Interface to GAP3#
This module implements an interface to GAP3.
AUTHORS:
Franco Saliola (February 2010)
Christian Stump (March 2016)
Warning
The experimental package for GAP3 is Jean Michel’s pre-packaged GAP3, which is a minimal GAP3 distribution containing packages that have no equivalent in GAP4, see github issue #20107 and also
Obtaining GAP3#
Instead of installing the experimental GAP3 package, one can as well install by hand either of the following two versions of GAP3:
Frank Luebeck maintains a GAP3 Linux executable, optimized for i686 and statically linked for jobs of 2 GByte or more:
or you can download GAP3 from the GAP website below. Since GAP3 is no longer supported, it may not be easy to install this version.
Changing which GAP3 is used#
Warning
There is a bug in the pexpect module (see github issue #8471) that
prevents the following from working correctly. For now, just make sure
that gap3 is in your PATH.
Sage assumes that GAP3 can be launched with the command gap3; that is,
Sage assumes that the command gap3 is in your PATH. If this is not
the case, then you can start GAP3 using the following command:
sage: gap3 = Gap3(command='/usr/local/bin/gap3') #not tested
Functionality and Examples#
The interface to GAP3 offers the following functionality.
gap3(expr)- Evaluation of arbitrary GAP3 expressions, with the result returned as a Sage object wrapping the corresponding GAP3 element:sage: a = gap3('3+2') #optional - gap3 sage: a #optional - gap3 5 sage: type(a) #optional - gap3 <class 'sage.interfaces.gap3.GAP3Element'>
sage: S5 = gap3('SymmetricGroup(5)') #optional - gap3 sage: S5 #optional - gap3 Group( (1,5), (2,5), (3,5), (4,5) ) sage: type(S5) #optional - gap3 <class 'sage.interfaces.gap3.GAP3Record'>
This provides a Pythonic interface to GAP3. If
gap_functionis the name of a GAP3 function, then the syntaxgap_element.gap_function()returns thegap_elementobtained by evaluating the commandgap_function(gap_element)in GAP3:sage: S5.Size() #optional - gap3 120 sage: S5.CharTable() #optional - gap3 CharTable( Group( (1,5), (2,5), (3,5), (4,5) ) )
Alternatively, you can instead use the syntax
gap3.gap_function(gap_element):sage: gap3.DerivedSeries(S5) #optional - gap3 [ Group( (1,5), (2,5), (3,5), (4,5) ), Subgroup( Group( (1,5), (2,5), (3,5), (4,5) ), [ (1,2,5), (1,3,5), (1,4,5) ] ) ]
If
gap_elementcorresponds to a GAP3 record, thengap_element.recfieldprovides a means to access the record element corresponding to the fieldrecfield:sage: S5.IsRec() #optional - gap3 true sage: S5.recfields() #optional - gap3 ['isDomain', 'isGroup', 'identity', 'generators', 'operations', 'isPermGroup', 'isFinite', '1', '2', '3', '4', 'degree'] sage: S5.identity #optional - gap3 () sage: S5.degree #optional - gap3 5 sage: S5.1 #optional - gap3 (1,5) sage: S5.2 #optional - gap3 (2,5)
By typing
%gap3orgap3.interact()at the command-line, you can interact directly with the underlying GAP3 session.sage: gap3.interact() #not tested --> Switching to Gap3 <-- gap3:
You can start a new GAP3 session as follows:
sage: gap3.console() #not tested ######## Lehrstuhl D fuer Mathematik ### #### RWTH Aachen ## ## ## # ####### ######### ## # ## ## # ## ## # # ## # ## #### ## ## # # ## ##### ### ## ## ## ## ######### # ######### ####### # # ## Version 3 # ### Release 4.4 # ## # 18 Apr 97 # ## # ## # Alice Niemeyer, Werner Nickel, Martin Schoenert ## # Johannes Meier, Alex Wegner, Thomas Bischops ## # Frank Celler, Juergen Mnich, Udo Polis ### ## Thomas Breuer, Goetz Pfeiffer, Hans U. Besche ###### Volkmar Felsch, Heiko Theissen, Alexander Hulpke Ansgar Kaup, Akos Seress, Erzsebet Horvath Bettina Eick For help enter: ?<return> gap>
The interface also has access to the GAP3 help system:
sage: gap3.help('help', pager=False) #not tested Help _______________________________________________________... This section describes together with the following sections the GAP help system. The help system lets you read the manual interactively...
Common Pitfalls#
If you want to pass a string to GAP3, then you need to wrap it in single quotes as follows:
sage: gap3('"This is a GAP3 string"') #optional - gap3 "This is a GAP3 string"
This is particularly important when a GAP3 package is loaded via the
RequirePackagemethod (note that one can instead use theload_packagemethod):sage: gap3.RequirePackage('"chevie"') #optional - gap3
Examples#
Load a GAP3 package:
sage: gap3.load_package("chevie") #optional - gap3
sage: gap3.version() # random #optional - gap3
'lib: v3r4p4 1997/04/18, src: v3r4p0 1994/07/10, sys: usg gcc ansi'
Working with GAP3 lists. Note that GAP3 lists are 1-indexed:
sage: L = gap3([1,2,3]) #optional - gap3
sage: L[1] #optional - gap3
1
sage: L[2] #optional - gap3
2
sage: 3 in L #optional - gap3
True
sage: 4 in L #optional - gap3
False
sage: m = gap3([[1,2],[3,4]]) #optional - gap3
sage: m[2,1] #optional - gap3
3
sage: [1,2] in m #optional - gap3
True
sage: [3,2] in m #optional - gap3
False
sage: gap3([1,2]) in m #optional - gap3
True
Controlling variable names used by GAP3:
sage: gap3('2', name='x') #optional - gap3
2
sage: gap3('x') #optional - gap3
2
sage: gap3.unbind('x') #optional - gap3
sage: gap3('x') #optional - gap3
Traceback (most recent call last):
...
TypeError: Gap3 produced error output
Error, Variable: 'x' must have a value
...
- class sage.interfaces.gap3.GAP3Element(parent, value, is_name=False, name=None)#
Bases:
GapElement_genericA GAP3 element
Note
If the corresponding GAP3 element is a GAP3 record, then the class is changed to a
GAP3Record.INPUT:
parent– the GAP3 sessionvalue– the GAP3 command as a stringis_name– bool (default: False); if True, thenvalueis the variable name for the objectname– str (default:None); the variable name to use for the object. IfNone, then a variable name is generated.
Note
If you pass
E,XorZforname, then an error is raised because these are sacred variable names in GAP3 that should never be redefined. Sage raises an error because GAP3 does not!EXAMPLES:
sage: from sage.interfaces.gap3 import GAP3Element #optional - gap3 sage: gap3 = Gap3() #optional - gap3 sage: GAP3Element(gap3, value='3+2') #optional - gap3 5 sage: GAP3Element(gap3, value='sage0', is_name=True) #optional - gap3 5
AUTHORS:
Franco Saliola (Feb 2010)
- class sage.interfaces.gap3.GAP3Record(parent, value, is_name=False, name=None)#
Bases:
GAP3ElementA GAP3 record
Note
This class should not be called directly, use GAP3Element instead. If the corresponding GAP3 element is a GAP3 record, then the class is changed to a
GAP3Record.AUTHORS:
Franco Saliola (Feb 2010)
- operations()#
Return a list of the GAP3 operations for the record.
OUTPUT:
list of strings - operations of the record
EXAMPLES:
sage: S5 = gap3.SymmetricGroup(5) #optional - gap3 sage: S5.operations() #optional - gap3 [..., 'NormalClosure', 'NormalIntersection', 'Normalizer', 'NumberConjugacyClasses', 'PCore', 'Radical', 'SylowSubgroup', 'TrivialSubgroup', 'FusionConjugacyClasses', 'DerivedSeries', ...] sage: S5.DerivedSeries() #optional - gap3 [ Group( (1,5), (2,5), (3,5), (4,5) ), Subgroup( Group( (1,5), (2,5), (3,5), (4,5) ), [ (1,2,5), (1,3,5), (1,4,5) ] ) ]
- recfields()#
Return a list of the fields for the record. (Record fields are akin to object attributes in Sage.)
OUTPUT:
list of strings - the field records
EXAMPLES:
sage: S5 = gap3.SymmetricGroup(5) #optional - gap3 sage: S5.recfields() #optional - gap3 ['isDomain', 'isGroup', 'identity', 'generators', 'operations', 'isPermGroup', 'isFinite', '1', '2', '3', '4', 'degree'] sage: S5.degree #optional - gap3 5
- class sage.interfaces.gap3.Gap3(command='gap3')#
Bases:
Gap_genericA simple Expect interface to GAP3.
EXAMPLES:
sage: from sage.interfaces.gap3 import Gap3 sage: gap3 = Gap3(command='gap3')
AUTHORS:
Franco Saliola (Feb 2010)
- console()#
Spawn a new GAP3 command-line session.
EXAMPLES:
sage: gap3.console() #not tested ######## Lehrstuhl D fuer Mathematik ### #### RWTH Aachen ## ## ## # ####### ######### ## # ## ## # ## ## # # ## # ## #### ## ## # # ## ##### ### ## ## ## ## ######### # ######### ####### # # ## Version 3 # ### Release 4.4 # ## # 18 Apr 97 # ## # ## # Alice Niemeyer, Werner Nickel, Martin Schoenert ## # Johannes Meier, Alex Wegner, Thomas Bischops ## # Frank Celler, Juergen Mnich, Udo Polis ### ## Thomas Breuer, Goetz Pfeiffer, Hans U. Besche ###### Volkmar Felsch, Heiko Theissen, Alexander Hulpke Ansgar Kaup, Akos Seress, Erzsebet Horvath Bettina Eick For help enter: ?<return> gap>
- cputime(t=None)#
Returns the amount of CPU time that the GAP session has used in seconds. If
tis not None, then it returns the difference between the current CPU time andt.EXAMPLES:
sage: t = gap3.cputime() #optional - gap3 sage: t #random #optional - gap3 0.02 sage: gap3.SymmetricGroup(5).Size() #optional - gap3 120 sage: gap3.cputime() #random #optional - gap3 0.14999999999999999 sage: gap3.cputime(t) #random #optional - gap3 0.13
- help(topic, pager=True)#
Print help on the given topic.
INPUT:
topic– string
EXAMPLES:
sage: gap3.help('help', pager=False) #optional - gap3 Help _______________________________________________________... This section describes together with the following sectio... help system. The help system lets you read the manual inter...
sage: gap3.help('SymmetricGroup', pager=False) #optional - gap3 no section with this name was found
- sage.interfaces.gap3.gap3_console()#
Spawn a new GAP3 command-line session.
EXAMPLES:
sage: gap3.console() #not tested ######## Lehrstuhl D fuer Mathematik ### #### RWTH Aachen ## ## ## # ####### ######### ## # ## ## # ## ## # # ## # ## #### ## ## # # ## ##### ### ## ## ## ## ######### # ######### ####### # # ## Version 3 # ### Release 4.4 # ## # 18 Apr 97 # ## # ## # Alice Niemeyer, Werner Nickel, Martin Schoenert ## # Johannes Meier, Alex Wegner, Thomas Bischops ## # Frank Celler, Juergen Mnich, Udo Polis ### ## Thomas Breuer, Goetz Pfeiffer, Hans U. Besche ###### Volkmar Felsch, Heiko Theissen, Alexander Hulpke Ansgar Kaup, Akos Seress, Erzsebet Horvath Bettina Eick For help enter: ?<return> gap>
- sage.interfaces.gap3.gap3_version()#
Return the version of GAP3 that you have in your PATH on your computer.
EXAMPLES:
sage: gap3_version() # random, optional - gap3 'lib: v3r4p4 1997/04/18, src: v3r4p0 1994/07/10, sys: usg gcc ansi'