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

## Synopsis

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

## 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