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Dom::MonomOrdering -- monomial orderings

Introduction

Dom::MonomOrdering represents the set of all possible monomial orderings. A monomial ordering is a well-ordering of the set of all k-tuples of nonnegative integers for some k.

Domain

Dom::MonomOrdering()

Details

Introduction

Monomial orderings are created by calling Dom::MonomOrdering(someIdentifier(parameters)), where someIdentifier is one of a certain set of predefined identifiers, as stated below. Converting someIdentifier into a string gives the order type of the monomial ordering.

Creating Elements

Dom::MonomOrdering(Lex(n))
Dom::MonomOrdering(RevLex(n))
Dom::MonomOrdering(DegLex(n))
Dom::MonomOrdering(DegRevLex(n))
Dom::MonomOrdering(DegInvLex(n))
Dom::MonomOrdering(WeightedLex(w1, ...,wn))
Dom::MonomOrdering(WeightedRevLex(w1, ...,wn))
Dom::MonomOrdering(WeightedDegLex(w1, ..,wn))
Dom::MonomOrdering(WeightedDegRevLex(w1, ..,wn))
Dom::MonomOrdering(Block(o1...))
Dom::MonomOrdering(Matrix(params))

Parameters

n - positive integer
w1... - numerical expressions
o1,.. - valid arguments to Dom::MonomOrdering
params - a sequence valid as the sequence of arguments to Dom::Matrix().

Categories

Cat::BaseCategory

Details

Method func_call: compare two lists of integers

Method ordertype: return the type of an order

Method orderlength: return the length of an order

Method nops: number of blocks

Method block: get a particular block

Method blocktype: get the order type of a particular block

Method blocklength: get the order length of a particular block

Method expr: return an expression from which the order can be restored

Example 1

We define ORD by prescribing that lists [a,b,c] are ordered according to their weighted degrees 5a + 2b + πc. For lists with equal weighted degree, the non-weighted degree a+b+c is used as a tie-break. Finally, the lexicographical order decides (in fact, this last step is not necessary because π is irrational).

>> ORD:=Dom::MonomOrdering(WeightedDegLex(5, 2, PI))
                         WeightedDegLex(5, 2, PI)

With respect to ORD, [1, 6, 1] is smaller than [2, 1, 3]:

>> ORD([1,6,1], [2,1,3])
                                    -1

Super-Domain

Dom::BaseDomain

Changes




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