For calculations in the curve complex
Curver is a program for performing calculations in the curve complex. It implements the Bell–Webb algorithm to determine the Nielsen–Thurston type of a mapping class. This algorithm runs in polynomial time but the constants involved currently make this implementation impractical.
A taste of curver:
>>> S = curver.load(0, 5) >>> S('s_0.s_1.s_0') == S('s_1.s_0.s_1') True >>> S('s_0.s_1.s_2.s_3').order(), S('s_0.s_1.s_3.s_2').order(), S('s_0.s_1.S_2.S_3').order() (5, 5, 5) >>> S('s_0.s_1.s_2.s_3').is_conjugate_to(S('s_0.s_1.s_3.s_2')) True >>> S('s_0.s_1.s_2.s_3').is_conjugate_to(S('s_0.s_1.S_2.S_3')) False
Solves the word problem for mapping class groups.
Performs Nielsen–Thurston classification of mapping classes.
Computes the asymptotic translation length of mapping classes on the curve complex.
Computes geodesics in the curve complex.
Computes quotient orbifolds and their quotient maps.
Computes the action of mapping classes on H_1.
Determines the topological type of multicurves.
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