Eigenvalues of morphic subshifts
Project description
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]
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