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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 = {(.988433 + .530996*ii)x  + (.941026 + .99188*ii)x*y + (.663467 +
     ------------------------------------------------------------------------
                                                                        2
     .487295*ii)x*z + (- .988433 - .530996*ii)y, (.398191 + .715058*ii)x  +
     ------------------------------------------------------------------------
     (.455177 + .418285*ii)x*y + (.768215 + .287315*ii)x*z + (- .398191 -
     ------------------------------------------------------------------------
     .715058*ii)y}

o3 : List

Ways to use generalEquations :

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