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 = {(.955107 + .442814*ii)x + (.663102 + .622962*ii)x*y + (.440215 + ------------------------------------------------------------------------ 2 .608387*ii)x*z + (- .955107 - .442814*ii)y, (.843271 + .495208*ii)x + ------------------------------------------------------------------------ (.837889 + .897184*ii)x*y + (.448074 + .39324*ii)x*z + (- .843271 - ------------------------------------------------------------------------ .495208*ii)y} o3 : List |