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 = {(.721525 + .537109*ii)x + (.411969 + .903863*ii)x*y + (.00665094 + ------------------------------------------------------------------------ 2 .377479*ii)x*z + (- .721525 - .537109*ii)y, (.328843 + .700012*ii)x + ------------------------------------------------------------------------ (.746836 + .821438*ii)x*y + (.583544 + .16657*ii)x*z + (- .328843 - ------------------------------------------------------------------------ .700012*ii)y} o3 : List |