11.5.3  Testing if a (list of) polynomial(s) belongs to an ideal given by a Gröbner basis

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 11.5.1), 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.

Examples