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 = {(.0855591 + .14254*ii)x + (.484529 + .381887*ii)x*y + (.710915 + ------------------------------------------------------------------------ 2 .818244*ii)x*z + (- .0855591 - .14254*ii)y, (.140985 + .825158*ii)x + ------------------------------------------------------------------------ (.579736 + .341784*ii)x*y + (.452502 + .98046*ii)x*z + (- .140985 - ------------------------------------------------------------------------ .825158*ii)y} o3 : List |