def is_rep(self, image, n, force=False):
"""
Returns `True` if the map generated by mapping the generators to the matrices defined in
`image` is an `n`-dimensional representation of `self`, and `False` otherwise. The entries
of `image` must be `n`-by-`n` matrices with entries in the algebraic closure of the base
field of `self`. Its length must match the number of generators of `self.`
Use `force=True` if the function does not recognize the base field as computable, but the
field is computable.
"""
if (not force and self.base_field() not in NumberFields
and self.base_field() not in FiniteFields):
raise TypeError('Base field must be computable. If %s is' %
self.base_field() +
' computable then use force=True to bypass this.')
if n not in ZZ or n < 1:
raise ValueError('Dimension must be a positive integer.')
M = MatrixSpace(self.base_field().algebraic_closure(), n, sparse=True)
if len(image) != self.ngens():
raise ValueError(
'Length of image does not match number of generators.')
if False in {mat in M for mat in image}:
raise TypeError('Improper image, must contain elements of %s.' %
M._repr_())
image = [M(image[i]) for i in range(len(image))]
for rel in self.rels():
if self._to_matrix(rel, M, image) != M.zero(): return False
return True
