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