inter-reduce a list of polynomials
InterReduce(G, T, characteristic=p)
a list or set of polynomials
a MonomialOrder or ShortMonomialOrder
The InterReduce command inter-reduces a list or set of polynomials G with respect to a monomial order T. The result is a list of polynomials defining the same ideal as G, but where no term of a polynomial is reducible by the leading term of another polynomial. See also the help page for Groebner[Reduce]. The resulting list is sorted in ascending order of leading monomial.
A typical use of this command is to construct a reduced Groebner basis from a Groebner basis computed outside of Maple. See the Monomial Orders help page for more information about the monomial orders that are available in Maple.
If T is a ShortMonomialOrder then the elements of G must be polynomials in the ring implied by T. If T is a MonomialOrder created with the Groebner[MonomialOrder] command, then the elements of G must be members of the algebra used to define T.
The optional argument characteristic=p can be used to specify the ring characteristic when T is a ShortMonomialOrder. The default value is zero.
Note that the inter_reduce command is deprecated. It may not be supported in a future Maple release.
F ≔ x2+x⁢y−2,x2−x⁢y
r ≔ Reduce⁡F1,F2,tdeg⁡x,y
r ≔ x⁢y−1
A set of inter-reduced (or autoreduced) polynomials is not a Groebner basis because syzygies are not considered.
The next example is a non-commutative (Weyl) algebra where Dn*n = n*Dn + 1
A ≔ diff_algebra⁡Dn,n
A ≔ Ore_algebra
T ≔ MonomialOrder⁡A,tdeg⁡Dn
T ≔ monomial_order
w1 ≔ n2⁢Dn2+n
w1 ≔ Dn2⁢n2+n
w2 ≔ n2⁢Dn2+Dn
w2 ≔ Dn2⁢n2+Dn
r ≔ Reduce⁡w2,w1,T
r ≔ Dn−n
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