polyd2
http://www.openmath.org/cd
http://www.openmath.org/cd/polyd2.ocd
2006-04-01
2004-07-07
experimental
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This CD defines symbols for ordering of monomial for
Distributed Multivariate Polynomials, which were defined in polyd1.
Original OpenMath v1.1 Poly 1997
Update to Current Format 1999-07-07 DPC
Move the names of rings to setname.ocd 1999-11-09 JHD
Delete those items moved to the new poly.ocd 1999-11-14 JHD
Delete those items pertaining to Groebner bases 2004-07-07 AMC
These are of use for canonical ways of writing polynomials and for Groebner bases
ordering
Used as an attribute to indicate an ordering of the monomials in a
polynomial or list of polynomials. The value of this attribute
should be one of the constructors specifying ordering.
The following orders on monomials have their standards definitions,
see, for example, "Ideals, Varieties and Algorithms", D. Cox,
J.B. Little and D. O'Shea, Springer Verlag.
lexicographic
The lexicographic ordering of monomials.
reverse_lexicographic
The reverse lexicographic ordering of monomials
graded_lexicographic
Total degree order, graded with the lexicographic ordering.
graded_reverse_lexicographic
Total degree order, graded with the reverse lexicographic ordering.
elimination
This is an ordering, which is partially in terms of one
ordering, and partially in terms of another.
First argument is a number of variables.
Second is ordering to apply on the first so many variables.
Third is an ordering on the rest, to be used to break ties.
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matrix_ordering
The argument is a matrix with as many columns as indeterminates
(= rank). Each row in turm is multiplied by the column vector of
exponents to produce a weighting for comparison purposes.
weighted
The first argument is a list of integers to act as variable weights,
and the second is an ordering. The result is an ordering.
We need a few more orderings...
Definition of some other constructors
weighted_degree
The total degree of its argument, taking into account any weights
declared. The value returned is an integer: non-negative if the
weights are. We note that the degree of 0 is undefined.
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