def change_base_module(self, other_base):
"""
change base_module to other_base_module
(i.e. represent with respect to base_module)
"""
if self.base == other_base:
return self
n = self.number_field.degree
if isinstance(other_base, list):
other_base = matrix.FieldSquareMatrix(n,
[vector.Vector(other_base[i]) for i in range(n)])
else: # matrix repr
other_base = other_base.copy()
tr_base_mat, tr_base_denom = _toIntegerMatrix(
other_base.inverse(self.base))
denom = tr_base_denom * self.denominator
mat_repr, numer = _toIntegerMatrix(
tr_base_mat * self.mat_repr, 2)
d = gcd.gcd(denom, numer)
if d != 1:
denom = ring.exact_division(denom, d)
numer = ring.exact_division(numer, d)
if numer != 1:
mat_repr = numer * mat_repr
return self.__class__([mat_repr, denom], self.number_field, other_base)
def __init__(self, pair_mat_repr, number_field, base=None, ishnf=False):
"""
pair_mat_repr: generators represented with respect to base_module
1: [[deg(number_field))-integral tuple/vector], denominator]
2: [integral matrix whose the number of row is deg(number_field),
denominator]
3: rational matrix whose the number of row is deg(number_field)
number_field: an instance of NumberField
base: a base module represented with respect to Z[theta]
1: [deg(number_field)-rational tuple/vector], which represents basis
2: deg(number_field)-square non-singular rational matrix
ishnf: if hnf_repr is already HNF-form, set True
"""
self.number_field = number_field
size = self.number_field.degree
if isinstance(base, bool):
ishnf = base
base = None
if base == None: # power basis
self.base = matrix.unitMatrix(size, rational.theIntegerRing)
self.base.toFieldMatrix()
elif isinstance(base, list): # list repr
self.base = matrix.FieldSquareMatrix(size, base)
else: # matrix repr
if base.row != size:
raise TypeError("The number of row of base is incorrect.")
self.base = base.copy()
self.base.toFieldMatrix()
if not isinstance(pair_mat_repr, list): #rational matrix repr
self.mat_repr, self.denominator = _toIntegerMatrix(
pair_mat_repr)
else:
self.denominator = pair_mat_repr[1]
if isinstance(pair_mat_repr[0], list): # list repr
column = len(pair_mat_repr[0])
self.mat_repr = Submodule(
size, column, pair_mat_repr[0], ishnf)
else: # integral matrix repr
self.mat_repr = Submodule.fromMatrix(
pair_mat_repr[0].copy(), ishnf)