This chapter is intended to give users who have experience with GAP 3 some information about what has changed in GAP 4.
In particular, it informs about changed command line options
(see Changed Command Line Options),
the new global variable fail
(see Fail),
some functions that have changed their behaviour
(see Changed Functionality) or their names
(see Changed Variable Names),
and some conventions used for variable names (see Naming Conventions).
Then the new concepts of GAP 4 are sketched, first that of mutability or immutability (see Immutability), with the explanation of related changes in functions that copy objects (see Copy), then the concepts of operations and method selection, which are compared with the use of operations records in GAP 3 (see Attributes vs. Record Components, Operations Records, and Operations vs. Dispatcher Functions).
More local changes affect the concepts of notions of generation
(see Different Notions of Generation),
of parents (see Parents and Subgroups),
of homomorphisms (see Homomorphisms vs. General Mappings,
Homomorphisms vs. Factor Structures,
and Isomorphisms vs. Isomorphic Structures),
how elements in finitely presented groups are treated
(see Elements of Finitely Presented Groups),
how information about progress of computations can be obtained
(see The Info Mechanism),
and how one gets information in a break
loop
(see Debugging).
While a ``GAP 3 compatibility mode'' is provided (see Compatibility Mode), its use will disable some of the new features of GAP 4. Also it certainly can only try to provide partial compatibility.
For a detailed explanation of the new features and concepts of GAP 4, see the manual ``Programming in GAP''.
In GAP 4, the -l
option is used to specify the root directory
(see GAP Root Directory in the Reference Manual)
of the GAP distribution,
which is the directory containing the lib
and doc
subdirectories.
Note that in GAP 3 this option was used to specify the path to the
lib
directory.
The -h
option of GAP 3 has been removed,
the path(s) for the documentation are deduced automatically in GAP 4.
The option -g
is now used to print information only about full garbage
collections.
The new option -g -g
generates information about partial
garbage collections too.
There is a new global variable
fail
in GAP 4.
It is intended as a return value of a function for the case that it
could not perform its task.
For example, Inverse
returns fail
if it is called with a singular
matrix, and Position
returns fail
if the second argument is not
contained in the list given as first argument.
GAP 3 handled such situations by either signalling an error,
for example if it was asked for the inverse of a singular matrix,
or by (mis)using false
as return value, as in the example Position
.
Note that in the first example, in GAP 3 it was necessary to check
the invertibility of a matrix before one could safely ask for its
inverse, which meant that roughly the same work was done twice.
Some functions that were already available in GAP 3 behave differently in GAP 4. This section lists them.
Orbit(
G,
pnt)
The GAP 3 manual promised that pnt would be the first entry of the resulting orbit. This was wrong already there in a few cases, therefore GAP 4 does not promise anything about the ordering of points in an orbit.
Order(
g )
only takes the element g and computes its multiplicative order.
Calling Order
with two arguments is permitted only in the
GAP 3 compatibility mode, see Compatibility Mode.
(Note that it does not make sense anymore to specify a group as
first argument w.r.t. which the order of the second argument shall
be computed, see Elements of Finitely Presented Groups.)
Position(
list,
obj )
If obj is not contained in the list list then fail
is returned
in GAP 4 (see Fail), whereas false
was returned in GAP 3.
PermGroupOps.ElementProperty(
G,
prop[,
K] )
In GAP 3, this function took either two or three arguments,
the optional argument K being a subgroup of G that stabilizes prop
in the sense that for any element g in G,
either all elements or no element in the coset g
*
K have the
property prop.
The GAP 4 function ElementProperty
, however,
takes between two and four arguments,
and the subgroup K known from GAP 3 has to be entered as the fourth
argument not the third.
(The third argument in the GAP 4 function denotes a subgroup U
stabilizing prop in the sense that either all elements or no element
in right cosets U
*
g have the property prop.)
(This discrepancy was discovered only in March 2002, short before the release of GAP 4.3.)
Print(
obj, ... )
Objects may appear on the screen in a different way,
depending on whether they are printed by the read eval print loop
or by an explicit call of Print
.
The reason is that the read eval print loop calls the operation ViewObj
and not PrintObj
, whereas Print
calls PrintObj
for each of its
arguments.
This permits the installation of methods for printing objects in a short form
in the read eval print loop while retaining Print
to display
the object completely.
See also Section View and Print in the Reference Manual.
(PrintObj
is installed as standard method ViewObj
, so it is
not really necessary to have a ViewObj
method for an object.)
PrintTo(
filename,
obj, ... )
In GAP 3, PrintTo
could be (mis)used to ``redirect'' the text
printed by a function (that is, not only the output of a function)
to a file by entering the function call as second argument.
This was used mainly in order to avoid many calls of AppendTo
.
In GAP 4, this feature has disappeared.
One can use streams (see Chapter Streams in the Reference Manual)
instead in order to write files efficiently.
Some functions have changed their name without changing the functionality. A -- probably incomplete -- list follows
GAP 3 GAP 4 AgGroup PcGroup # (also composita) ApplyFunc CallFuncList Backtrace Where CharTable CharacterTable # (also composita) Denominator DenominatorRat DepthVector PositionNot Elements AsSSortedList IsBijection IsBijective IsFunc IsFunction IsMat IsMatrix IsRec IsRecord IsSet IsSSortedList LengthWord Length NOfCyc Conductor Numerator NumeratorRat NormedVector NormedRowVector Operation Action # (also composita) Order(G,g) Order(g) OrderMat Order OrderPerm Order RandomInvertableMat RandomInvertibleMat RecFields RecNames X Indeterminate
See Section Compatibility Mode for a way to make the old names available again.
The way functions are named has been unified in GAP 4. This might help to memorize or even guess names of library functions.
If a variable name consists of several words then the first letter of each word is capitalized.
If the first part of the name of a function is a verb then the function
may modify its argument(s) but does not return anything,
for example Append
appends the list given as second argument to the
list given as first argument.
Otherwise the function returns an object without changing the arguments,
for example Concatenation
returns the concatenation of the lists
given as arguments.
If the name of a function contains the word By
then the return value is
thought of as built in a certain way from the parts given as arguments.
For example, GroupByGenerators
returns a group built from its group
generators, and creating a group as a factor group of a given group
by a normal subgroup can be done by taking the image of
NaturalHomomorphismByNormalSubgroup
(see also Homomorphisms vs. Factor Structures).
Other examples of ``By
'' functions are GroupHomomorphismByImages
and
UnivariateLaurentPolynomialByCoefficients
.
If the name of a function contains the word Of
then the return value is
thought of as information deduced from the arguments.
Usually such functions are attributes
(see Attributes in this Tutorial and Attributes
in the Reference Manual).
Examples are GeneratorsOfGroup
, which returns a list of generators for
the group entered as argument, or DiagonalOfMat
.
For the setter and tester functions of an attribute attr
(see Attributes vs. Record Components in this Tutorial
and Attributes in the Reference Manual)
the names Set
attr resp.
Has
attr are available.
If the name of a function fun1 ends with NC
then there is another
function fun2 with the same name except that the NC
is missing.
NC
stands for ``no check''.
When fun2 is called then it checks whether its arguments are valid,
and if so then it calls fun1.
The functions SubgroupNC
and Subgroup
are a typical example.
The idea is that the possibly time consuming check of the arguments
can be omitted if one is sure that they are unnecessary.
For example, if an algorithm produces generators of the derived subgroup
of a group then it is guaranteed that they lie in the original group;
Subgroup
would check this, and SubgroupNC
omits the check.
Needless to say, all these rules are not followed slavishly,
for example there is one operation Zero
instead of two operations
ZeroOfElement
and ZeroOfAdditiveGroup
.
GAP 4 supports ``immutable'' objects. Such objects cannot be
changed, attempting to do so issues an error. Typically attribute
values are immutable, and also the results of those binary arithmetic
operations where both arguments are immutable, see Section Vectors and Matrices. For example, [ 1 .. 100 ] + [ 1 .. 100 ]
is a
mutable list and 2 * Immutable( [ 1 .. 100 ] )
is an immutable
list, both are equal to the (mutable) list [ 2, 4 .. 200 ]
.
There is no way to make an immutable object mutable, one can only
get a mutable copy by ShallowCopy
. The other way round,
MakeImmutable
makes a (mutable or immutable) object and all its
subobjects immutable; one must be very careful to use MakeImmutable
only for those objects that are really newly created, for such objects
the advantage over Immutable
is that no copy is made.
More about immutability can be found in Sections Immutability in this tutorial and Mutability and Copyability in the Reference Manual.
The function Copy
of GAP 3 is not supported in GAP 4. This
function was used to create a copy cop of its argument obj with
the properties that cop and obj had no subobjects in common and
that if two subobjects of obj were identical then also the
corresponding subobjects of cop were identical.
The possibility of having immutable objects (see Immutability) can and
should be used to avoid unnecessary copying.
Namely, given an immutable object one needs to copy it only if one wants
to get a modified object, and in such a situation usually it is
sufficient to use ShallowCopy
, or at least one knows how deep one must
copy in order to do the changes one has in mind.
For example, suppose you have a matrix group, and you want to
construct a list of matrices by modifying the group generators. This
list of generators is immutable, so you call ShallowCopy
to get a
mutable list that contains the same matrices. If you only want to
exchange some of them, or to append some other matrices, this shallow
copy is already what you need. So suppose that you are interested in
a list of matrices where some rows are also changed. For that, you
call ShallowCopy
for the matrices in question, and you get matrices
whose rows can be changed. If you want to change single entries in
some rows, ShallowCopy
must be called to get mutable copies of these
rows. Note that in all these situations there is no danger to change,
i.e., to destroy the original generators of the matrix group.
If one needs the facility of the Copy
function of GAP 3 to get a
copy with the same structure then one can use the new GAP 4
function StructuralCopy
. It returns a structural copy that has no
mutable subobject in common with its argument. So if
StructuralCopy
is called with an immutable object then this object
itself is returned, and if StructuralCopy
is called with a mutable
list of immutable objects then a shallow copy of this list is
returned.
Note that ShallowCopy
now is an operation. So if you create your
own type of (copyable) objects then you must define what a shallow
copy of these objects is, and install an appropriate method.
In GAP 3, many complex objects were represented via records, for
example all domains. Information about these objects was stored in
components of these records. For the user, this was usually not
relevant, since there were functions for computing information about
the objects in question. For example, if one was interested in the
size of a group then one could call Size
.
But since it was guaranteed that the size of a domain D was stored
as value of the component size
, it was allowed to access D
.size
if this component was bound, and a check for this was possible via
IsBound(
D.size )
.
In GAP 4, only the access via functions is admissible. One reason is the following basic rule.
From the information that a given GAP 4 object is for example a domain, one cannot conclude that this object has a certain representation.
For attributes like Size
, GAP 4 provides two related functions,
the setter and the tester of the attribute, which can be used to
set an attribute value and to check whether the value of an attribute
is already stored for an object (see also Attributes in the
Reference Manual). For example, if D is a domain in GAP 4 then
HasSize(
D )
is true
if the size of D is already stored, and
false
otherwise. In the latter case, if you know that the size of
D is size then you may store it by SetSize(
D,
size )
.
Besides the flexibility in the internal representation of objects, storing information only via function calls has also the advantage that GAP 4 is able to draw conclusions automatically. For example, as soon as it is stored that a group is nilpotent, it is also stored that it is solvable, see Chapters Types of Objects in the Reference Manual and Method Selection in ``Programming in GAP'' for the details.
As a consequence, you cannot put your favourite information into a
domain D by assigning it to a new component like
D
.myPrivateInfo
. Instead you can introduce a new attribute and
then use its setter, see Attributes in the Reference Manual.
As in GAP 3, a domain in GAP 4 is a structured set.
The same set can have different structures, for example a field can be regarded as a ring or as an algebra or vector space over a subfield.
In GAP 3, however, an object representing a ring did not represent
a field, and an object representing a field did not represent a ring.
One reason for this was that the record component generators
was
used to denote the appropriate generators of the domain. For a ring
R, the component R
.generators
was a list of ring generators, and
for a field F, F
.generators
was a list of field generators.
GAP 4 cleans this up, see Notions of Generation. It supports many different notions of generation, for example one can ask for magma generators of a group or for generators of a field as an additive group. A subtle but important distinction is that between generators of an algebra and of an algebra-with-one.
So the attributes GeneratorsOfGroup
, GeneratorsOfMagma
,
GeneratorsOfRing
, GeneratorsOfField
, GeneratorsOfVectorSpace
,
and so on, replace the access to the generators
component.
Already in GAP 3 there were several functions that were applicable
to many different kinds of objects, for example Size
could be
applied to any domain, and the binary infix multiplication *
could
be used to multiply two matrices, an integer with a row vector, or a
permutation with a permutation group. This was implemented as
follows. Functions like Size
and *
tried to find out what
situation was described by its arguments, and then it called a more
specific function to compute the desired information. These more
specific functions, let us call them methods as they are also called
in GAP 4, were stored in so-called operations records of the
arguments.
For example, every domain in GAP 3 was represented as a record, and
the operations record was stored in the record component operations
.
If Size
was called for the domain then the method to compute the
size of the domain was found as value of the Size
component of the
operations record.
This was fine for functions taking only one argument, and in principle it is possible that for those functions an object stored an optimal method in its operations record. But in the case of more arguments this is not possible. In a multiplication of two objects in GAP 3, one had to choose between the methods stored in the operations records of the arguments, and if for example the method stored for the left operand was called, this method had to handle all possible right operands.
So operations records turned out to be not flexible enough. In GAP 4, operations records are not supported (see Compatibility Mode for a possibility to use your GAP 3 code that utilizes operations records, at least to some extent). A detailed description of the new mechanism to select methods can be found in Chapter Method Selection in ``Programming in GAP''.
An important point is that the new mechanism allows GAP to take the relation between arguments into account. So it is possible (and recommended) to install different methods for different relations between the arguments. Note that such methods need not do the extensive argument checking that was necessary in GAP 3, because most of the checks are done already by the method selection mechanism.
GAP 3 functions like Size
, CommutatorSubgroup
, or
SylowSubgroup
did mainly call an appropriate method (see Operations Records) after they had checked their arguments. Such functions were
called dispatchers in GAP 3. In GAP 4, many dispatchers have
been replaced by operations, due to the fact that methods are no
longer stored in operations records (see Method Selection in
``Programming in GAP'' for the details).
Most dispatchers taking only one argument were treated in a special
way in GAP 3, they had the additional task of storing computed
values and using these values in subsequent calls. For example, the
dispatcher Size
first checked whether the size of the argument was
already stored, and if so then this value was returned; otherwise a
method was called, the value returned by this method was stored in the
argument, and then returned by Size
.
In GAP 4, computed values of operations that take one argument (these operations are called attributes) are also stored, only the mechanism to achieve this has changed, see Attributes and Properties in the Reference Manual.
So the behaviour of Size
is the same in GAP 3 and GAP 4. But
note that in GAP 4, it is not possible to access D
.size
,
see Attributes vs. Record Components. As described in Operations Records, GAP 4 does not admit ``bypassing the dispatcher'' by
calling for example D
.operations.Size
. This was done in GAP 3
often for efficiency reasons, but the method selection mechanism of
GAP 4 is fast enough to make this unnecessary.
If you had written your own dispatchers and put your own methods into existing operations records then this code will not work in GAP 4. See Creating New Objects and Method Selection in ``Programming in GAP'' for a description of how to define operations and to install methods.
Finally, some functions in GAP 3 were hidden in
operations records, e.g., PermGroupOps.MovedPoints
.
These functions became proper operations in GAP 4.
In GAP 3 there was a strict distinction between parent groups and subgroups. The use of the name ``parent'' (instead of ``supergroup'') was chosen to indicate that the parent of an object was more than just useful information. In fact the main reason for the introduction of parents was to provide a common roof for example for all groups of polycyclic words that belonged to the same PC-presentation, or for all subgroups of a finitely presented group (see Elements of Finitely Presented Groups). A subgroup was never a parent group, and it was possible to create subgroups only of parent groups.
In GAP 4 this common roof is provided already by the concept of families, see Families in the Reference Manual. Thus it is no longer compulsory to use parent groups at all. On the other hand, parents may be used in GAP 4 to provide information about an object, for example the normalizer of a group in its parent group may be stored as an attribute value. Note that there is no restriction on the supergroup that is set to be the parent, it is possible to create a subgroup of any group, this group then being the parent of the new subgroup. This permits for example chains of subgroups with respective parents, of arbitrary length.
As a consequence, the Parent
command cannot be used in GAP 4 to
test whether the two arguments of CommutatorSubgroup
fit together,
this is now a question that concerns the relation between the families
of the groups. So the 2-argument version of Parent
and the now
meaningless function IsParent
have been abolished.
In GAP 3 there had been a confusion between group homomorphisms and
general mappings, as GroupHomomorphismByImages
created only a
general mapping that did not store whether it was a mapping. This
caused expensive, unwanted, and unnecessary tests whether the mapping
was in fact a group homomorphism. Moreover, the ``official''
workaround to set some components of the mapping record was quite
unwieldy.
In GAP 4, GroupHomomorphismByImages
checks whether the desired
mapping is indeed a group homomorphism; if so then this property is
stored in the returned mapping, otherwise fail
is returned. If you
want to avoid the checks then you can use
GroupHomomorphismByImagesNC
. If you want to check whether a general
mapping that respects the group operations is really a group
homomorphism, you can construct it via GroupGeneralMappingByImages
and then call IsGroupHomomorphism
for it. (Note that
IsGroupHomomorphism
returns true
if and only if both
IsGroupGeneralMapping
and IsMapping
do, so one does in fact check
IsMapping
in this case.)
There is no function IsHomomorphism
in GAP 4,
since there are several different operations with respect to which a
mapping can be a homomorphism.
If F is a factor structure of G, with kernel N, complete information about the connection between F and G is provided by the natural homomorphism.
In GAP 3, the ``official way'' to construct this natural homomorphism
was to create first the factor structure F, and then to call
NaturalHomomorphism
with the arguments G and F.
For that, the data necessary to compute the homomorphism was stored in
F when F was constructed.
In GAP 4, factor structures are not treated in a special way,
in particular they do not store information about a homomorphism.
Instead, the more natural way is taken to construct the natural
homomorphism from G and N by NaturalHomomorphismByNormalSubgroup
if N is a normal subgroup of the group G,
or by NaturalHomomorphismByIdeal
if N is an ideal in the ring G.
The factor F can then be accessed as the image of this homomorphism,
and of course G is the preimage and N is the kernel.
Note that GAP 4 does not guarantee anything about the representation of the factor F, it may be a permutation group or a polycyclically presented group or another kind of group. Also note that a natural homomorphism need not be surjective.
A consequence of this change is that GAP 4 does not allow you to construct a natural homomorphism from the groups G and F.
The other common type of homomorphism in GAP 3, ``operation homomorphisms'', have been replaced (just a name change) by action homomorphisms, which are handled in a similar fashion. That is, an action homomorphism is constructed from an acting group, an action domain, and a function describing the operation. The permutation group arising by the induced action is then the image of this operation homomorphism.
The GAP 3 function Operation
is still supported, under the name Action
,
but from the original group and the result of Action
it is not
possible to construct the action homomorphism.
In GAP 3, a different representation of a group could be obtained by
calling AgGroup
to get an isomorphic polycyclically presented group,
PermGroup
to get an isomorphic permutation group, and so on.
The returned objects stored an isomorphism in the record component
bijection
.
For the same reason as in Homomorphisms vs. Factor Structures,
GAP 4 puts emphasis on the isomorphism,
and the isomorphic object in the desired representation can be accessed
as its image.
So you can call IsomorphismPcGroup
or IsomorphismPermGroup
in order
to get an isomorphism to a polycyclically presented group or a
permutation group, respectively, and then call Image
to get the
isomorphic group.
Note that the image of an action homomorphism with trivial kernel is also an isomorphic permutation group, but an action homomorphism need not be surjective, since it may be easier to define it into the full symmetric group.
Further note that in GAP 3, a usual application of isomorphisms to polycyclically presented groups was to utilize the usually more effective algorithms for solvable groups. However, the new concept of polycyclic generating systems in GAP 4 makes it possible to apply these algorithms to arbitrary solvable groups, independent of the representation. For example, GAP 4 can handle polycyclic generating systems of solvable permutation groups. So in many cases, a change of the representation for efficiency reasons may be not necessary any longer.
In general IsomorphismFpGroup
will define a presentation on generators
chosen by the algorithm. The corresponding elements of the original
group can be obtained by the command
gens:=List(GeneratorsOfGroup(Image(isofp)),i->PreImagesRepresentative(isofp,i));If a presentation in the given generators is needed, the command
IsomorphismFpGroupByGenerators(
G,
gens)
will produce one.
Strictly speaking, GAP 3 did not support elements of finitely presented groups. Instead, the ``words in abstract generators'' of the underlying free groups were (mis)used. This caused problems whenever calculations with elements were involved, the most obvious ones being wrong results of element comparisons. Also functions that should in principle work for any group were not applicable to finitely presented groups. In effect, a finitely presented group had to be treated in a special way in GAP 3.
GAP 4 distinguishes free groups and their elements from finitely presented groups and their elements. Comparing two elements of a finitely presented group will yield either the correct result or no result at all.
Note that in GAP 4, the arithmetic and comparison operations for
group elements do not depend on a context provided by a group that
contains the elements. In particular, in GAP 4 it is not
meaningful to call Order(
G,
g )
for a group G and an element
g.
In GAP 3, polynomials were defined over a field. So a polynomial over
GF(3)
was different from a polynomial over GF(9)
, even if the
coefficients were exactly the same.
GAP 4 defines polynomials only over a characteristic. This makes it
possible for example to multiply a polynomial over GF(3)
with a polynomial
over GF(9)
without the need to convert the former to the larger field.
However it has an effect on the result of DefaultRing
for polynomials:
In GAP 3 the default ring for a polynomial was the polynomial ring of the
field over which the polynomial was defined. In GAP 4 no field is
associated, so (to avoid having to define the algebraic closure as the only
other sensible alternative) the default ring of a polynomial is the
DefaultRing
of its coefficients.
This has an effect on Factors
: If no ring is given, a polynomial is
factorized over its DefaultRing
and so Factors(
poly)
might return different results.
To be safe from this problem, if you are not working over prime fields,
rather call Factors(
pring,
poly)
with the appropriate polynomial ring
and change your code accordingly.
Sometimes it is useful to get information about the progress of a calculation. Many GAP functions contain statements to display such information under certain conditions.
In GAP 3, these statements were calls to functions such as
InfoGroup1
or InfoGroup2
, and if the user assigned Print
to
these variables then this had the effect to switch on the printing of
information.
InfoGroup2
was used for more detailed information than InfoGroup1
.
One could switch off the printing again by assigning Ignore
to the
variables, and Ignore
was also the default value.
GAP 4 uses one function Info
for the same purpose,
which is a function that takes as first argument an info class such as
InfoGroup
, as second argument an info level, and the print statements
as remaining arguments.
The level of an info class class is set to level by calling
SetInfoLevel(
class,
level )
.
An Info
statement is printed only if its second argument is smaller than
or equal to the current info level.
For example,
gap> test:= function( obj ) > Info( InfoGroup, 2, "This is useful, isn't it?" ); > return obj; > end;; gap> test( 1 ); 1 gap> SetInfoLevel( InfoGroup, 2 ); gap> test( 1 ); #I This is useful, isn't it? 1
As in GAP 3, if an info statement is ignored then its arguments are not evaluated.
If GAP 4 runs into an error or is interrupted,
it enters a break loop.
The command Where(
number )
, which replaces Backtrace
of GAP 3,
can be used to display number lines of information about the current
function call stack.
As in GAP 3, access is only possible to the variables of the current
level in the function stack,
but in GAP 4 the function DownEnv
, with a positive or negative
integer as argument, permits one to step down or up in the
stack.
When interrupting, the first line printed by Where
actually may be
one level higher, as the following example shows
gap> OnBreak := function() Where(0); end;; # eliminate back-tracing on gap> # entry to break loop gap> test:= function( n ) > if n > 3 then Error( "!\n" ); fi; test( n+1 ); end;; gap> test( 1 ); Error, ! Entering break read-eval-print loop ... you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> Where(); called from test( n + 1 ); called from test( n + 1 ); called from test( n + 1 ); called from <function>( <arguments> ) called from read-eval-loop brk> n; 4 brk> DownEnv(); brk> n; 3 brk> Where(); called from test( n + 1 ); called from test( n + 1 ); called from <function>( <arguments> ) called from read-eval-loop brk> DownEnv( 2 ); brk> n; 1 brk> Where(); called from <function>( <arguments> ) called from read-eval-loop brk> DownEnv( -2 ); brk> n; 3 brk> quit; gap> OnBreak := Where;; # restore OnBreak to its default value
For purposes of debugging, it can be helpful sometimes, to see what
information is stored within an object. In GAP 3 this was possible using
RecFields
because the objects in question were represented via records.
For component objects, GAP 4 permits the same by
NamesOfComponents(
object )
, which will list all components present.
For users who want to use GAP 3 code with as little changes as possible, a compatibility mode is provided by GAP 4. This mode must be turned on explicitly by the user.
It should be noted that this compatibility mode has not been tested thoroughly.
The compatibility mode can be turned on by loading some of the following
files with ReadLib
.
The different files address different aspects of compatibility.
compat3a.g
CharTable
and SubgroupFusions
,
are available after compat3a.g
has been read;
the only exceptions are names of operations records.
compat3b.g
D.myInfo
, there are components associated to
attributes; for example
D.size
is redirected to the call of the
attribute Size
, IsBound(
D.size )
to the call of its tester,
and
D.size:=
val
to the call of its setter.
(An important special case is the component operations
, see below.)
compat3c.g
Print
method and
the basic arithmetic operations.
When using operations records, it is probably a good idea to
use immutable operations records; for example, if the results
of arithmetic operations are records with operations records then
this avoids to create shallow copies of the operations records
in the call to Immutable
for the results.
The following features are accessible only via starting GAP with
the command line option -O
and may damage some features of GAP 4
permanently for the current session.
With this option, also the files listed above are read automatically.
compat3d.g
Domain
, simulates the
GAP 3 behaviour of IsString
(to convert a list to string
representation if possible), and replaces fail
by false
;
these changes destroy parts of the functionality of GAP 4.
Some words concerning the simulation of operations records may be necessary.
The operations records of the GAP 3 library, such as DomainOps
and GroupOps
, are available only for access to their components,
whose values are GAP 4 operations; for example, the value of both
DomainOps.Size
and GroupOps.Size
is the operation Size
. So it
is not safely possible to delegate from a Size
method in another
operations record to DomainOps.Size
. Also it is not possible to
change these predefined operations records.
If one wants to install individual methods for a given object obj
via the mechanism of operations records then one can construct a new
operations record with OperationsRecord
, assign the desired methods
to components of this record, and then assign the operations record to
obj
.operations
. Whenever an operation that is associated with a
component nam of the operations record is called with obj as first
argument, the value of nam is chosen as the method.
In the case of the binary operations =
, <
, +
, -
, *
, /
,
Comm
, and LeftQuotient
,
this also happens if obj is the right-hand argument.
As in GAP 3, if both arguments of one of the above binary operations
have operations records containing a function for this operation,
then the function in the operations record of the right-hand argument
is chosen.
We give a small example how the compatibility mode works.
Suppose we want to deal with new objects that are derived from known field elements by distorting their multiplication. Namely, let a′ and b′ be the new objects corresponding to the field elements a, b, and define a′* b′ = a b − a − b + 2.
In GAP 3, this problem was solved by representing each new object
by a record that stored the corresponding ``old'' object and an
operations record, where the latter was a record containing the
functions applicable to the new object. After the library file
compat3c.g
has been read, we can use this construction of the
operations record and of the new objects. Note that operations
records must be created with the function OperationsRecord
(this was
also the norm in GAP 3), starting with an empty record would not work.
For our intended application, we thus start with the following two
lines of code.
gap> ReadLib( "compat3c.g" ); gap> MyOps:= OperationsRecord( "MyOps" );; HasMyOps := NewFilter( "HasMyOps" );
In order to make the translation from GAP 3 code to GAP 4
easier, GAP prints the definition of filters associated with
operations records and the method installations for operations
corresponding to components of the operations records. The output
line printed by GAP after the call of OperationsRecord
is one
such case.
Now we add our multiplication function to the operations record, and again GAP 4 prints a translation to GAP 4 code.
gap> MyOps.\* := function( a, b ) > return rec( x:= a.x * b.x - a.x - b.x + 2, > operations := MyOps ); > end;; # If the following method installation matches the requirements # of the operation `PROD' then `InstallMethod' should be used. # It might be useful to replace the rank `SUM_FLAGS' by `0'. InstallOtherMethod( PROD, "for object with `MyOps' as first argument", true, [ HasMyOps, IsObject ], SUM_FLAGS, MyOps.\* ); # For binary infix operators, a second method is installed # for the case that the object with `MyOps' is the right operand; # since this case has higher priority in GAP 3, the method is # installed with higher rank `SUM_FLAGS + 1'. InstallOtherMethod( PROD, "for object with `MyOps' as second argument", true, [ IsObject, HasMyOps ], SUM_FLAGS + 1, MyOps.\* );
Let us look how this installation works.
gap> a:= rec( x:= 3, operations:= MyOps ); rec( x := 3, operations := MyOps ) gap> b:= rec( x:= 5, operations:= MyOps ); rec( x := 5, operations := MyOps ) gap> a * b; rec( x := 9, operations := MyOps )
(In more complicated cases, we might run into problems, but this was already the case in GAP 3. For example, suppose we want to support the multiplication of two operands having different operations records; then it is not clear which of the two multiplication functions is to be chosen, and in GAP 3, the only way out was to change the multiplication functions, in order to make them aware of such situations.)
If we are now interested to translate the code to GAP 4 in the sense that no compatibility mode is needed, we can use what GAP 4 has printed above. (The same example is dealt with in Chapter An Example -- Designing Arithmetic Operations of ``Programming in GAP''.)
The objects will no longer be records with operations
component.
Instead of records we may use so-called component objects
with record-like access to components,
and instead of the operations
component, we give the objects a
type that has the filter HasMyOps
set.
HasMyOps := NewFilter( "HasMyOps" ); MyType := NewType( NewFamily( "MyFamily" ), HasMyOps and IsComponentObjectRep );(More about families and representations in this context can be found in the chapter of ``Programming in GAP'' mentioned above.)
The next step is to write a function that creates a new object. It may look as follows.
MyObject := function( val ) return Objectify( MyType, rec( x:= val ) ); end;
The multiplication function shall return an object with the
filter HasMyOp
, so we change it as follows.
gap> MyMult := function( a, b ) > return MyObject( x:= a!.x * b!.x - a!.x - b!.x + 2 ); > end;;Note that the component access for these objects works via
!.
instead of .
;
further note that no operations record needs to appear here,
the filter takes its role.
Finally, we install the multiplication for at least one argument with the new filter, as had been printed by GAP 4 in the session shown above.
InstallOtherMethod( PROD, "for object with `MyOps' as first argument", true, [ HasMyOps, IsObject ], 0, MyMult ); InstallOtherMethod( PROD, "for object with `MyOps' as second argument", true, [ IsObject, HasMyOps ], 1, MyMult );And now the example works (again).
gap> a:= MyObject( 3 ); <object> gap> b:= MyObject( 5 ); <object> gap> a * b; <object> gap> last!.x 9
We may install a method to print our objects in a nice way;
we could have done this for the operations record MyOps
in the compatibility mode,
the printed output would look similar to the following.
InstallOtherMethod( PRINT_OBJ, "for object with `MyOps' as first argument", true, [ HasMyOps ], 0, function( obj ) Print( "MyObject( ", obj!.x, " )" ); end );
Now the example behaves as follows.
gap> a; b; a * b; MyObject( 3 ) MyObject( 5 ) MyObject( 9 )
Maybe now we want to improve the installation.
The multiplication function we want to use is apparently
thought only for the case that both operands have
the filter HasMyOps
(and a component x
).
So it is reasonable to replace the two methods for
the multiplication by one method for which both arguments
are required to have the filter.
InstallOtherMethod( PROD, "for two objects with `MyOps'", true, [ HasMyOps, HasMyOps ], 0, MyMult );
At first sight, the GAP 4 approach seems to be much more
complicated.
But the last example shows that in GAP 4,
each method can be installed more specifically for the appropriate
situation.
Moreover, it is for example possible to install a method
for the multiplication of an integer and a HasMyOps
object;
note that --contrary to the situation in GAP 3--
such a method is independent from already existing methods
in the sense that these need not be changed when
new functionality is added.
Another example that uses this part of the compatibility mode can be
found in the file tst/compat3.tst
of the GAP 4 distribution.
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GAP 4 manual
March 2006