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areEqual -- determine if solutions are equal

Synopsis

Description

Comparisons are done coordinatewise using Tolerance as the measure for closeness.
i1 : R = CC[x,y];
i2 : s = solveSystem {x^2+y^2-1, x*y}

o2 = {{{-1.97657e-15-5.64773e-16*ii, -1}}, {{-1,
     ------------------------------------------------------------------------
     1.33994e-15+3.11506e-16*ii}}, {{1, -1.33994e-15-3.1259e-16*ii}},
     ------------------------------------------------------------------------
     {{1.97657e-15+5.64773e-16*ii, 1}}}

o2 : List
i3 : areEqual(sortSolutions s, {{{-1, 0}}, {{0, -1}}, {{0, 1}}, {{1, 0}}})

o3 = true

Ways to use areEqual :