eigenmorphic 0.1.4

Eigenvalues of morphic subshifts

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]