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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 = {(.0856349 + .0480955*ii)x  + (.712109 + .732808*ii)x*y + (.178676 +
     ------------------------------------------------------------------------
                                                                           2
     .245189*ii)x*z + (- .0856349 - .0480955*ii)y, (.0932618 + .461275*ii)x 
     ------------------------------------------------------------------------
     + (.0484582 + .269176*ii)x*y + (.0991063 + .969216*ii)x*z + (- .0932618
     ------------------------------------------------------------------------
     - .461275*ii)y}

o3 : List

Ways to use generalEquations :

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