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 = {(.612234 + .60414*ii)x + (.792049 + .038907*ii)x*y + (.739559 + ------------------------------------------------------------------------ 2 .0943074*ii)x*z + (- .612234 - .60414*ii)y, (.0461599 + .990126*ii)x + ------------------------------------------------------------------------ (.536366 + .171869*ii)x*y + (.11519 + .827378*ii)x*z + (- .0461599 - ------------------------------------------------------------------------ .990126*ii)y} o3 : List |