# areEqual(DualSpace,DualSpace) -- approximate equality of dual spaces

## 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 dual spaces are approximately equal if the have (approximately) the same base point(DualSpace) and the linear spaces spanned by the differential operators are equal approximately.

 i1 : R = CC[x,y]; i2 : A = dualSpace(matrix{{y^2,x^2+x*y}},point{{1,1}}) o2 = | y2 x2+xy | o2 : DualSpace i3 : B = dualSpace(matrix{{x^2+x*y+y^2,y^2+0.00000001}},point{{1,1+0.00000001}}) o3 = | x2+xy+y2 y2+1e-8 | o3 : DualSpace i4 : b = areEqual(A,B) o4 = true