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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 = {(.790217 + .937972*ii)x  + (.577401 + .32535*ii)x*y + (.420206 +
     ------------------------------------------------------------------------
                                                                        2
     .385624*ii)x*z + (- .790217 - .937972*ii)y, (.170527 + .587609*ii)x  +
     ------------------------------------------------------------------------
     (.856732 + .541504*ii)x*y + (.897345 + .666045*ii)x*z + (- .170527 -
     ------------------------------------------------------------------------
     .587609*ii)y}

o3 : List

Ways to use generalEquations :

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