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Disallow scaling of quaternion fractional ideals by zero #38963

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vbraun merged 1 commit into from
Nov 16, 2024
Merged

Disallow scaling of quaternion fractional ideals by zero #38963

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23 changes: 19 additions & 4 deletions src/sage/algebras/quatalg/quaternion_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2609,7 +2609,7 @@ def scale(self, alpha, left=False):

INPUT:

- `\alpha` -- element of quaternion algebra
- `\alpha` -- nonzero element of quaternion algebra

- ``left`` -- boolean (default: ``False``); if ``True`` multiply
`\alpha` on the left, otherwise multiply `\alpha` on the right
Expand All @@ -2632,6 +2632,15 @@ def scale(self, alpha, left=False):
sage: I.gens()[0] * i
4*i

The scaling element must be nonzero::

sage: B.<i,j,k> = QuaternionAlgebra(419)
sage: O = B.quaternion_order([1/2 + 3/2*j, 1/6*i + 2/3*j + 1/2*k, 3*j, k])
sage: O * O.zero()
Traceback (most recent call last):
...
ValueError: the scaling factor must be nonzero

TESTS:

Scaling by `1` should not change anything (see :issue:`32245`)::
Expand All @@ -2657,6 +2666,8 @@ def scale(self, alpha, left=False):
"""
Q = self.quaternion_algebra()
alpha = Q(alpha)
if alpha.is_zero():
raise ValueError("the scaling factor must be nonzero")
if left:
gens = basis_for_quaternion_lattice([alpha * b for b in self.basis()])
else:
Expand Down Expand Up @@ -3657,7 +3668,9 @@ def is_right_equivalent(self, J, B=10, certificate=False):
sage: B = QuaternionAlgebra(101)
sage: i,j,k = B.gens()
sage: I = B.maximal_order().unit_ideal()
sage: beta = B.random_element() # random
sage: beta = B.random_element()
sage: while beta.is_zero():
....: beta = B.random_element()
sage: J = beta*I
sage: bool, alpha = I.is_right_equivalent(J, certificate=True)
sage: bool
Expand Down Expand Up @@ -3711,7 +3724,9 @@ def is_principal(self, certificate=False):

sage: B.<i,j,k> = QuaternionAlgebra(419)
sage: O = B.quaternion_order([1/2 + 3/2*j, 1/6*i + 2/3*j + 1/2*k, 3*j, k])
sage: beta = O.random_element() # random
sage: beta = O.random_element()
sage: while beta.is_zero():
....: beta = O.random_element()
sage: I = O*beta
sage: bool, alpha = I.is_principal(True)
sage: bool
Expand Down Expand Up @@ -3951,7 +3966,7 @@ def primitive_decomposition(self):

Check that randomly generated ideals decompose as expected::

sage: for d in ( m for m in range(400, 750) if is_squarefree(m) ):
sage: for d in ( m for m in range(400, 750) if is_squarefree(m) ): # long time (7s)
....: A = QuaternionAlgebra(d)
....: O = A.maximal_order()
....: for _ in range(10):
Expand Down
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