squareUp -- square up a polynomial system

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

o3 : PolySystem

i4 : peek F

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