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 = {(.0373473 + .288284*ii)x + (.526112 + .657666*ii)x*y + (.69341 + ------------------------------------------------------------------------ 2 .787889*ii)x*z + (- .0373473 - .288284*ii)y, (.482937 + .89083*ii)x + ------------------------------------------------------------------------ (.528714 + .0629771*ii)x*y + (.891593 + .270377*ii)x*z + (- .482937 - ------------------------------------------------------------------------ .89083*ii)y} o3 : List |