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 = {(.716549 + .0108331*ii)x + (.987945 + .513637*ii)x*y + (.435741 + ------------------------------------------------------------------------ 2 .715786*ii)x*z + (- .716549 - .0108331*ii)y, (.811208 + .16236*ii)x + ------------------------------------------------------------------------ (.478351 + .987201*ii)x*y + (.656897 + .58772*ii)x*z + (- .811208 - ------------------------------------------------------------------------ .16236*ii)y} o3 : List |