i1 : loadPackage "NumericalAlgebraicGeometry"; --warning: symbol "generalEquations" in PHCpack#"private dictionary" is shadowed by a symbol in NAGtypes.Dictionary -- no synonym is available --warning: symbol "addSlackVariables" in PHCpack#"private dictionary" is shadowed by a symbol in NAGtypes.Dictionary -- no synonym is available --warning: symbol "tDegree" in NumericalAlgebraicGeometry#"private dictionary" is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$tDegree --warning: symbol "gamma" in NumericalAlgebraicGeometry#"private dictionary" is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$gamma --warning: symbol "tDegree" in NumericalAlgebraicGeometry.Dictionary is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$tDegree --warning: symbol "gamma" in NumericalAlgebraicGeometry.Dictionary is shadowed by a symbol in PHCpack.Dictionary -- use the synonym NumericalAlgebraicGeometry$gamma |
i2 : R = CC[x,y]; |
i3 : sols = solveSystem{x^2+y^2-3, x^3-y^3-7} o3 = {{-1.7957-1.31322*ii, 1.7957-1.31322*ii}, {-.101284+.779159*ii, ------------------------------------------------------------------------ -1.89699-.041601*ii}, {-1.7957+1.31322*ii, 1.7957+1.31322*ii}, ------------------------------------------------------------------------ {-.101284-.779159*ii, -1.89699+.041601*ii}, {1.89699+.041601*ii, ------------------------------------------------------------------------ .101284-.779159*ii}, {1.89699-.041601*ii, .101284+.779159*ii}} o3 : List |
i4 : pt = first sols o4 = {-1.7957-1.31322*ii, 1.7957-1.31322*ii} o4 : Point |
i5 : peek pt o5 = Point{ConditionNumber => 5.99383 } Coordinates => {-1.7957-1.31322*ii, 1.7957-1.31322*ii} ErrorBoundEstimate => 7.28774e-16 LastT => 1 SolutionStatus => Regular |
i6 : coordinates pt o6 = {-1.7957-1.31322*ii, 1.7957-1.31322*ii} o6 : List |
i7 : status pt o7 = Regular o7 : Symbol |
For example, one may see the condition number of the Jacobian of the polynomial system, evaluated at this point (the smaller the value, the better) as follows.
i8 : pt.ConditionNumber o8 = 5.99382650733725 o8 : RR (of precision 53) |
The other keys that may be attached include
The object Point is a type, with ancestor classes MutableHashTable < HashTable < Thing.