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 = {(.657182 + .311455*ii)x + (.784109 + .442705*ii)x*y + (.575004 + ------------------------------------------------------------------------ 2 .754072*ii)x*z + (- .657182 - .311455*ii)y, (.990027 + .322879*ii)x + ------------------------------------------------------------------------ (.55886 + .766444*ii)x*y + (.980736 + .668184*ii)x*z + (- .990027 - ------------------------------------------------------------------------ .322879*ii)y} o3 : List |