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isGeneratedByIndeterminates -- checks whether the ideal is generated by indeterminates

Usage:

isGeneratedByIndeterminates I
Inputs:
- I, an ideal,
Outputs:
- a Boolean value,

Description

An ideal is generated by indeterminates if the generators are a (possibly empty) subset of the indeterminates in the ring.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : isGeneratedByIndeterminates ideal 0

o2 = true

i3 : isGeneratedByIndeterminates ideal 1

o3 = false

i4 : isGeneratedByIndeterminates ideal(x,y)

o4 = true

i5 : isGeneratedByIndeterminates ideal(x*y)

o5 = false

See also

isGVD -- checks whether an ideal is geometrically vertex decomposable
isLexCompatiblyGVD -- checks whether an ideal is <-compatibly geometrically vertex decomposable for a given order
isWeaklyGVD -- checks whether an ideal is weakly geometrically vertex decomposable

Ways to use isGeneratedByIndeterminates:

isGeneratedByIndeterminates(Ideal)

For the programmer

The object isGeneratedByIndeterminates is a method function.

The source of this document is in GeometricDecomposability.m2:1151:0.