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 = {(.276458 + .216557*ii)x + (.594659 + .468895*ii)x*y + (.62245 + ------------------------------------------------------------------------ 2 .992969*ii)x*z + (- .276458 - .216557*ii)y, (.954616 + .875973*ii)x + ------------------------------------------------------------------------ (.852615 + .547411*ii)x*y + (.765622 + .40989*ii)x*z + (- .954616 - ------------------------------------------------------------------------ .875973*ii)y} o3 : List |