# squareUp -- square up a polynomial system

## Synopsis

• Usage:
G = squareUp F\nG = squareUp(F,M)\nsquareUp(F,n)
• Inputs:
• M, , the matrix used to square up the system (by default a random matrix is picked)
• n, an integer, the number of polynomials to be formed (by default, this equals the number of variables)
• Outputs:

## 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 |