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 = {(.999565 + .382145*ii)x + (.17601 + .267598*ii)x*y + (.702663 + ------------------------------------------------------------------------ 2 .112144*ii)x*z + (- .999565 - .382145*ii)y, (.285618 + .0449131*ii)x + ------------------------------------------------------------------------ (.601225 + .545471*ii)x*y + (.731115 + .0269921*ii)x*z + (- .285618 - ------------------------------------------------------------------------ .0449131*ii)y} o3 : List |