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 = {(.298111 + .399998*ii)x + (.799867 + .538814*ii)x*y + (.765609 + ------------------------------------------------------------------------ 2 .208188*ii)x*z + (- .298111 - .399998*ii)y, (.502057 + .681134*ii)x + ------------------------------------------------------------------------ (.770914 + .452901*ii)x*y + (.328798 + .890092*ii)x*z + (- .502057 - ------------------------------------------------------------------------ .681134*ii)y} o3 : List |