libGAP element wrapper¶

libGAP element wrapper

This document describes the individual wrappers for various GAP elements. For general information about libGAP, you should read the libgap module documentation.

class sage.libs.gap.element.GapElement¶

Bases: sage.structure.element.RingElement

Wrapper for all Gap objects.

Note

In order to create GapElements you should use the libgap instance (the parent of all Gap elements) to convert things into GapElement. You must not create GapElement instances manually.

EXAMPLES:

sage: libgap(0)
0

If Gap finds an error while evaluating, a corresponding assertion is raised:

sage: libgap.eval('1/0')
Traceback (most recent call last):
...
ValueError: libGAP: Error, Rational operations: <divisor> must not be zero

Also, a ValueError is raised if the input is not a simple expression:

sage: libgap.eval('1; 2; 3')
Traceback (most recent call last):
...
ValueError: can only evaluate a single statement

is_bool()¶

Return whether the wrapped GAP object is a GAP boolean.

OUTPUT:

Boolean.

EXAMPLES:

sage: libgap(True).is_bool()
True

is_function()¶

Return whether the wrapped GAP object is a function.

OUTPUT:

Boolean.

EXAMPLES:

sage: a = libgap.eval("NormalSubgroups")
sage: a.is_function()
True
sage: a = libgap(2/3)
sage: a.is_function()
False

is_int()¶

Return whether the wrapped GAP object is a GAP integer.

OUTPUT:

Boolean.

EXAMPLES:

sage: libgap(1).is_int()
True

is_list()¶

Return whether the wrapped GAP object is a GAP List.

OUTPUT:

Boolean.

EXAMPLES:

sage: libgap.eval('[1, 2,,,, 5]').is_list()
True
sage: libgap.eval('3/2').is_list()
False

is_permutation()¶

Return whether the wrapped GAP object is a GAP permutation.

OUTPUT:

Boolean.

EXAMPLES:

sage: perm = libgap.PermList( libgap([1,5,2,3,4]) );  perm
(2,5,4,3)
sage: perm.is_permutation()
True
sage: libgap('this is a string').is_permutation()
False

is_record()¶

Return whether the wrapped GAP object is a GAP record.

OUTPUT:

Boolean.

EXAMPLES:

sage: libgap.eval('[1, 2,,,, 5]').is_record()
False
sage: libgap.eval('rec(a:=1, b:=3)').is_record()
True

is_string()¶

Return whether the wrapped GAP object is a GAP string.

OUTPUT:

Boolean.

EXAMPLES:

sage: libgap('this is a string').is_string()
True

sage()¶

Return the Sage equivalent of the GapElement

EXAMPLES:

sage: libgap(1).sage()
1
sage: type(_)
<type 'sage.rings.integer.Integer'>

sage: libgap(3/7).sage()
3/7
sage: type(_)
<type 'sage.rings.rational.Rational'>

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

sage: libgap(True).sage()
True
sage: libgap(False).sage()
False
sage: type(_)
<type 'bool'>

sage: libgap('this is a string').sage()
'this is a string'
sage: type(_)
<type 'str'>

trait_names()¶

Return all Gap function names.

OUTPUT:

A list of strings.

EXAMPLES:

sage: x = libgap(1)
sage: len(x.trait_names()) > 1000
True

class sage.libs.gap.element.GapElement_Boolean¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP boolean values.

EXAMPLES:

sage: b = libgap(True)
sage: type(b)
<type 'sage.libs.gap.element.GapElement_Boolean'>

sage()¶

Return the Sage equivalent of the GapElement

OUTPUT:

A Python boolean if the values is either true or false. GAP booleans can have the third value Fail, in which case a ValueError is raised.

EXAMPLES:

sage: b = libgap.eval('true');  b
true
sage: type(_)
<type 'sage.libs.gap.element.GapElement_Boolean'>
sage: b.sage()
True
sage: type(_)
<type 'bool'>

sage: libgap.eval('fail')
fail
sage: _.sage()
Traceback (most recent call last):
...
ValueError: the GAP boolean value "fail" cannot be represented in Sage

class sage.libs.gap.element.GapElement_Function¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP functions.

EXAMPLES:

sage: f = libgap.Cycles
sage: type(f)
<type 'sage.libs.gap.element.GapElement_Function'>

class sage.libs.gap.element.GapElement_Integer¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP rational numbers.

EXAMPLES:

sage: i = libgap(123)
sage: type(i)
<type 'sage.libs.gap.element.GapElement_Integer'>

sage()¶

Return the Sage equivalent of the GapElement_Integer

OUTPUT:

An integer

EXAMPLES:

sage: libgap([ 1, 3, 4 ]).sage()
[1, 3, 4]
sage: all( x in ZZ for x in _ )
True

class sage.libs.gap.element.GapElement_List¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP Lists.

Note

Lists are indexed by \(0..len(l)-1\), as expected from Python. This differs from the GAP convention where lists start at \(1\).

EXAMPLES:

sage: lst = libgap.SymmetricGroup(3).List(); lst
[ (), (1,3), (1,2,3), (2,3), (1,3,2), (1,2) ]
sage: type(lst)
<type 'sage.libs.gap.element.GapElement_List'>
sage: len(lst)
6
sage: lst[3]
(2,3)

We can easily convert a Gap List object into a Python list:

sage: list(lst)
[(), (1,3), (1,2,3), (2,3), (1,3,2), (1,2)]
sage: type(_)
<type 'list'>

Range checking is performed:

sage: lst[10]
Traceback (most recent call last):
...
IndexError: index out of range.

sage()¶

Return the Sage equivalent of the GapElement

OUTPUT:

A Python list.

EXAMPLES:

sage: libgap([ 1, 3, 4 ]).sage()
[1, 3, 4]
sage: all( x in ZZ for x in _ )
True

class sage.libs.gap.element.GapElement_MethodProxy¶

Bases: sage.libs.gap.element.GapElement_Function

Helper class returned by GapElement.__getattr__.

Derived class of GapElement for GAP functions. Like its parent, you can call instances to implement function call syntax. The only difference is that a fixed first argument is prepended to the argument list.

EXAMPLES:

sage: lst = libgap([])
sage: lst.Add
<Gap function "Add">
sage: type(_)
<type 'sage.libs.gap.element.GapElement_MethodProxy'>
sage: lst.Add(1)
sage: lst
[ 1 ]

class sage.libs.gap.element.GapElement_Permutation¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP permutations.

Note

Permutations in GAP act on the numbers starting with 1.

EXAMPLES:

sage: perm = libgap.eval('(1,5,2)(4,3,8)')
sage: type(perm)
<type 'sage.libs.gap.element.GapElement_Permutation'>

sage()¶

Return the Sage equivalent of the GapElement

EXAMPLES:

sage: perm_gap = libgap.eval('(1,5,2)(4,3,8)');  perm_gap
(1,5,2)(3,8,4)
sage: perm_gap.sage()
(1,5,2)(3,8,4)
sage: type(_)
<type 'sage.groups.perm_gps.permgroup_element.PermutationGroupElement'>

class sage.libs.gap.element.GapElement_Rational¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP rational numbers.

EXAMPLES:

sage: r = libgap(123/456)
sage: type(r)
<type 'sage.libs.gap.element.GapElement_Rational'>

sage()¶

Return the Sage equivalent of the GapElement

OUTPUT:

A Python list.

EXAMPLES:

sage: r = libgap(123/456);  r
41/152
sage: type(_)
<type 'sage.libs.gap.element.GapElement_Rational'>
sage: r.sage()
41/152
sage: type(_)
<type 'sage.rings.rational.Rational'>

class sage.libs.gap.element.GapElement_Record¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP records.

EXAMPLES:

sage: rec = libgap.eval('rec(a:=123, b:=456)')
sage: type(rec)
<type 'sage.libs.gap.element.GapElement_Record'>
sage: len(rec)
2
sage: rec['a']
123

We can easily convert a Gap rec object into a Python dict:

sage: dict(rec)
{'a': 123, 'b': 456}
sage: type(_)
<type 'dict'>

Range checking is performed:

sage: rec['no_such_element']
Traceback (most recent call last):
...
IndexError: libGAP: Error, Record: '<rec>.no_such_element' must have an assigned value

record_name_to_index(py_name)¶

Convert string to GAP record index.

INPUT:

py_name – a python string.

OUTPUT:

A UInt, which is a GAP hash of the string. If this is the first time the string is encountered, a new integer is returned(!)

EXAMPLE:

sage: rec = libgap.eval('rec(first:=123, second:=456)')
sage: rec.record_name_to_index('first')   # random output
1812L
sage: rec.record_name_to_index('no_such_name') # random output
3776L

sage()¶

Return the Sage equivalent of the GapElement

EXAMPLES:

sage: libgap.eval('rec(a:=1, b:=2)').sage()
{'a': 1, 'b': 2}
sage: all( isinstance(key,str) and val in ZZ for key,val in _.items() )
True

sage: rec = libgap.eval('rec(a:=123, b:=456, Sym3:=SymmetricGroup(3))')
sage: rec.sage()
{'a': 123, 
 'Sym3': NotImplementedError('cannot construct equivalent Sage object',), 
 'b': 456}

class sage.libs.gap.element.GapElement_RecordIterator¶

Bases: object

Iterator for GapElement_Record

Since Cython does not support generators yet, we implement the older iterator specification with this auxiliary class.

INPUT:

rec – the GapElement_Record to iterate over.

EXAMPLES:

sage: rec = libgap.eval('rec(a:=123, b:=456)')
sage: list(rec)
[('a', 123), ('b', 456)]
sage: dict(rec)
{'a': 123, 'b': 456}

next()¶: x.next() -> the next value, or raise StopIteration

class sage.libs.gap.element.GapElement_String¶

Bases: sage.libs.gap.element.GapElement

Derived class of GapElement for GAP strings.

EXAMPLES:

sage: s = libgap('string')
sage: type(s)
<type 'sage.libs.gap.element.GapElement_String'>

sage()¶

Return the Sage equivalent of the GapElement

OUTPUT:

A Python list.

EXAMPLES:

sage: s = libgap.eval(' "string" '); s
"string"
sage: type(_)
<type 'sage.libs.gap.element.GapElement_String'>
sage: s.sage()
'string'
sage: type(_)
<type 'str'>

libGAP element wrapper¶

Previous topic

Next topic

This Page

Navigation

libGAP element wrapper¶

Previous topic

Next topic

This Page

Quick search

Navigation