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 = {(.988433 + .530996*ii)x + (.941026 + .99188*ii)x*y + (.663467 + ------------------------------------------------------------------------ 2 .487295*ii)x*z + (- .988433 - .530996*ii)y, (.398191 + .715058*ii)x + ------------------------------------------------------------------------ (.455177 + .418285*ii)x*y + (.768215 + .287315*ii)x*z + (- .398191 - ------------------------------------------------------------------------ .715058*ii)y} o3 : List |