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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 = {(.276458 + .216557*ii)x  + (.594659 + .468895*ii)x*y + (.62245 +
     ------------------------------------------------------------------------
                                                                        2
     .992969*ii)x*z + (- .276458 - .216557*ii)y, (.954616 + .875973*ii)x  +
     ------------------------------------------------------------------------
     (.852615 + .547411*ii)x*y + (.765622 + .40989*ii)x*z + (- .954616 -
     ------------------------------------------------------------------------
     .875973*ii)y}

o3 : List

Ways to use generalEquations :

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