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# areEqual(PolySpace,PolySpace) -- approximate equality of subspaces spanned by polynomials

- Function: areEqual
- Usage:
    `b = areEqual(A,B)`
- Inputs:
  - A, an instance of the type PolySpace,
  - B, an instance of the type PolySpace,
- Optional inputs:
  - Projective => ..., default value false, determine if solutions are equal
  - Tolerance => ..., default value .000001, the tolerance of a numerical computation
- Outputs:
  - b, a Boolean value,

## Description

Two spaces are approximately equal if the numericalImage of their union of their generators has the same dimension as both of them.

    i1 : R = CC[x,y];

    i2 : b = areEqual(polySpace matrix{{y^2,x^2+x*y}}, polySpace matrix{{x^2+x*y+y^2,y^2+0.00000001}})

    o2 = true

## Ways to use this method:

- areEqual(PolySpace,PolySpace) -- approximate equality of subspaces spanned by polynomials

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NAGtypes/doc-NAGtypes.m2:960:0.