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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 = {(.00812973 + .397029*ii)x  + (.550521 + .340483*ii)x*y + (.0979551 +
     ------------------------------------------------------------------------
                                                                          2
     .748261*ii)x*z + (- .00812973 - .397029*ii)y, (.750105 + .413972*ii)x  +
     ------------------------------------------------------------------------
     (.774951 + .282332*ii)x*y + (.11345 + .317204*ii)x*z + (- .750105 -
     ------------------------------------------------------------------------
     .413972*ii)y}

o3 : List

Ways to use generalEquations :

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