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 = {(.851793 + .292786*ii)x + (.233807 + .619585*ii)x*y + (.200108 + ------------------------------------------------------------------------ 2 .826485*ii)x*z + (- .851793 - .292786*ii)y, (.0521553 + .151213*ii)x + ------------------------------------------------------------------------ (.630232 + .76525*ii)x*y + (.461052 + .49486*ii)x*z + (- .0521553 - ------------------------------------------------------------------------ .151213*ii)y} o3 : List |