23 May 2007
CoCoA::PPOrdering Class Reference
Collaboration diagram for CoCoA::PPOrdering:
[legend]List of all members.
Copyright (c) 2005 John Abbott
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A copy of the licence is included in the file COPYING in this directory.
User documentation for PPOrdering
An object of the class PPOrdering represents an "arithmetic" ordering on
the (multiplicative) monoid of power products, i.e. such that the
ordering respects the monoid operation (viz. s < t => r*s < r*t for all
r,s,t in the monoid). In CoCoALib orderings and gradings are
intimately linked (for gradings see also degree.txt).
Currently, the most typical use for a PPOrdering object is as a constructor
argument to a concrete PPMonoid (see file PPMonoid.txt). At the moment
there are four functions which create new PPOrderings:
NewMatrixOrdering(NumIndets, GradingDim, OrderMatrix);
The first three create respectively lex, DegLex and DevRevLex orderings on
the given number of indeterminates. Note the use of "Std" in the names to
emphasise that they are only for standard graded polynomial rings.
The last function creates a PPOrdering given a matrix. GradingDim
specifies how many of the rows of OrderMatrix are to be taken as
specifying the grading.
The operations on a PPOrdering object are:
out << PPO;
Thus CoCoALib supports graded polynomial rings with the restriction that the
grading be compatible with the PP ordering: i.e. the grading comprises
simply the first k entries of the "order vector". The GradingDim is merely
the integer k (which may be zero if there is no grading).
A normal CoCoA library user need know no more than this about PPOrderings.
CoCoA Library contributors and the curious should read on.
A recent addition. There is also a member function:
PPO.myMatrixCopy(M) where M is a matrix
It fills M with a matrix which specifies the ordering PPO. Don't use it yet.
Maintainer documentation for PPOrdering
The general ideas behind the implementations of PPOrdering and
PPOrderingBase are analogous to those used for ring and RingBase.
PPOrdering is a simple reference counting smart-pointer class, while
PPOrderingBase hosts the intrusive reference count (so that every concrete
derived class will inherit it).
The only remaining observation to make about the simple class PPOrdering is
that I have chosen to disable assignment -- I find it hard to imagine when
it could be useful to be able to assign PPOrderings, and suspect that
allowing assignment is more likely to lead to confusion and poor programming
There are four concrete PPOrderings in the namespace CoCoA::PPO. The
implementations are all simple and straightforward except for the matrix
ordering which is a little longer and messier but still easy enough to
Bugs, shortcomings and other ideas
Must resolve the restrictions on order matrices in NewMatrixOrdering
(matrix must be square).
We need better ways to "compose" PPOrderings, i.e. to build new ones
starting from existing ones. Max knows the sorts of operation needed
here. Something similar to CoCoA4's BlockMatrix command is needed.
Definition at line 43 of file PPOrdering.H.
Constructor & Destructor Documentation
||const PPOrderingBase *
Member Function Documentation
|const PPOrderingBase* CoCoA::PPOrdering::operator->
Member Data Documentation
The documentation for this class was generated from the following file:
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