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 = {(.73208 + .771013*ii)x + (.626562 + .193633*ii)x*y + (.695181 + ------------------------------------------------------------------------ 2 .857647*ii)x*z + (- .73208 - .771013*ii)y, (.125604 + .243443*ii)x + ------------------------------------------------------------------------ (.804463 + .303225*ii)x*y + (.592152 + .535181*ii)x*z + (- .125604 - ------------------------------------------------------------------------ .243443*ii)y} o3 : List |