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NumericalAlgebraicGeometry :: squareUp

squareUp -- square up a polynomial system

Synopsis

Description

Squares up an overdetermined polynomial system. Attaches keys SquareUpMatrix and SquaredUpSystem to F. 
i1 : CC[x,y]; F = polySystem {x^2+y^2,x^3+y^3,x^4+y^4}

o2 = F

o2 : PolySystem
 
i3 : G := squareUp F

o3 = | (.296025-.479811ii)x4+(.296025-.479811ii)y4+(-.605892-.324075ii)x3+(-.605892-.324075ii)y3+(.448215+.0955171ii)x2+(.448215+.0955171ii)y2 |
     | (-.085187-.0688326ii)x4+(-.085187-.0688326ii)y4+(.54886+.147995ii)x3+(.54886+.147995ii)y3+(.80766+.111983ii)x2+(.80766+.111983ii)y2     |

o3 : PolySystem
 
i4 : peek F

o4 = PolySystem{NumberOfPolys => 3                                                                                                                                            }
                NumberOfVariables => 2
                PolyMap => {-2} | x2+y2 |
                           {-3} | x3+y3 |
                           {-4} | x4+y4 |
                SquaredUpSystem => | (.296025-.479811ii)x4+(.296025-.479811ii)y4+(-.605892-.324075ii)x3+(-.605892-.324075ii)y3+(.448215+.0955171ii)x2+(.448215+.0955171ii)y2 |
                                   | (-.085187-.0688326ii)x4+(-.085187-.0688326ii)y4+(.54886+.147995ii)x3+(.54886+.147995ii)y3+(.80766+.111983ii)x2+(.80766+.111983ii)y2     |
                SquareUpMatrix => | .448215+.0955171ii -.605892-.324075ii .296025-.479811ii   |
                                  | .80766+.111983ii   .54886+.147995ii   -.085187-.0688326ii |

See also

Ways to use squareUp :

For the programmer

The object squareUp is a method function.