6.31.3 Testing if a polynomial or list of polynomials belongs to an ideal given by a Gröbner basis: in_ideal
The in_ideal command determines whether or not a polynomial
is in an ideal.
in_ideal takes three mandatory arguments and one
optional argument:
P, a polynomial or a list of polynomials.
gbasis, a list giving a Gröbner basis.
vars, the list of polynomial variables.
If gbasis is computed with a different order from the
default, then vars must use the same order.
Optionally, an optional argument from gbasic (see
Section 6.31.1), such as plex or tdeg. By
default it will be plex.
in_ideal(P,gbasis,vars ⟨, option
⟩)
returns the value true (1) or false (0), or a list
of trues and falses, indicating whether or not the
polynomial(s) in P are in the ideal generated by
gbasis using the variables in vars.