def relation_matrix_wtk_g0(syms, sign, field, sparse):
r"""
Compute the matrix of relations. Despite the name, this is used for all
spaces (not just for Gamma0). For a description of the algorithm, see the
docstring for ``compute_presentation``.
INPUT:
- ``syms``: sage.modular.modsym.manin_symbols.ManinSymbolList object
- ``sign``: integer (0, 1 or -1)
- ``field``: the base field (non-field base rings not supported at present)
- ``sparse``: (True or False) whether to use sparse arithmetic.
Note that ManinSymbolList objects already have a specific weight, so there
is no need for an extra ``weight`` parameter.
OUTPUT: a pair (R, mod) where
- R is a matrix as output by ``T_relation_matrix_wtk_g0``
- mod is a set of 2-term relations as output by ``sparse_2term_quotient``
EXAMPLE::
sage: L = sage.modular.modsym.manin_symbols.ManinSymbolList_gamma0(8,2)
sage: A = sage.modular.modsym.relation_matrix.relation_matrix_wtk_g0(L, 0, GF(2), True); A
(
[0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0], [(1, 1), (1, 1), (8, 1), (10, 1), (6, 1), (11, 1), (6, 1), (9, 1), (8, 1), (9, 1), (10, 1), (11, 1)]
)
sage: A[0].is_sparse()
True
"""
rels = modS_relations(syms)
if sign != 0:
# Let rels = rels union I relations.
rels.update(modI_relations(syms, sign))
if syms._apply_S_only_0pm1() and rings.is_RationalField(field):
import relation_matrix_pyx
mod = relation_matrix_pyx.sparse_2term_quotient_only_pm1(
rels, len(syms))
else:
mod = sparse_2term_quotient(rels, len(syms), field)
R = T_relation_matrix_wtk_g0(syms, mod, field, sparse)
return R, mod
def relation_matrix_wtk_g0(syms, sign, field, sparse):
r"""
Compute the matrix of relations. Despite the name, this is used for all
spaces (not just for Gamma0). For a description of the algorithm, see the
docstring for ``compute_presentation``.
INPUT:
- ``syms``: sage.modular.modsym.manin_symbols.ManinSymbolList object
- ``sign``: integer (0, 1 or -1)
- ``field``: the base field (non-field base rings not supported at present)
- ``sparse``: (True or False) whether to use sparse arithmetic.
Note that ManinSymbolList objects already have a specific weight, so there
is no need for an extra ``weight`` parameter.
OUTPUT: a pair (R, mod) where
- R is a matrix as output by ``T_relation_matrix_wtk_g0``
- mod is a set of 2-term relations as output by ``sparse_2term_quotient``
EXAMPLE::
sage: L = sage.modular.modsym.manin_symbols.ManinSymbolList_gamma0(8,2)
sage: A = sage.modular.modsym.relation_matrix.relation_matrix_wtk_g0(L, 0, GF(2), True); A
(
[0 0 0 0 0 0 0 0 1 0 0 0]
[0 0 0 0 0 0 0 0 1 1 1 0]
[0 0 0 0 0 0 1 0 0 1 1 0]
[0 0 0 0 0 0 1 0 0 0 0 0], [(1, 1), (1, 1), (8, 1), (10, 1), (6, 1), (11, 1), (6, 1), (9, 1), (8, 1), (9, 1), (10, 1), (11, 1)]
)
sage: A[0].is_sparse()
True
"""
rels = modS_relations(syms)
if sign != 0:
# Let rels = rels union I relations.
rels.update(modI_relations(syms, sign))
if syms._apply_S_only_0pm1() and rings.is_RationalField(field):
import relation_matrix_pyx
mod = relation_matrix_pyx.sparse_2term_quotient_only_pm1(rels, len(syms))
else:
mod = sparse_2term_quotient(rels, len(syms), field)
R = T_relation_matrix_wtk_g0(syms, mod, field, sparse)
return R, mod