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

• Function: areEqual

• Usage:

  b = areEqual(A,B)

• Inputs:
  • A, an instance of the type DualSpace,
  • B, an instance of the type DualSpace,
• 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,

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