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check coprimality of moduli in CRT_basis() #36457

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Dec 6, 2023
Merged

check coprimality of moduli in CRT_basis() #36457

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13 changes: 8 additions & 5 deletions src/sage/arith/misc.py
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Original file line number Diff line number Diff line change
Expand Up @@ -3584,10 +3584,6 @@ def CRT_basis(moduli):
`a_i` is congruent to 1 modulo `m_i` and to 0 modulo `m_j` for
`j\not=i`.

.. note::

The pairwise coprimality of the input is not checked.

EXAMPLES::

sage: a1 = ZZ(mod(42,5))
Expand All @@ -3610,7 +3606,14 @@ def CRT_basis(moduli):
if n == 0:
return []
M = prod(moduli)
return [((xgcd(m,M//m)[2])*(M//m)) % M for m in moduli]
cs = []
for m in moduli:
Mm = M // m
d, _, v = xgcd(m, Mm)
if not d.is_one():
raise ValueError('moduli must be coprime')
cs.append((v * Mm) % M)
return cs


def CRT_vectors(X, moduli):
Expand Down