7 8]\r\n[ 5 12 21 32]\r\n70\r\n[0.18257418583505536  0.3651483716701107  0.5477225575051661  0.7302967433402214]\r\n[1.1820279130506308, 1.0985826410133916, 1.0114070854293842, 0.9191723423169716]\r\n\"\"\"\r\n\r\nprint(consts.TB)\r\nprint(consts.e)\r\nprint(consts.h)\r\nprint(consts.phi)\r\nprint(consts.pi)\r\nprint(consts.tera)\r\n\r\n\"\"\"\r\n1099511627776\r\n2.718281828459045\r\n6.62607015e-34\r\n1.618033988749895\r\n3.141592653589793\r\n1000000000000\r\n\"\"\"\r\n\r\np = [1, -2, -3, 4]\r\nm = [\r\n    [\r\n        [1, 2, 3],\r\n        [6, 10, 12],\r\n        [7, 16, 9]\r\n    ],\r\n    [-1, -2, -3]\r\n]\r\nprint(equations.poly_eq(p))\r\nprint(equations.lin_eq(*m))\r\n\r\n\"\"\"\r\n[(-1.5615528128088307-6.5209667308287455e-24j), (1.0000000000000007+3.241554513744382e-25j), (2.5615528128088294+4.456233626665941e-24j)]\r\n[1.6666666666666665, -0.6666666666666666, -0.4444444444444444]\r\n\"\"\"\r\n\r\nprint(maths.cot(consts.pi / 3))\r\nprint(maths.gamma(1.5))\r\nprint(maths.pi(1, 10, lambda x: x ** 2))\r\nprint(maths.product([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))\r\nprint(maths.sigma(1, 10, lambda x: x ** 2))\r\nprint(maths.var([2, 3, 5, 7, 11, 13, 17, 19, 23, 29]))\r\n\r\n\"\"\"\r\n0.577350269189626\r\n0.886226925452758\r\n13168189440000\r\n6469693230\r\n385\r\n73.29\r\n\"\"\"\r\n\r\nplt = plotting.unary(lambda x: x ** 2, top=10, bottom=0, character=\"+\")\r\nprint(plt)\r\nprint(plotting.binary(lambda x, y: x ** 2 + y ** 2 - 10, right=10, left=0, compare=\"<=\", basic=plotting.change(plt)))\r\nprint(plotting.c_unary(lambda x: x ** x, right=2, left=-2, top=2, bottom=-2, complexity=20, character=\"-\"))\r\n\r\n\"\"\"\r\n  1.00e+01|         +                               +         \r\n          |                                                   \r\n          |          +                             +          \r\n          |                                                   \r\n          |           +                           +           \r\n          |            +                         +            \r\n          |                                                   \r\n          |             +                       +             \r\n  5.00e+00|_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _\r\n          |              +                     +              \r\n          |               +                   +               \r\n          |                +                 +                \r\n          |                 +               +                 \r\n          |                  +             +                  \r\n          |                   +           +                   \r\n          |                    +         +                    \r\n          |                     +++   +++                     \r\n  0.00e+00|________________________+++________________________\r\n           -5.00e+00             0.00e+00             5.00e+00\r\n  1.00e+01|         +                               +         \r\n          |                                                   \r\n          |          +                             +          \r\n          |                                                   \r\n          |.........  +                           +           \r\n          |.............                         +            \r\n          |..............                                     \r\n          |................                     +             \r\n  5.00e+00|................_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _\r\n          |................                    +              \r\n          |................                   +               \r\n          |..............  +                 +                \r\n          |.............    +               +                 \r\n          |.........         +             +                  \r\n          |                   +           +                   \r\n          |                    +         +                    \r\n          |                     +++   +++                     \r\n  0.00e+00|________________________+++________________________\r\n           -5.00e+00             0.00e+00             5.00e+00\r\n  2.00e+00|           -                 -           -          -          -            -    \r\n          |               -  -            -          -         -         -           -      \r\n          |                     -           -         -        -        -          -        \r\n          |-                       -          -       -       -        -         -          \r\n          |     -   -                - -       --      -      -       -        -            \r\n          |            -  -              -       -      -     -      -       -             -\r\n          |                  -  - -       - --  - ---  -- -  --     -     - -         - -   \r\n          |                         - -   -  --    --    -   -  - --     -       - -        \r\n          |  -   -  - - -  -          - -- -   ---  ---  -   -   ---   --     - -           \r\n          |             -    -  - - - --    ----- -- -- --- --  --  ---    --           -  -\r\n          |               - -      -     ------------ ----  - --  -- - ---       - - -      \r\n          |    -  -  -  - -  ----- - -- ----------------------- -- ----  - -- --            \r\n          |   -  -   - -         - ---- ---------------------------------      - - - - -  - \r\n  0.00e+00|_ _ _ _ _ _ _ _-_-_-_-_---- ------------------------------------_-- _ _ _ _ _ _ _\r\n          |            -  -   - - ----------------------------------------- -- - - - -      \r\n          |   -  --  -  -       -- -  -  --------------------------------- -           -  - \r\n          |    -          - ---- - - -- --------------------- ----- ----    - -- -          \r\n          |               -         - -- --------- -- -- -  -----  ---  -- -       - -  -   \r\n          |             -  - -  - - - -    ---- --- --- --- --  --  ---     - -            -\r\n          |  -   -  - -               - --     --   --   -   -    --   --       --          \r\n          |                       - -     -  --    -    --   -- -  -     --        -  -     \r\n          |                  -  -         - -   - - -  -- -   -     --      -           -   \r\n          |            -  -            - -      --     --     -      -       - -           -\r\n          |     -   -                -         -       -      -       -          -          \r\n          |-                    -  -          -       -        -       -           -        \r\n          |                  -              -         -        -        -            -      \r\n          |               -               -          -         -         -                  \r\n -2.00e+00|___________-_________________-___________-_____________________-____________-____\r\n           -2.00e+00                            0.00e+00                            2.00e+00\r\n\"\"\"\r\n\r\nprint(random.gauss(0, 1, [2, 3, 4]))\r\nprint(random.rand([2, 3, 4]))\r\nprint(random.randint(0, 9, [2, 3, 4]))\r\nprint(random.uniform(0, 9, [2, 3, 4]))\r\n\r\n\"\"\"\r\n[[[0.19564108603837504, 1.01920370166293, -0.0432622197313817, 1.8767392228517594], [-0.9372140720220945, 0.6455939848661518, 0.06219926062283103, -0.03646501719525719], [-0.6575861228704779, -1.627831653990843, 1.4669927522358261, -2.1082184047042944]], [[-0.4550416369776341, 0.5921202822490813, 0.1393176939653395, -0.1994214479986489], [-0.559257919413219, -1.629764620332396, 0.04658277611512766, 0.20529751771180757], [0.492656546311569, 0.9731757491363898, -0.3281597719355017, -0.6855996837842998]]]\r\n[[[0.9897608447208633, 0.9091539554606014, 0.839742901348473, 0.7483640950392159], [0.1271954637618754, 0.23914774960655272, 0.6603167703557995, 0.09706202212722614], [0.1020987366479954, 0.16628877700140854, 0.9844464087410161, 0.8213963537473721]], [[0.268434775377716, 0.8021623176316018, 0.48319517625501174, 0.30410149780944096], [0.8970313978138931, 0.9980790184879383, 0.1185467392465952, 0.19570961919567464], [0.08626090792820118, 0.5790211560246683, 0.7475290741004703, 0.8048613204213184]]]\r\n[[[9, 0, 7, 5], [2, 7, 3, 5], [7, 6, 4, 2]], [[3, 4, 2, 0], [4, 2, 2, 1], [4, 5, 4, 9]]]\r\n[[[8.067902792666303, 3.1398970785364244, 7.875028237778611, 7.766921948037462], [3.337337214716076, 2.852783099370506, 1.028257336777862, 7.822605535085232], [7.111199916783942, 5.890725764603359, 3.038605829888671, 6.272148674191553]], [[1.076715403659712, 6.806086377982102, 5.699002266942416, 1.1654651363361368], [1.3920577362733448, 8.527352563852686, 2.359964996027981, 5.183071574749471], [7.8250627862940725, 1.6259461468536924, 8.333173856724002, 5.068032713313034]]]\r\n\"\"\"\r\n\r\nprint(regs.lin_reg(list(range(5)), [2, 4, 6, 7, 8]))\r\nprint(regs.par_reg(list(range(5)), [2, 4, 6, 7, 8]))\r\nprint(regs.poly_reg(list(range(5)), [2, 4, 6, 7, 8], 4))\r\n\r\n\"\"\"\r\n[1.5, 2.4000000000000004]\r\n[-0.21428571428571563, 2.3571428571428625, 1.971428571428569]\r\n[0.08333333333320592, -0.666666666666571, 1.4166666666628345, 1.1666666666688208, 1.9999999999999258]\r\n\"\"\"\r\n\r\nprint(tools.classify([1, 2.3, 4 + 5j, \"string\", list, True, 3.14, False, tuple, tools]))\r\nprint(tools.dedup([\"Python\", 6, \"NumPy\", int, \"PyPyNum\", 9, \"pypynum\", \"NumPy\", 6, True]))\r\nprint(tools.frange(0, 3, 0.4))\r\nprint(tools.linspace(0, 2.8, 8))\r\n\r\n\"\"\"\r\n{<class 'int'>: [1], <class 'float'>: [2.3, 3.14], <class 'complex'>: [(4+5j)], <class 'str'>: ['string'], <class 'type'>: [<class 'list'>, <class 'tuple'>], <class 'bool'>: [True, False], <class 'module'>: [<module 'pypynum.tools' from 'C:\\\\Users\\\\Administrator\\\\PycharmProjects\\\\pythonProject\\\\pypynum\\\\tools.py'>]}\r\n['Python', 6, 'NumPy', <class 'int'>, 'PyPyNum', 9, 'pypynum', True]\r\n[0.0, 0.4, 0.8, 1.2000000000000002, 1.6, 2.0, 2.4000000000000004, 2.8000000000000003, 3.2]\r\n[0.0, 0.39999999999999997, 0.7999999999999999, 1.2, 1.5999999999999999, 1.9999999999999998, 2.4, 2.8]\r\n\"\"\"\r\n\r\n# Tip:\r\n# The test has been successfully passed and ended.\r\n# These tests are only part of the functionality of this package.\r\n# More features need to be explored and tried by yourself!\r\n```\r\n",
    "bugtrack_url": null,
    "license": "GNU AFFERO GENERAL PUBLIC LICENSE Version 3, 19 November 2007  Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/> Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.  Preamble  The GNU Affero General Public License is a free, copyleft license for software and other kinds of works, specifically designed to ensure cooperation with the community in the case of network server software.  The licenses for most software and other practical works are designed to take away your freedom to share and change the works.  By contrast, our General Public Licenses are intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users.  When we speak of free software, we are referring to freedom, not price.  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