With singular 4 on sage I have now:
sage: P.<a,b,c> = PolynomialRing(QQ,3, order='lex')
sage: toto=ideal([7*a - 420*c^3 + 158*c^2 + 8*c - 7, 7*b + 210*c^3 - 79*c^2
+ 3*c, 84*c^4 - 40*c^3 + c^2 + c])
sage: toto.interreduced_basis?
sage: g=toto.interreduced_basis()
sage: g[0].lc()
7
sage: toto.base_ring()
Rational Field
sage: g
[7*a - 420*c^3 + 158*c^2 + 8*c - 7, 7*b + 210*c^3 - 79*c^2 + 3*c, 84*c^4 -
40*c^3 + c^2 + c]
while with singular 3 I had:
[a - 60*c^3 + 158/7*c^2 + 8/7*c - 1, b + 30*c^3 - 79/7*c^2 + 3/7*c, c^4 -
10/21*c^3 + 1/84*c^2 + 1/84*c]
moreover the doc says:
If this ideal is spanned by (f_1, ..., f_n) this method returns
(g_1, ..., g_s) such that:
* (f_1,...,f_n) = (g_1,...,g_s)
* LT(g_i) != LT(g_j) for all i != j
* LT(g_i) does not divide m for all monomials m of
{g_1,...,g_{i-1},g_{i+1},...,g_s}
* LC(g_i) == 1 for all i if the coefficient ring is a field.
Am I missing something? (I need to know if I should change my doctest
output or not in #21884)
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