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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 = {(.110833 + .423386*ii)x  + (.723255 + .218173*ii)x*y + (.726508 +
     ------------------------------------------------------------------------
                                                                        2
     .143367*ii)x*z + (- .110833 - .423386*ii)y, (.269993 + .378599*ii)x  +
     ------------------------------------------------------------------------
     (.141967 + .907837*ii)x*y + (.780017 + .217285*ii)x*z + (- .269993 -
     ------------------------------------------------------------------------
     .378599*ii)y}

o3 : List

Ways to use generalEquations :

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