Abstract class for Python internal interfaces

This class contains common functionality of interfaces to packages that can be installed (using pip) as a Python library (called a Python-CAS in the sequel) such as Regina or SnapPy.

AUTHORS:

  • Sebastian Oehms (2026): first version (refactored from regina.py)

class sage.interfaces.python_internal.PythonInternalElement(parent, value, is_name=False, name=None)[source]

Bases: ExtraTabCompletion, InterfaceElement

Element class of the Python internal interface.

Its instances are usually constructed via the instance call of its parent. It wrapes the Python internal library for this object. In a session Python internal methods can be obtained using tab completion.

EXAMPLES:

sage: b = BraidGroup(3)((1,2,-1))
sage: re = regina(b); re
<regina.GroupExpression: g0 g1 g0^-1>
sage: type(re)
<class 'sage.interfaces.regina.ReginaElement'>
sage: P = re.parent(); P
Regina
sage: type(P)
<class 'sage.interfaces.regina.Regina'>

>>> from sage.all import *
>>> b = BraidGroup(Integer(3))((Integer(1),Integer(2),-Integer(1)))
>>> re = regina(b); re
<regina.GroupExpression: g0 g1 g0^-1>
>>> type(re)
<class 'sage.interfaces.regina.ReginaElement'>
>>> P = re.parent(); P
Regina
>>> type(P)
<class 'sage.interfaces.regina.Regina'>

Access to the Python-CAS expression objects:

sage: res = re._inst
sage: type(res)
 <class 'regina.engine.GroupExpression'>
[Python] 
>>> from sage.all import *
>>> res = re._inst
>>> type(res)
 <class 'regina.engine.GroupExpression'>

Applying Python-CAS methods:

sage: re.cycleLeft(); re
<regina.GroupExpression: g0^-1 g0 g1>

>>> from sage.all import *
>>> re.cycleLeft(); re
<regina.GroupExpression: g0^-1 g0 g1>

Conversion to Sage:

sage: re.sage() == b
False
sage: re.cycleRight()
sage: re.sage() == b
True
[Python] 
>>> from sage.all import *
>>> re.sage() == b
False
>>> re.cycleRight()
>>> re.sage() == b
True
class sage.interfaces.python_internal.PythonInternalFunction(parent, name)[source]

Bases: InterfaceFunction

Interface Function.

EXAMPLES:

sage: m = regina.MatrixInt; m
<class 'regina.engine.MatrixInt'>
sage: type(m)
<class 'sage.interfaces.python_internal.PythonInternalFunction'>

>>> from sage.all import *
>>> m = regina.MatrixInt; m
<class 'regina.engine.MatrixInt'>
>>> type(m)
<class 'sage.interfaces.python_internal.PythonInternalFunction'>
class sage.interfaces.python_internal.PythonInternalFunctionElement(obj, name)[source]

Bases: InterfaceFunctionElement

Interface methods of interface elements.

EXAMPLES:

sage: A = regina.AbelianGroup()
sage: type(A.addRank)
<class 'sage.interfaces.python_internal.PythonInternalFunctionElement'>
sage: M = snappy.Manifold('9_42')
sage: M.DT_code
<bound method Triangulation.DT_code of 9_42(0,0)>
sage: type(M.DT_code)
<class 'sage.interfaces.python_internal.PythonInternalFunctionElement'>

>>> from sage.all import *
>>> A = regina.AbelianGroup()
>>> type(A.addRank)
<class 'sage.interfaces.python_internal.PythonInternalFunctionElement'>
>>> M = snappy.Manifold('9_42')
>>> M.DT_code
<bound method Triangulation.DT_code of 9_42(0,0)>
>>> type(M.DT_code)
<class 'sage.interfaces.python_internal.PythonInternalFunctionElement'>
class sage.interfaces.python_internal.PythonInternalInterface(name)[source]

Bases: ExtraTabCompletion, Interface

Python internal interface.

EXAMPLES:

sage: K = Knots().from_table(8, 21)
sage: Kr = regina(K); Kr
<regina.Link: 8-crossing knot: ----++-- ( _5 _0 ^1 _2 _3 ^6 _7 ^3 _4 ^5 _6 ^7 ^0 _1 ^2 ^4 )>
sage: Kr.knotSig()
'iabcdbefcdghaefghRsgF+m'

>>> from sage.all import *
>>> K = Knots().from_table(Integer(8), Integer(21))
>>> Kr = regina(K); Kr
<regina.Link: 8-crossing knot: ----++-- ( _5 _0 ^1 _2 _3 ^6 _7 ^3 _4 ^5 _6 ^7 ^0 _1 ^2 ^4 )>
>>> Kr.knotSig()
'iabcdbefcdghaefghRsgF+m'

More examples can be found in the module header.

eval(code, *args, **kwds)[source]

Evaluates a command inside the Python-CAS interpreter and returns the output in printable form.

EXAMPLES:

sage: regina.eval('1+1')
'2'

>>> from sage.all import *
>>> regina.eval('1+1')
'2'
get(var)[source]

Get the value of the variable var.

EXAMPLES:

sage: regina.get('Link')
<class 'regina.engine.Link'>
sage: snappy.get('Triangulation')
<class 'SnapPy.Triangulation'>

>>> from sage.all import *
>>> regina.get('Link')
<class 'regina.engine.Link'>
>>> snappy.get('Triangulation')
<class 'SnapPy.Triangulation'>
help(cmd, long=False)[source]

Return the documentation of the given command via the Python internal interface.

EXAMPLES:

sage: regina.help('AbelianGroup')
Represents a finitely generated abelian group.

The torsion elements of the group are stored in terms of their
invariant factors. For instance, Z_2+Z_3 will appear as Z_6, and
Z_2+Z_2+Z_3 will appear as Z_2+Z_6.

In general the factors will appear as Z_*d0*+...+Z_*dn*, where the
invariant factors *di* are all greater than 1 and satisfy
*d0*|*d1*|...|*dn*. Note that this representation is unique.

This class implements C++ move semantics and adheres to the C++
Swappable requirement. It is designed to avoid deep copies wherever
possible, even when passing or returning objects by value.

sage: snappy.help('AbelianGroup')

An AbelianGroup object represents a finitely generated abelian group,
usually the first homology group of a snappy Manifold.

Instantiate an abelian group by its elementary divisors:
...

>>> from sage.all import *
>>> regina.help('AbelianGroup')
Represents a finitely generated abelian group.
<BLANKLINE>
The torsion elements of the group are stored in terms of their
invariant factors. For instance, Z_2+Z_3 will appear as Z_6, and
Z_2+Z_2+Z_3 will appear as Z_2+Z_6.
<BLANKLINE>
In general the factors will appear as Z_*d0*+...+Z_*dn*, where the
invariant factors *di* are all greater than 1 and satisfy
*d0*|*d1*|...|*dn*. Note that this representation is unique.
<BLANKLINE>
This class implements C++ move semantics and adheres to the C++
Swappable requirement. It is designed to avoid deep copies wherever
possible, even when passing or returning objects by value.

>>> snappy.help('AbelianGroup')
<BLANKLINE>
An AbelianGroup object represents a finitely generated abelian group,
usually the first homology group of a snappy Manifold.
<BLANKLINE>
Instantiate an abelian group by its elementary divisors:
...
set(var, value)[source]

Set the variable var to the given value.

EXAMPLES:

sage: regina.set('myLink', 'Link')
sage: regina.get('myLink')
<class 'regina.engine.Link'>
sage: snappy.set('K9_15', 'Link("9_15")')
sage: snappy.get('K9_15')
<Link 9_15: 1 comp; 9 cross>

>>> from sage.all import *
>>> regina.set('myLink', 'Link')
>>> regina.get('myLink')
<class 'regina.engine.Link'>
>>> snappy.set('K9_15', 'Link("9_15")')
>>> snappy.get('K9_15')
<Link 9_15: 1 comp; 9 cross>