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 = {(.00812973 + .397029*ii)x + (.550521 + .340483*ii)x*y + (.0979551 + ------------------------------------------------------------------------ 2 .748261*ii)x*z + (- .00812973 - .397029*ii)y, (.750105 + .413972*ii)x + ------------------------------------------------------------------------ (.774951 + .282332*ii)x*y + (.11345 + .317204*ii)x*z + (- .750105 - ------------------------------------------------------------------------ .413972*ii)y} o3 : List |