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 = {(.853262 + .182607*ii)x + (.994038 + .0775227*ii)x*y + (.600385 + ------------------------------------------------------------------------ 2 .351016*ii)x*z + (- .853262 - .182607*ii)y, (.599595 + .55305*ii)x + ------------------------------------------------------------------------ (.59978 + .307019*ii)x*y + (.388118 + .753667*ii)x*z + (- .599595 - ------------------------------------------------------------------------ .55305*ii)y} o3 : List |