switching to high quality piper tts and added label translations

2026-01-29 23:48:19 +01:00
commit d80c619df9
3934 changed files with 1451600 additions and 0 deletions
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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',
+]