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- """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
- >>> 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]))
- >>> B.represent(a2)
- Traceback (most recent call last):
- ...
- 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',
- ]
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