A monomial $m$ is standard with respect to a monomial ideal $M$ and a generator $g$ of $M$ if $m$ is of the same degree as $g$ but is not an element of $M$.
Inputting an ideal $M$ returns the standard monomials of each of the given generators of the ideal.
i1 : R = ZZ/32003[a..d]; |
i2 : M = ideal (a^2, a*b, b^3, a*c); o2 : Ideal of R |
i3 : L1 = standardMonomials M
2 2 2 2 2 2
o3 = {{b , b*c, c , a*d, b*d, c*d, d }, {b , b*c, c , a*d, b*d, c*d, d },
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2 2 3 2 2 2 2 2 3 2 2
{b c, b*c , c , b d, b*c*d, c d, a*d , b*d , c*d , d }, {b , b*c, c ,
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2
a*d, b*d, c*d, d }}
o3 : List
|
i4 : standardMonomials({3}, M)
2 2 3 2 2 2 2 2 3
o4 = {b c, b*c , c , b d, b*c*d, c d, a*d , b*d , c*d , d }
o4 : List
|
Inputting an integer $d$ (or degree $d$) and an ideal gives the standard monomials for the specified ideal in degree $d$.
i5 : standardMonomials(2, M)
2 2 2
o5 = {b , b*c, c , a*d, b*d, c*d, d }
o5 : List
|
The object standardMonomials is a method function.