gh-36457: check coprimality of moduli in CRT_basis()

    
The `xgcd()` calls used in this function to compute modular inverses
already compute the greatest common divisor as a byproduct, so we might
as well add the cheap `.is_one()` check. Benchmarking reveals no
measurable timing difference between the two versions.
    
URL: #36457
Reported by: Lorenz Panny
Reviewer(s): Kwankyu Lee

src/sage/arith/misc.py

@@ -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))
@@ -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):