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 = {(.658948 + .165444*ii)x + (.860783 + .523581*ii)x*y + (.939805 + ------------------------------------------------------------------------ 2 .236309*ii)x*z + (- .658948 - .165444*ii)y, (.890541 + .490088*ii)x + ------------------------------------------------------------------------ (.110989 + .678884*ii)x*y + (.758564 + .708196*ii)x*z + (- .890541 - ------------------------------------------------------------------------ .490088*ii)y} o3 : List |