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isElement -- test whether a ring element lies in a monomial ideal

Usage:

isElement(f, I)
Inputs:
- f, a ring element,
- I, a monomial ideal,
Outputs:
- a Boolean value, whether f lies in I

Description

An element of a polynomial ring lies in a monomial ideal if and only if every one of its terms is divisible by some minimal generator of the ideal.

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = monomialIdeal(x*y, x^3*z)

                          3
o2 = monomialIdeal (x*y, x z)

o2 : MonomialIdeal of R

i3 : isElement(x^2*y + x*y*z + x^3*z^3, I)

o3 = true

i4 : isElement(x*y^2 + x^3*y*z + z^2, I)

o4 = false

See also

isStable -- test whether a monomial ideal is stable
isSQStable -- test whether a squarefree monomial ideal is squarefree stable

Ways to use isElement:

isElement(RingElement,MonomialIdeal)

For the programmer

The object isElement is a method function.

The source of this document is in ChainComplexExtras.m2:1941:0.