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minimalPresentation(Ring) -- compute a minimal presentation of a quotient ring

Synopsis

Description

The computation is accomplished by considering the relations of R. If a variable occurs as a term of a relation of R and in no other terms of the same polynomial, then the variable is replaced by the remaining terms and removed from the ring. A minimal generating set for the resulting defining ideal is then computed and the new quotient ring is returned. If R is not homogeneous, then an attempt is made to improve the presentation.
i1 : R = ZZ/101[x,y,z,u,w]/ideal(x-x^2-y,z+x*y,w^2-u^2);
i2 : minimalPresentation(R)

      ZZ
     --- [x, u, w]
     101
o2 = -------------
         2    2
        u  - w

o2 : QuotientRing
i3 : R.minimalPresentationMap

          ZZ
         --- [x, u, w]
         101                    2       3    2
o3 = map(-------------,R,{x, - x  + x, x  - x , u, w})
             2    2
            u  - w

              ZZ
             --- [x, u, w]
             101
o3 : RingMap ------------- <--- R
                 2    2
                u  - w
i4 : R.minimalPresentationMapInv

            ZZ
           --- [x, u, w]
           101
o4 = map(R,-------------,{x, u, w})
               2    2
              u  - w

                     ZZ
                    --- [x, u, w]
                    101
o4 : RingMap R <--- -------------
                        2    2
                       u  - w

See also