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.
- Solves the conjugacy problem for periodic 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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