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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 = {(.851793 + .292786*ii)x  + (.233807 + .619585*ii)x*y + (.200108 +
     ------------------------------------------------------------------------
                                                                         2
     .826485*ii)x*z + (- .851793 - .292786*ii)y, (.0521553 + .151213*ii)x  +
     ------------------------------------------------------------------------
     (.630232 + .76525*ii)x*y + (.461052 + .49486*ii)x*z + (- .0521553 -
     ------------------------------------------------------------------------
     .151213*ii)y}

o3 : List

Ways to use generalEquations :

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