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 = {(.814498 + .683884*ii)x + (.298215 + .964649*ii)x*y + (.781015 + ------------------------------------------------------------------------ 2 .526516*ii)x*z + (- .814498 - .683884*ii)y, (.210988 + .712223*ii)x + ------------------------------------------------------------------------ (.369312 + .237127*ii)x*y + (.893963 + .473042*ii)x*z + (- .210988 - ------------------------------------------------------------------------ .712223*ii)y} o3 : List |