A variety V (that is not necessarily a complete intersection) of codimension k is a component of a complete intersection of codimension k defined by k general linear combinations of any generating set of the defining ideal of V.
This function automates the above construction.
i1 : R = CC[x,y,z]; |
i2 : F = {x*y, x^2 - y, x*z}; |
i3 : L = generalEquations(2,F) 2 o3 = {(.709662 + .543222*ii)x + (.594692 + .899584*ii)x*y + (.660749 + ------------------------------------------------------------------------ 2 .589713*ii)x*z + (- .709662 - .543222*ii)y, (.859112 + .620403*ii)x + ------------------------------------------------------------------------ (.204602 + .389621*ii)x*y + (.0469157 + .893803*ii)x*z + (- .859112 - ------------------------------------------------------------------------ .620403*ii)y} o3 : List |