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 = {(.945478 + .865839*ii)x + (.529708 + .634172*ii)x*y + (.0653654 + ------------------------------------------------------------------------ 2 .976277*ii)x*z + (- .945478 - .865839*ii)y, (.412847 + .592188*ii)x + ------------------------------------------------------------------------ (.571127 + .899345*ii)x*y + (.300066 + .0373054*ii)x*z + (- .412847 - ------------------------------------------------------------------------ .592188*ii)y} o3 : List |