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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 = {(.955107 + .442814*ii)x  + (.663102 + .622962*ii)x*y + (.440215 +
     ------------------------------------------------------------------------
                                                                        2
     .608387*ii)x*z + (- .955107 - .442814*ii)y, (.843271 + .495208*ii)x  +
     ------------------------------------------------------------------------
     (.837889 + .897184*ii)x*y + (.448074 + .39324*ii)x*z + (- .843271 -
     ------------------------------------------------------------------------
     .495208*ii)y}

o3 : List

Ways to use generalEquations :

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