The in_ideal command takes three mandatory arguments and one
optional argument. The mandatory arguments are a polynomial (or list
of polynomials), a list giving a Gröbner basis, and the list of
polynomial variables. The optional fourth argument can be an optional
argument from gbasic (see section 5.32.1), such as
plex or tdeg. By default it will be plex.
If a Gröbner basis is computed with a different order from the
default, then in_ideal must use the same order.
in_basis returns the value true (1) or
false (0),
or a list of trues and falses, indicating whether or
not the polynomial(s) in the first argument are in the ideal generated
by the Gröbner basis in the second argument, using the variables
from the third argument.
Input:
Output:
Input:
Output:
Input:
Output: