next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
NAGtypes :: generalEquations

generalEquations -- random linear combinations of equations/generators

Synopsis

Description

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 = {(.709662 + .543222*ii)x  + (.594692 + .899584*ii)x*y + (.660749 +
     ------------------------------------------------------------------------
                                                                        2
     .589713*ii)x*z + (- .709662 - .543222*ii)y, (.859112 + .620403*ii)x  +
     ------------------------------------------------------------------------
     (.204602 + .389621*ii)x*y + (.0469157 + .893803*ii)x*z + (- .859112 -
     ------------------------------------------------------------------------
     .620403*ii)y}

o3 : List

Ways to use generalEquations :

  • generalEquations(ZZ,Ideal)
  • generalEquations(ZZ,List)