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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 = {(.0855591 + .14254*ii)x  + (.484529 + .381887*ii)x*y + (.710915 +
     ------------------------------------------------------------------------
                                                                        2
     .818244*ii)x*z + (- .0855591 - .14254*ii)y, (.140985 + .825158*ii)x  +
     ------------------------------------------------------------------------
     (.579736 + .341784*ii)x*y + (.452502 + .98046*ii)x*z + (- .140985 -
     ------------------------------------------------------------------------
     .825158*ii)y}

o3 : List

Ways to use generalEquations :

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