7^(h:RdZGddeZGddeZGddeZgdZy) z,Special exception classes for numberfields. ceZdZdZy)ClosureFailureaG 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. N__name__ __module__ __qualname____doc__a/var/www/skyplay_api_hub/venv/lib/python3.12/site-packages/sympy/polys/numberfields/exceptions.pyrrs > r rceZdZdZy)StructureErrorz Represents cases in which an algebraic structure was expected to have a certain property, or be of a certain type, but was not. Nrr r r r r 's  r r ceZdZdZy)MissingUnityErrorz6Structure should contain a unity element but does not.Nrr r r rr/sAr r)rr rN)r Exceptionrr r__all__r r r rs42  Y  F Y    r