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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 = {(.0373473 + .288284*ii)x  + (.526112 + .657666*ii)x*y + (.69341 +
     ------------------------------------------------------------------------
                                                                        2
     .787889*ii)x*z + (- .0373473 - .288284*ii)y, (.482937 + .89083*ii)x  +
     ------------------------------------------------------------------------
     (.528714 + .0629771*ii)x*y + (.891593 + .270377*ii)x*z + (- .482937 -
     ------------------------------------------------------------------------
     .89083*ii)y}

o3 : List

Ways to use generalEquations :

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