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 = {(.0856349 + .0480955*ii)x + (.712109 + .732808*ii)x*y + (.178676 + ------------------------------------------------------------------------ 2 .245189*ii)x*z + (- .0856349 - .0480955*ii)y, (.0932618 + .461275*ii)x ------------------------------------------------------------------------ + (.0484582 + .269176*ii)x*y + (.0991063 + .969216*ii)x*z + (- .0932618 ------------------------------------------------------------------------ - .461275*ii)y} o3 : List |