eigenmorphic
================
Eigenvalues of morphic subshifts.
This is a Sage optional package.
It contains code to compute exact additive eigenvalues
of morphic subshifts, that is a substitution subshift or
the subshift generated by its image by another substitution.
Installation::
sage -pip install eigenmorphic
Usage::
sage: from eigenmorphic import *
After this command, you can compute eigenvalues of morphic subshifts::
sage: s = WordMorphism("a->ab,b->ac,c->a")
sage: morphic_eigenvalues(s)
Z*{1, b, b^2}
where b is root of x^3 - x^2 - x - 1
sage: t = WordMorphism('a->0,b->1,c->1')
sage: morphic_eigenvalues(s, t)
Z*{1, b, b^2}
where b is root of x^3 - x^2 - x - 1
sage: # regular paperfolding
sage: t = WordMorphism('a->00,b->01,c->10,d->11')
sage: s = WordMorphism('a->ca,b->cb,c->da,d->db')
sage: t(s.fixed_points()[0])
word: 1101100111001001110110001100100111011001...
sage: morphic_eigenvalues(s,t)
1/8Z[1/2]
Raw data
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"description": "eigenmorphic\n================\n\nEigenvalues of morphic subshifts.\n\nThis is a Sage optional package.\nIt contains code to compute exact additive eigenvalues\nof morphic subshifts, that is a substitution subshift or\nthe subshift generated by its image by another substitution.\n\nInstallation::\n\n sage -pip install eigenmorphic\n \nUsage::\n\n sage: from eigenmorphic import *\n\n\nAfter this command, you can compute eigenvalues of morphic subshifts::\n\n sage: s = WordMorphism(\"a->ab,b->ac,c->a\")\n sage: morphic_eigenvalues(s)\n Z*{1, b, b^2}\n\twhere b is root of x^3 - x^2 - x - 1\n\t\n\tsage: t = WordMorphism('a->0,b->1,c->1')\n\tsage: morphic_eigenvalues(s, t)\n\tZ*{1, b, b^2}\n\twhere b is root of x^3 - x^2 - x - 1\n\n\tsage: # regular paperfolding\n\tsage: t = WordMorphism('a->00,b->01,c->10,d->11')\n\tsage: s = WordMorphism('a->ca,b->cb,c->da,d->db')\n\tsage: t(s.fixed_points()[0])\n\tword: 1101100111001001110110001100100111011001...\n\tsage: morphic_eigenvalues(s,t)\n\t1/8Z[1/2]\n\n",
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