Poor Man’s map

class sage.categories.poor_man_map.PoorManMap(function, domain=None, codomain=None, name=None)

Bases: SageObject

A class for maps between sets which are not (yet) modeled by parents.

Could possibly disappear when all combinatorial classes / enumerated sets will be parents.

INPUT:

• function – a callable or an iterable of callables. This represents the underlying function used to implement this map. If it is an iterable, then the callables will be composed to implement this map.

• domain – the domain of this map or None if the domain is not known or should remain unspecified

• codomain – the codomain of this map or None if the codomain is not known or should remain unspecified

• name – a name for this map or None if this map has no particular name

EXAMPLES:

Sage

sage: from sage.categories.poor_man_map import PoorManMap
sage: f = PoorManMap(factorial, domain=(1, 2, 3), codomain=(1, 2, 6))
sage: f
A map from (1, 2, 3) to (1, 2, 6)
sage: f(3)
6

Python

>>> from sage.all import *
>>> from sage.categories.poor_man_map import PoorManMap
>>> f = PoorManMap(factorial, domain=(Integer(1), Integer(2), Integer(3)), codomain=(Integer(1), Integer(2), Integer(6)))
>>> f
A map from (1, 2, 3) to (1, 2, 6)
>>> f(Integer(3))
6

The composition of several functions can be created by passing in a tuple of functions:

Sage

sage: i = PoorManMap((factorial, sqrt), domain=(1, 4, 9), codomain=(1, 2, 6))

Python

>>> from sage.all import *
>>> i = PoorManMap((factorial, sqrt), domain=(Integer(1), Integer(4), Integer(9)), codomain=(Integer(1), Integer(2), Integer(6)))

However, the same effect can also be achieved by just composing maps:

Sage

sage: g = PoorManMap(factorial, domain=(1, 2, 3), codomain=(1, 2, 6))
sage: h = PoorManMap(sqrt, domain=(1, 4, 9), codomain=(1, 2, 3))
sage: i == g*h
True

Python

>>> from sage.all import *
>>> g = PoorManMap(factorial, domain=(Integer(1), Integer(2), Integer(3)), codomain=(Integer(1), Integer(2), Integer(6)))
>>> h = PoorManMap(sqrt, domain=(Integer(1), Integer(4), Integer(9)), codomain=(Integer(1), Integer(2), Integer(3)))
>>> i == g*h
True

codomain()

Return the codomain of self.

EXAMPLES:

Sage

sage: from sage.categories.poor_man_map import PoorManMap
sage: PoorManMap(lambda x: x+1, domain=(1,2,3), codomain=(2,3,4)).codomain()
(2, 3, 4)

Python

>>> from sage.all import *
>>> from sage.categories.poor_man_map import PoorManMap
>>> PoorManMap(lambda x: x+Integer(1), domain=(Integer(1),Integer(2),Integer(3)), codomain=(Integer(2),Integer(3),Integer(4))).codomain()
(2, 3, 4)

domain()

Return the domain of self.

EXAMPLES:

Sage

sage: from sage.categories.poor_man_map import PoorManMap
sage: PoorManMap(lambda x: x+1, domain=(1,2,3), codomain=(2,3,4)).domain()
(1, 2, 3)

Python

>>> from sage.all import *
>>> from sage.categories.poor_man_map import PoorManMap
>>> PoorManMap(lambda x: x+Integer(1), domain=(Integer(1),Integer(2),Integer(3)), codomain=(Integer(2),Integer(3),Integer(4))).domain()
(1, 2, 3)