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# libGAP shared library Interface to GAP

libGAP shared library Interface to GAP

This module implements a fast C library interface to GAP. To use libGAP you simply call `libgap` (the parent of all `GapElement` instances) and use it to convert Sage objects into GAP objects.

EXAMPLES:

    sage: a = libgap(10)
    sage: a
    10
    sage: type(a)
    <type 'sage.libs.gap.element.GapElement_Integer'>
    sage: a*a
    100
    sage: timeit('a*a')   # random output
    625 loops, best of 3: 898 ns per loop

Compared to the expect interface this is >1000 times faster:

    sage: b = gap('10')
    sage: timeit('b*b')   # random output; long time
    125 loops, best of 3: 2.05 ms per loop

If you want to evaluate GAP commands, use the `Gap.eval()` method:

    sage: libgap.eval('List([1..10], i->i^2)')
    [ 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 ]

not to be confused with the `libgap` call, which converts Sage objects to GAP objects, for example strings to strings:

    sage: libgap('List([1..10], i->i^2)')
    "List([1..10], i->i^2)"
    sage: type(_)
    <type 'sage.libs.gap.element.GapElement_String'>

You can usually use the `sage()` method to convert the resulting GAP element back to its Sage equivalent:

    sage: a.sage()
    10
    sage: type(_)
    <type 'sage.rings.integer.Integer'>

    sage: libgap.eval('5/3 + 7*E(3)').sage()
    7*zeta3 + 5/3

    sage: generators = libgap.AlternatingGroup(4).GeneratorsOfGroup().sage()
    sage: generators   # a Sage list of Sage permutations!
    [(1,2,3), (2,3,4)]
    sage: PermutationGroup(generators).cardinality()   # computed in Sage
    12
    sage: libgap.AlternatingGroup(4).Size()            # computed in GAP
    12

So far, the following GAP data types can be directly converted to the corresponding Sage datatype:

1. GAP booleans `true` / `false` to Sage booleans `True` / `False`. The third GAP boolean value `fail` raises a `ValueError`.
2. GAP integers to Sage integers.
3. GAP rational numbers to Sage rational numbers.
4. GAP cyclotomic numbers to Sage cyclotomic numbers.
5. GAP permutations to Sage permutations.
6. The GAP containers `List` and `rec` are converted to Sage containers `list` and `dict`. Furthermore, the `sage()` method is applied recursively to the entries.

Special support is available for the GAP container classes. GAP lists can be used as follows:

    sage: lst = libgap([1,5,7]);  lst
    [ 1, 5, 7 ]
    sage: type(lst)
    <type 'sage.libs.gap.element.GapElement_List'>
    sage: len(lst)
    3
    sage: lst[0]
    1
    sage: [ x^2 for x in lst ]
    [1, 25, 49]
    sage: type(_[0])
    <type 'sage.libs.gap.element.GapElement_Integer'>

Note that you can access the elements of GAP `List` objects as you would expect from Python (with indexing starting at 0), but the elements are still of type `GapElement`. The other GAP container type are records, which are similar to Python dictionaries. You can construct them directly from Python dictionaries:

    sage: libgap({'a':123, 'b':456})
    rec( a := 123, b := 456 )

Or get them as results of computations:

    sage: rec = libgap.eval('rec(a:=123, b:=456, Sym3:=SymmetricGroup(3))')
    sage: rec['Sym3']
    Sym( [ 1 .. 3 ] )
    sage: dict(rec)
    {'Sym3': Sym( [ 1 .. 3 ] ), 'a': 123, 'b': 456}

The output is a Sage dictionary whose keys are Sage strings and whose Values are instances of `GapElement()`. So, for example, `rec['a']` is not a Sage integer. To recursively convert the entries into Sage objects, you should use the `sage()` method:

    sage: rec.sage()
    {'Sym3': NotImplementedError('cannot construct equivalent Sage object',),
     'a': 123,
     'b': 456}

Now `rec['a']` is a Sage integer. We have not implemented the conversion of the GAP symmetric group to the Sage symmetric group yet, so you end up with a `NotImplementedError` exception object. The exception is returned and not raised so that you can work with the partial result.

While we don’t directly support matrices yet, you can convert them to Gap List of Lists. These lists are then easily converted into Sage using the recursive expansion of the `sage()` method:

    sage: M = libgap.eval('BlockMatrix([[1,1,[[1, 2],[ 3, 4]]], [1,2,[[9,10],[11,12]]], [2,2,[[5, 6],[ 7, 8]]]],2,2)')
    sage: M
    <block matrix of dimensions (2*2)x(2*2)>
    sage: M.List()   # returns a GAP List of Lists
    [ [ 1, 2, 9, 10 ], [ 3, 4, 11, 12 ], [ 0, 0, 5, 6 ], [ 0, 0, 7, 8 ] ]
    sage: M.List().sage()   # returns a Sage list of lists
    [[1, 2, 9, 10], [3, 4, 11, 12], [0, 0, 5, 6], [0, 0, 7, 8]]
    sage: matrix(ZZ, _)
    [ 1  2  9 10]
    [ 3  4 11 12]
    [ 0  0  5  6]
    [ 0  0  7  8]

## Using the libGAP C library from Cython

The lower-case `libgap_foobar` functions are ones that we added to make the libGAP C shared library. The `libGAP_foobar` methods are the original GAP methods simply prefixed with the string `libGAP_`. The latter were originally not designed to be in a library, so some care needs to be taken to call them.

In particular, you must call `libgap_mark_stack_bottom()` in every function that calls into the libGAP C functions. The reason is that the GAP memory manager will automatically keep objects alive that are referenced in local (stack-allocated) variables. While convenient, this requires to look through the stack to find anything that looks like an address to a memory bag. But this requires vigilance against the following pattern:

    cdef f()
      libgap_mark_stack_bottom()
      libGAP_function()

    cdef g()
      libgap_mark_stack_bottom();
      f()                #  f() changed the stack bottom marker
      libGAP_function()  #  boom

The solution is to re-order `g()` to first call `f()`. In order to catch this error, it is recommended that you wrap calls into libGAP in `libgap_enter` / `libgap_exit` blocks and not call `libgap_mark_stack_bottom` manually. So instead, always write

> cdef f()
>   libgap_enter() libGAP_function() libgap_exit()
> cdef g()
>   f() libgap_enter() libGAP_function() libgap_exit()

If you accidentally call `libgap_enter()` twice then an error message is printed to help you debug this:

    sage: from sage.libs.gap.util import error_enter_libgap_block_twice
    sage: error_enter_libgap_block_twice()
    Traceback (most recent call last):
    ...
    RuntimeError: Entered a critical block twice

AUTHORS:

> - William Stein, Robert Miller (2009-06-23): first version
> - Volker Braun, Dmitrii Pasechnik, Ivan Andrus (2011-03-25, Sage Days 29): almost complete rewrite; first usable version.
> - Volker Braun (2012-08-28, GAP/Singular workshop): update to gap-4.5.5, make it ready for public consumption.

class `sage.libs.gap.libgap.``Gap`

  Bases: `sage.structure.parent.Parent`

  The libgap interpreter object.

  Note

  This object must be instantiated exactly once by the libgap. Always use the provided `libgap` instance, and never instantiate `Gap` manually.

  EXAMPLES:

      sage: libgap.eval('SymmetricGroup(4)')
      Sym( [ 1 .. 4 ] )

  TESTS:

      sage: TestSuite(libgap).run(skip=['_test_category', '_test_elements', '_test_pickling'])

  `Element`

    alias of `GapElement`

  `collect`()

    Manually run the garbage collector

    EXAMPLES:

        sage: a = libgap(123)
        sage: del a
        sage: libgap.collect()

  `count_GAP_objects`()

    Return the number of GAP objects that are being tracked by libGAP

    OUTPUT:

    An integer

    EXAMPLES:

        sage: libgap.count_GAP_objects()   # random output
        5

  `eval`(gap_command)

    Evaluate a gap command and wrap the result.

    INPUT:

    - `gap_command` – a string containing a valid gap command without the trailing semicolon.

    OUTPUT:

    A `GapElement`.

    EXAMPLES:

        sage: libgap.eval('0')
        0
        sage: libgap.eval('"string"')
        "string"

  `function_factory`(function_name)

    Return a GAP function wrapper

    This is almost the same as calling `libgap.eval(function_name)`, but faster and makes it obvious in your code that you are wrapping a function.

    INPUT:

    - `function_name` – string. The name of a GAP function.

    OUTPUT:

    A function wrapper `GapElement_Function` for the GAP function. Calling it from Sage is equivalent to calling the wrapped function from GAP.

    EXAMPLES:

        sage: libgap.function_factory('Print')
        <Gap function "Print">

  `get_global`(variable)

    Get a GAP global variable

    INPUT:

    - `variable` – string. The variable name.

    OUTPUT:

    A `GapElement` wrapping the GAP output. A `ValueError` is raised if there is no such variable in GAP.

    EXAMPLES:

        sage: libgap.set_global('FooBar', 1)
        sage: libgap.get_global('FooBar')
        1
        sage: libgap.unset_global('FooBar')
        sage: libgap.get_global('FooBar')
        Traceback (most recent call last):
        ...
        ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar

  `global_context`(variable, value)

    Temporarily change a global variable

    INPUT:

    - `variable` – string. The variable name.
    - `value` – anything that defines a GAP object.

    OUTPUT:

    A context manager that sets/reverts the given global variable.

    EXAMPLES:

        sage: libgap.set_global('FooBar', 1)
        sage: with libgap.global_context('FooBar', 2):
        ....:     print libgap.get_global('FooBar')
        2
        sage: libgap.get_global('FooBar')
        1

  `mem`()

    Return information about libGAP memory usage

    The GAP workspace is partitioned into 5 pieces (see gasman.c in the GAP sources for more details):

    - The masterpointer area contains all the masterpointers of the bags.
    - The old bags area contains the bodies of all the bags that survived at least one garbage collection. This area is only scanned for dead bags during a full garbage collection.
    - The young bags area contains the bodies of all the bags that have been allocated since the last garbage collection. This area is scanned for dead bags during each garbage collection.
    - The allocation area is the storage that is available for allocation of new bags. When a new bag is allocated the storage for the body is taken from the beginning of this area, and this area is correspondingly reduced. If the body does not fit in the allocation area a garbage collection is performed.
    - The unavailable area is the free storage that is not available for allocation.

    OUTPUT:

    This function returns a tuple containing 5 integers. Each is the size (in bytes) of the five partitions of the workspace. This will potentially change after each GAP garbage collection.

    EXAMPLES:

        sage: libgap.collect()
        sage: libgap.mem()   # random output
        (1048576, 6706782, 0, 960930, 0)

        sage: libgap.FreeGroup(3)
        <free group on the generators [ f1, f2, f3 ]>
        sage: libgap.mem()   # random output
        (1048576, 6706782, 47571, 913359, 0)

        sage: libgap.collect()
        sage: libgap.mem()   # random output
        (1048576, 6734785, 0, 998463, 0)

  `set_global`(variable, value)

    Set a GAP global variable

    INPUT:

    - `variable` – string. The variable name.
    - `value` – anything that defines a GAP object.

    EXAMPLES:

        sage: libgap.set_global('FooBar', 1)
        sage: libgap.get_global('FooBar')
        1
        sage: libgap.unset_global('FooBar')
        sage: libgap.get_global('FooBar')
        Traceback (most recent call last):
        ...
        ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar

  `show`()

    Print statistics about the GAP owned object list

    Slight complication is that we want to do it without accessing libgap objects, so we don’t create new GapElements as a side effect.

    EXAMPLES:

        sage: a = libgap(123)
        sage: b = libgap(456)
        sage: c = libgap(789)
        sage: del b
        sage: libgap.show() # random output
        11 LibGAP elements currently alive
        rec( full := rec( cumulative := 122, deadbags := 9,
        deadkb := 0, freekb := 7785, livebags := 304915,
        livekb := 47367, time := 33, totalkb := 68608 ),
        nfull := 3, npartial := 14 )

  `trait_names`()

    Return all Gap function names.

    OUTPUT:

    A list of strings.

    EXAMPLES:

        sage: len(libgap.trait_names()) > 1000
        True

  `unset_global`(variable)

    Remove a GAP global variable

    INPUT:

    - `variable` – string. The variable name.

    EXAMPLES:

        sage: libgap.set_global('FooBar', 1)
        sage: libgap.get_global('FooBar')
        1
        sage: libgap.unset_global('FooBar')
        sage: libgap.get_global('FooBar')
        Traceback (most recent call last):
        ...
        ValueError: libGAP: Error, VAL_GVAR: No value bound to FooBar

  `zero_element`()

    Return (integer) zero in GAP.

    OUTPUT:

    A `GapElement`.

    EXAMPLES:

        sage: libgap.zero_element()
        0

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