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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 = {(.73208 + .771013*ii)x  + (.626562 + .193633*ii)x*y + (.695181 +
     ------------------------------------------------------------------------
                                                                       2
     .857647*ii)x*z + (- .73208 - .771013*ii)y, (.125604 + .243443*ii)x  +
     ------------------------------------------------------------------------
     (.804463 + .303225*ii)x*y + (.592152 + .535181*ii)x*z + (- .125604 -
     ------------------------------------------------------------------------
     .243443*ii)y}

o3 : List

Ways to use generalEquations :

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