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# numericalIrreducibleDecomposition(Ideal) -- constructs a numerical variety defined by the given ideal

- Function: numericalIrreducibleDecomposition
- Usage:
    `V = numericalIrreducibleDecomposition I`
- Inputs:
  - I, an ideal, contained in the ring of polynomials with complex coefficients
- Optional inputs:
  - Software => ..., default value null, specify internal or external software
- Outputs:
  - V

## Description

The witness sets of the numerical variety V are in one-to-one correspondence with irreducible components of the variety defined by I.

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

    o1 = R

    o1 : PolynomialRing

    i2 : sph = (x^2+y^2+z^2-1);

    i3 : I = ideal {sph*(y-x^2), sph*(z-x^3)};

    o3 : Ideal of R

    i4 : numericalIrreducibleDecomposition I

    o4 = a "numerical variety" with components in
         dim 1:  (dim=1,deg=3)
         dim 2:  (dim=2,deg=2)

    o4 : NumericalVariety

## Caveat

This function is under development. It may not work well if the input represents a nonreduced scheme.

## See also

- decompose(WitnessSet)

## Ways to use this method:

- numericalIrreducibleDecomposition(Ideal) -- constructs a numerical variety defined by the given ideal

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NumericalAlgebraicGeometry/doc.m2:648:0.