54 lines
1.6 KiB
Python
54 lines
1.6 KiB
Python
|
"""Special exception classes for numberfields. """
|
||
|
|
|
||
|
|
|
||
|
|
class ClosureFailure(Exception):
|
||
|
|
r"""
|
||
|
|
Signals that a :py:class:`ModuleElement` which we tried to represent in a
|
||
|
|
certain :py:class:`Module` cannot in fact be represented there.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
========
|
||
|
|
|
||
|
|
>>> from sympy.polys import Poly, cyclotomic_poly, ZZ
|
||
|
|
>>> from sympy.polys.matrices import DomainMatrix
|
||
|
|
>>> from sympy.polys.numberfields.modules import PowerBasis, to_col, ClosureFailure
|
||
|
|
>>> from sympy.testing.pytest import raises
|
||
|
|
>>> T = Poly(cyclotomic_poly(5))
|
||
|
|
>>> A = PowerBasis(T)
|
||
|
|
>>> B = A.submodule_from_matrix(2 * DomainMatrix.eye(4, ZZ))
|
||
|
|
|
||
|
|
Because we are in a cyclotomic field, the power basis ``A`` is an integral
|
||
|
|
basis, and the submodule ``B`` is just the ideal $(2)$. Therefore ``B`` can
|
||
|
|
represent an element having all even coefficients over the power basis:
|
||
|
|
|
||
|
|
>>> a1 = A(to_col([2, 4, 6, 8]))
|
||
|
|
>>> print(B.represent(a1))
|
||
|
|
DomainMatrix([[1], [2], [3], [4]], (4, 1), ZZ)
|
||
|
|
|
||
|
|
but ``B`` cannot represent an element with an odd coefficient:
|
||
|
|
|
||
|
|
>>> a2 = A(to_col([1, 2, 2, 2]))
|
||
|
|
>>> print(raises(ClosureFailure, lambda: B.represent(a2)))
|
||
|
|
<ExceptionInfo ClosureFailure('Element in QQ-span but not ZZ-span of this basis.')>
|
||
|
|
|
||
|
|
"""
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
class StructureError(Exception):
|
||
|
|
r"""
|
||
|
|
Represents cases in which an algebraic structure was expected to have a
|
||
|
|
certain property, or be of a certain type, but was not.
|
||
|
|
"""
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
class MissingUnityError(StructureError):
|
||
|
|
r"""Structure should contain a unity element but does not."""
|
||
|
|
pass
|
||
|
|
|
||
|
|
|
||
|
|
__all__ = [
|
||
|
|
'ClosureFailure', 'StructureError', 'MissingUnityError',
|
||
|
|
]
|