CoCoALib-0.9905 date: 23 May 2007

# CoCoA::degree Class Reference

`#include <degree.H>`

List of all members.

## Public Member Functions

degree (std::size_t dim)
const ZZoperator[] (std::size_t index) const
void mySetComponent (std::size_t index, const ZZ &VALUE)
deg[index] = VALUE
void mySetComponent (std::size_t index, long value)
deg[index] = value
degreeoperator+= (const degree &d)
Computes deg1+=deg2.
degreeoperator-= (const degree &d)
Computes deg1-=deg2.

## Static Public Member Functions

static void CheckCompatible (const degree &d1, const degree &d2, const char *fn)
checks dims are equal, throws if not.

## Friends

int FastCmp (const degree &d1, const degree &d2)
like cmp but inline and no checks
bool IsZero (const degree &d)

## Detailed Description

```      Copyright (c)  2005 John Abbott
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.2;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the licence is included in the file COPYING in this directory.

User documentation for the class degree
=======================================

The class degree is used to represent the values returned by the "deg"
function applied to power products and (multivariate) polynomials.
Recall that in general a degree is a value in Z^k; the value of k and
the way the degree is computed (equiv. weight matrix) are specified when
creating the PPOrdering object used for making the PPMonoid of the
polynomial ring -- see the function NewPolyRing.

If t1 and t2 are two power products then the degree of their product is
just the sum of their individual degrees; and naturally, if t1 divides
t2 then the degree of the quotient is the difference of their degrees.
The degree values are totally ordered using a lexicographic ordering.
Note that a degree may have negative components.

The following functions are available for objects of type degree:
degree d1(k); create a new degree object with value (0,0,...,0) [k zeroes]
d1 = d2      assignment, d1 must be non-const
d1 + d2      sum
d1 - d2      difference (there might be no PP with such a degree)
d1 += d2     equivalent to d1 = d1 + d2
d1 -= d2     equivalent to d1 = d1 - d2
cmp(d1, d2)  (int) result is <0, =0, >0 according as d1 <,=,> d2
top(d1, d2)  coordinate-by-coordinate maximum (a sort of "lcm")
cout << d1   print out the degree
GradingDim(d)  get the number of the components
d1[s]        get the s-th component of the degree (as a ZZ) (for 0 <= s < k)
IsZero(d1)   true iff d1 is the zero degree
d1.mySetComponent(k, n)  sets the k-th component of d1 to n
[you probably shouldn't be using this function]

The six comparison operators may be used for comparing degrees (using
the lexicographic ordering).

A [degree] object may be created by using one of the following functions:
wdeg(f)     where f is a RingElem belonging to a PolyRing (see PolyRing.txt)
wdeg(t)     where t is a PPMonoidElem  (see PPMonoid.txt)

Maintainer documentation for the class degree
=============================================

So far the implementation is very simple.  The primary design choice was to
use C++ std::vector<>s for holding the values -- indeed a [degree] object is
just a "wrapped up" vector of values of type [degree::ElementType].  For a
first implementation this conveniently hides issues of memory management
etc.  Since I do not expect huge numbers of [degree] objects to created and
destroyed, there seems little benefit in trying to use [MemPool]s (except it
might be simpler to detect memory leaks...)  I have preferred to make most
functions friends rather than members, mostly because I prefer the syntax
of normal function calls.

The [CheckCompatible] function is simple so I made it inline.  Note the type
of the third argument: it is deliberately not (a reference to) a
[std::string] because I wanted to avoid calling a ctor for a [std::string]
unless an error is definitely to be signalled.  I made it a private
static member function so that within it there is free access to
[myCoords], the data member of a [degree] object; also the call
]degree::CheckCompatible] makes it clear that it is special to degrees.

In implementations of functions on degrees I have preferred to place the
lengths of the degree vectors in a const local variable: it seems cleaner
than calling repeatedly [myCoords.size()], and might even be fractionally
faster.

[operator<<] handles the case of one-dimensional degrees specially so that
the value is not printed inside parentheses.

Bugs, Shortcomings and other ideas
==================================

How best to handle large and small degrees?
Always using ZZs would avoid problems associated with limits BUT may lead

There is public write-access to the components of a degree object.  Is this a bug?

No special handling for the case of a grading over Z (i.e. k=1) other
than for printing.  Is this really a shortcoming?

Printing via [operator<<] is perhaps rather crude?
Is the special printing for k=1 really such a clever idea?

GradingDim(const degree&) seems a bit redundant,
but it is clearer than "dim" or "size"

Why does mySetComponent only use CoCoA_ASSERT for the index range check?
Make operator[] return a proxy?
```

Definition at line 45 of file degree.H.

## Constructor & Destructor Documentation

 CoCoA::degree::degree ( std::size_t dim ) ` [inline]`
 Definition at line 76 of file degree.H.

## Member Function Documentation

 const ZZ& CoCoA::degree::operator[] ( std::size_t index ) const

 std::size_t CoCoA::degree::myGradingDim ( ) const` [inline]`
 Definition at line 81 of file degree.H. Referenced by CoCoA::FastCmp(), and CoCoA::GradingDim().

 void CoCoA::degree::mySetComponent ( std::size_t index, const ZZ & VALUE )
 deg[index] = VALUE

 void CoCoA::degree::mySetComponent ( std::size_t index, long value )
 deg[index] = value

 degree& CoCoA::degree::operator+= ( const degree & d )
 Computes deg1+=deg2.

 degree& CoCoA::degree::operator-= ( const degree & d )
 Computes deg1-=deg2.

 static void CoCoA::degree::CheckCompatible ( const degree & d1, const degree & d2, const char * fn ) ` [static]`
 checks dims are equal, throws if not.

## Friends And Related Function Documentation

 int FastCmp ( const degree & d1, const degree & d2 ) ` [friend]`
 like cmp but inline and no checks Definition at line 88 of file degree.H.

 bool IsZero ( const degree & d ) ` [friend]`

The documentation for this class was generated from the following file:
Generated on Wed May 23 13:46:14 2007 for CoCoALib by 1.4.6