# Python quartic equation solver for exact values
A Python module for the exact solutions of a quartic equation: a x^4 + b x^3 + c x^2 + d x + e = 0
## Usage
### Calculate quartic solution
The solutions are four symexpress3 objects: x1Optimized, x2Optimized, x3Optimized, x4Optimized
```py
>>> import quarticequation
>>> objQuartic = quarticequation.QuarticEquation()
>>> objQuartic.a = "1"
>>> objQuartic.b = "2"
>>> objQuartic.c = "3"
>>> objQuartic.d = "4"
>>> objQuartic.e = "5"
>>> objQuartic.calcSolutions()
>>> print( f"x1: {objQuartic.x1Optimized}\nx2: {objQuartic.x2Optimized}\nx3: {objQuartic.x3Optimized}\nx3: {objQuartic.x4Optimized}\n" )
x1: (-1/2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) * (-1/2) + (1/2) * ((-2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) * 4 + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2)
x2: (-1/2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) * (-1/2) + ((-2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) * 4 + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2) * (-1/2)
x3: (-1/2) + (1/2) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) + (1/2) * ((-2) + (-4) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2)
x4: (-1/2) + (1/2) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) + ((-2) + (-4) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2) * (-1/2)```
```
### Numeric input values
The parameters may be real numbers or symexpress3 strings
```py
>>> import quarticequation
>>> objQuartic = quarticequation.QuarticEquation()
>>> objQuartic.a = 1.0
>>> objQuartic.b = -28
>>> objQuartic.c = "200 + 66"
>>> objQuartic.d = "-1028"
>>> objQuartic.e = "2730 / 2"
>>> objQuartic.calcSolutions()
>>> print( f"x1: {objQuartic.x1Optimized}\nx2: {objQuartic.x2Optimized}\nx3: {objQuartic.x3Optimized}\nx3: {objQuartic.x4Optimized}\n" )
x1: 5
x2: 3
x3: 13
x4: 7
```
### Calculate real values
```py
>>> import quarticequation
>>> objQuartic = quarticequation.QuarticEquation()
>>> objQuartic.a = 1
>>> objQuartic.b = 2
>>> objQuartic.c = 3
>>> objQuartic.d = 4
>>> objQuartic.e = 5
>>> objQuartic.calcSolutions()
>>> print( f"x1: {objQuartic.x1Value}\nx2: {objQuartic.x2Value}\nx3: {objQuartic.x3Value}\nx4: {objQuartic.x4Value}\n" )
x1: (-1.287815479557648+0.8578967583284903j)
x2: (-1.287815479557648-0.8578967583284903j)
x3: (0.2878154795576482+1.4160930801719078j)
x4: (0.28781547955764797-1.4160930801719078j)
```
### Command line
python -m quarticequation
- *Help*: python -m quarticequation -h
- *Quartic solution*: python -m quarticequation 1 2 3 4 5
### Graphical user interface
https://github.com/SWVandenEnden/websym3
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"description": "# Python quartic equation solver for exact values\n\nA Python module for the exact solutions of a quartic equation: a x^4 + b x^3 + c x^2 + d x + e = 0\n\n## Usage\n\n### Calculate quartic solution\nThe solutions are four symexpress3 objects: x1Optimized, x2Optimized, x3Optimized, x4Optimized\n```py\n>>> import quarticequation\n>>> objQuartic = quarticequation.QuarticEquation()\n>>> objQuartic.a = \"1\"\n>>> objQuartic.b = \"2\"\n>>> objQuartic.c = \"3\"\n>>> objQuartic.d = \"4\"\n>>> objQuartic.e = \"5\"\n>>> objQuartic.calcSolutions()\n>>> print( f\"x1: {objQuartic.x1Optimized}\\nx2: {objQuartic.x2Optimized}\\nx3: {objQuartic.x3Optimized}\\nx3: {objQuartic.x4Optimized}\\n\" )\nx1: (-1/2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) * (-1/2) + (1/2) * ((-2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) * 4 + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2)\nx2: (-1/2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) * (-1/2) + ((-2) + ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) * 4 + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2) * (-1/2)\nx3: (-1/2) + (1/2) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) + (1/2) * ((-2) + (-4) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2)\nx4: (-1/2) + (1/2) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(1/2) + ((-2) + (-4) * ((-1) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ) * (-1))^^(-1/2) + cos( (1/3) * atan( (1/2) ) ) * 15^^(1/2) * (-1) + 5^^(1/2) * sin( (1/3) * atan( (1/2) ) ))^^(1/2) * (-1/2)```\n```\n\n### Numeric input values\nThe parameters may be real numbers or symexpress3 strings\n```py\n>>> import quarticequation\n>>> objQuartic = quarticequation.QuarticEquation()\n>>> objQuartic.a = 1.0\n>>> objQuartic.b = -28\n>>> objQuartic.c = \"200 + 66\"\n>>> objQuartic.d = \"-1028\"\n>>> objQuartic.e = \"2730 / 2\"\n>>> objQuartic.calcSolutions()\n>>> print( f\"x1: {objQuartic.x1Optimized}\\nx2: {objQuartic.x2Optimized}\\nx3: {objQuartic.x3Optimized}\\nx3: {objQuartic.x4Optimized}\\n\" )\nx1: 5\nx2: 3\nx3: 13\nx4: 7\n```\n\n### Calculate real values\n```py\n>>> import quarticequation\n>>> objQuartic = quarticequation.QuarticEquation()\n>>> objQuartic.a = 1\n>>> objQuartic.b = 2\n>>> objQuartic.c = 3\n>>> objQuartic.d = 4\n>>> objQuartic.e = 5\n>>> objQuartic.calcSolutions()\n>>> print( f\"x1: {objQuartic.x1Value}\\nx2: {objQuartic.x2Value}\\nx3: {objQuartic.x3Value}\\nx4: {objQuartic.x4Value}\\n\" )\nx1: (-1.287815479557648+0.8578967583284903j)\nx2: (-1.287815479557648-0.8578967583284903j)\nx3: (0.2878154795576482+1.4160930801719078j)\nx4: (0.28781547955764797-1.4160930801719078j)\n```\n\n\n### Command line\npython -m quarticequation\n\n- *Help*: python -m quarticequation -h\n- *Quartic solution*: python -m quarticequation 1 2 3 4 5\n\n### Graphical user interface\nhttps://github.com/SWVandenEnden/websym3\n",
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