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 = {(.604029 + .307657*ii)x + (.243678 + .89134*ii)x*y + (.460512 + ------------------------------------------------------------------------ 2 .716473*ii)x*z + (- .604029 - .307657*ii)y, (.633506 + .32384*ii)x + ------------------------------------------------------------------------ (.862136 + .333761*ii)x*y + (.543207 + .820284*ii)x*z + (- .633506 - ------------------------------------------------------------------------ .32384*ii)y} o3 : List |