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 = {(.110833 + .423386*ii)x + (.723255 + .218173*ii)x*y + (.726508 + ------------------------------------------------------------------------ 2 .143367*ii)x*z + (- .110833 - .423386*ii)y, (.269993 + .378599*ii)x + ------------------------------------------------------------------------ (.141967 + .907837*ii)x*y + (.780017 + .217285*ii)x*z + (- .269993 - ------------------------------------------------------------------------ .378599*ii)y} o3 : List |