      module
      Copyright (c)  2005,2009 John Abbott
      GNU Free Documentation License, Version 1.2
%!includeconf: ../aux-txt2tags/config.t2t
      TeXTitle{module}{John Abbott}



== User documentation for the classes module, ModuleBase, ModuleElem ==
%======================================================================

You may also wish to look at the documentation for [[FGModule]]
the type which represents (explicitly) Finitely Generated Modules.

The classes ``module``, ``ModuleBase`` and ``ModuleElem`` are closely linked
together (analogously to the triple ``ring``, ``RingBase`` and ``RingElem``).

The class ``module`` is a reference counting smart pointer to an object of
type derived from ``ModuleBase``; all concrete types for representing modules
are derived from ``ModuleBase``.  For a library implementor the class
``ModuleBase`` defines the minimal interface which every concrete module
class must offer; indeed the concrete class must be derived from
``ModuleBase``.


A user of CoCoALib who does not wish to add to the library need
know only what it is in this section.

Analogously to ``ring``s and ``RingElem``s, every ``ModuleElem`` belongs to some
``module``.  So before you can compute with ``ModuleElem``s you must create the
``module``(s) which contain them.

To create a ``module`` you must a pseudo-constructor for one of the concrete
module classes (refer to their documentation for details): //e.g.//
```  NewFreeModule(R, n)   -- create a new FreeModule of n components over R


The functions which one may apply directly to a module are:
```
  NumCompts(M) -- the number of components an element of M has
  BaseRing(M)  -- the base ring of M (i.e. M is a module over this ring)
  gens(M)      -- a read only C++ vector containing the generators of M
  zero(M)      -- a read only ModuleElem which is the zero of M
  M1 == M2     -- are the two modules identical (same repr in memory)?
  M1 != M2     -- opposite of M1 == M2
```
As you can see there is not a lot one can do to a module.  Primarily
they exist to "give the correct type" to module elements; internally
they play a crucial role in applying operations to module elements.  A
C++ value of type ``ModuleElem`` represents an element of some concrete
module.  The module to which the value belongs is called the ``owner`` of
that value.  The owner of an object of type ``ModuleElem`` must be specified
(explicitly or implicitly) when it is created, and cannot be changed
during the lifetime of the object; the value it contains may, however,
be changed (C++ const rules permitting).


==== Functions on ModuleElems ====

Let ``v`` be a non-const ``ModuleElem``, and ``v1, v2`` be ``const ModuleElems`` all
belonging to the same concrete module ``M``.  Let ``R`` be the base ring of ``M``,
and ``r`` a const element of ``R``.  Then we summarize the possible operations
using C++ syntax:
```
owner(v1)   // gives the module to which v1 belongs

-v1                                       // Usual arithmetic operations
v1 + v2                    v1 - v2        // between ModuleElems and
r * v1                     v1 * r         // RingElems.
                           v1 / r
v = v1
v += v1                    v -= v1
v *= r                     v /= r
v1 == v2                   v1 != v2
IsZero(v1)                 cout << v1

v[pos]  // throws if the module is not FGModule 
```

In every case it is an error to combine/compare ``ModuleElems`` belonging to
different modules.  As you would expect, instead of multiplying or dividing
by a [[RingElem]] you may also multiply or divide by a machine integer, a
[[BigInt]] or a [[BigRat]].



== Maintainer documentation for the classes module, and ModuleElem ==
%======================================================================

I shall suppose that the user documentation has already been read and
digested.  It could also be helpful to have read the documentation for
[[ring]] since the design philosophy here imitates that used for rings.

The class ``module`` is simply a reference counting smart pointer class to a
concrete module (//i.e.// an object belonging to a class derived from
``ModuleBase``).

A ``ModuleElem``, like a ``RingElem``, comprises two components: one specifying
the algebraic structure to which the value belongs, and the other being
an opaque representation of the value which can be correctly interpreted
only by the owning module.  The data members are:
```
  module myM;             // the module to which the ModuleElem belongs
  ModuleRawValue myValue; // "opaque" representation of the value,
                          // concrete modules must "import" this value.
```



The design philosophy for modules follows closely that used for rings.  This means
that every operation on ``ModuleElem``s is actually effected by calling
the appropriate member function of the owning ``module``.  These member
functions expect raw values as input.  A normal ``ModuleElem`` stores
within itself both the identity of the ``module`` to which it belongs and
its value as an element of that particular module -- we call the first
datum the ``owner`` and the second datum the ``RawValue``.  A RawValue can
be correctly interpreted only if supplied as argument to a member
function of the owning module -- calling module member functions for
an incompatible concrete module and RawValue will very likely have
grave consequences (officially stated as //undefined behaviour//, and
most probably perceived as a program crash).

The member functions of a module **do not check** their arguments for being
sensible.  This decision is largely just a design policy imitating
that used for rings, but may also lead to some slight beneficial effect
on run-time performance.  It does naturally imply that the programmer
bears a considerable burden of responsibility.


==== (2.1) Member functions for operations on raw values  [IGNORE THIS -- OUT OF DATE] ====

For ring elements (especially those in a small finite field), noticeable
speed gains arise from using directly raw values and ring member
functions.  For modules the analogous effect exists in theory but will
likely be negligible in practice.  Nevertheless we list here the member
functions of a module; this list will be useful to library authors who
wish to create their own concrete module classes.

Let ``v`` be a non-const RawValue, and ``v1, v2`` const RawValues belonging to ``M``.
Let ``r`` be a RingBase::RawValue belonging to the base ring of ``M``.
```
M.myNumCompts()
M.myBaseRing()
M.myGens()        -- returns a const ref to a C++ vector of module:elems
M.myZero()        -- returns a const ref to a ModuleElem

M.myNew(v)       -- allocates resources, apply only to uninitialized RawValue
M.myNew(v, v1)   -- allocates resources, apply only to uninitialized RawValue
M.myDelete(v)    -- releases resources
M.mySwap(v, w)
M.myAssign(v, v1)
M.myNegate(v, v1)
M.myAdd(v, v1, v2)
M.mySub(v, v1, v2)
M.myMul(v, r, v1)
M.myDiv(v, r, v1) -- NOTE funny arg order!
M.myOutput(out, v1)
M.myOutputSelf(out)
M.myIsZero(v1)
M.myIsEqual(v1, v2)
```


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

This code is too new, largely untried/untested.  As soon as it gets
some use, there will be some material to put here :-)

The documentation is very incomplete.  Will be fixed (eventually).
Maintainer documentation is incompleter than user doc.

