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 = {(.307698 + .299597*ii)x + (.521544 + .101801*ii)x*y + (.870885 + ------------------------------------------------------------------------ 2 .686642*ii)x*z + (- .307698 - .299597*ii)y, (.290343 + .418491*ii)x + ------------------------------------------------------------------------ (.862878 + .559959*ii)x*y + (.487815 + .906541*ii)x*z + (- .290343 - ------------------------------------------------------------------------ .418491*ii)y} o3 : List |