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"Cremona modular symbols" from __future__ import absolute_import
def CremonaModularSymbols(level, sign=0, cuspidal=False, verbose=0): """ Return the space of Cremona modular symbols with given level, sign, etc.
INPUT:
- ``level`` -- an integer >= 2 (at least 2, not just positive!) - ``sign`` -- an integer either 0 (the default) or 1 or -1. - ``cuspidal`` -- (default: False); if True, compute only the cuspidal subspace - ``verbose`` -- (default: False): if True, print verbose information while creating space
EXAMPLES::
sage: M = CremonaModularSymbols(43); M Cremona Modular Symbols space of dimension 7 for Gamma_0(43) of weight 2 with sign 0 sage: M = CremonaModularSymbols(43, sign=1); M Cremona Modular Symbols space of dimension 4 for Gamma_0(43) of weight 2 with sign 1 sage: M = CremonaModularSymbols(43, cuspidal=True); M Cremona Cuspidal Modular Symbols space of dimension 6 for Gamma_0(43) of weight 2 with sign 0 sage: M = CremonaModularSymbols(43, cuspidal=True, sign=1); M Cremona Cuspidal Modular Symbols space of dimension 3 for Gamma_0(43) of weight 2 with sign 1
When run interactively, the following command will display verbose output::
sage: M = CremonaModularSymbols(43, verbose=1) After 2-term relations, ngens = 22 ngens = 22 maxnumrel = 32 relation matrix has = 704 entries... Finished 3-term relations: numrel = 16 ( maxnumrel = 32) relmat has 42 nonzero entries (density = 0.0596591) Computing kernel... time to compute kernel = (... seconds) rk = 7 Number of cusps is 2 ncusps = 2 About to compute matrix of delta delta matrix done: size 2x7. About to compute kernel of delta done Finished constructing homspace. sage: M Cremona Modular Symbols space of dimension 7 for Gamma_0(43) of weight 2 with sign 0
The input must be valid or a ValueError is raised::
sage: M = CremonaModularSymbols(-1) Traceback (most recent call last): ... ValueError: the level (= -1) must be at least 2 sage: M = CremonaModularSymbols(0) Traceback (most recent call last): ... ValueError: the level (= 0) must be at least 2
The sign can only be 0 or 1 or -1::
sage: M = CremonaModularSymbols(10, sign = -2) Traceback (most recent call last): ... ValueError: sign (= -2) is not supported; use 0, +1 or -1
We do allow -1 as a sign (see :trac:`9476`)::
sage: CremonaModularSymbols(10, sign = -1) Cremona Modular Symbols space of dimension 0 for Gamma_0(10) of weight 2 with sign -1 """ |