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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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GeometricDecomposability.m2:1151:0.