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 = {(.60002 + .468437*ii)x + (.0254988 + .451115*ii)x*y + (.0817482 + ------------------------------------------------------------------------ 2 .296958*ii)x*z + (- .60002 - .468437*ii)y, (.61514 + .278146*ii)x + ------------------------------------------------------------------------ (.114012 + .299296*ii)x*y + (.692332 + .911618*ii)x*z + (- .61514 - ------------------------------------------------------------------------ .278146*ii)y} o3 : List |