def repr_short_to_parent(s):
r"""
Helper method for the growth group factory, which converts a short
representation string to a parent.
INPUT:
- ``s`` -- a string, short representation of a parent.
OUTPUT:
A parent.
The possible short representations are shown in the examples below.
EXAMPLES::
sage: from sage.rings.asymptotic.misc import repr_short_to_parent
sage: repr_short_to_parent('ZZ')
Integer Ring
sage: repr_short_to_parent('QQ')
Rational Field
sage: repr_short_to_parent('SR')
Symbolic Ring
sage: repr_short_to_parent('NN')
Non negative integer semiring
TESTS::
sage: repr_short_to_parent('abcdef')
Traceback (most recent call last):
...
ValueError: Cannot create a parent out of 'abcdef'.
> *previous* NameError: name 'abcdef' is not defined
"""
from sage.misc.sage_eval import sage_eval
try:
P = sage_eval(s)
except Exception as e:
raise combine_exceptions(
ValueError("Cannot create a parent out of '%s'." % (s,)), e)
from sage.misc.lazy_import import LazyImport
if type(P) is LazyImport:
P = P._get_object()
from sage.structure.parent import is_Parent
if not is_Parent(P):
raise ValueError("'%s' does not describe a parent." % (s,))
return P
def __mul__(self, other):
r"""
Composition
INPUT:
- ``self`` -- a map `f`
- ``other`` -- a map `g`
Returns the composition map `f\circ g` of `f`` and `g`
EXAMPLES::
sage: from sage.categories.poor_man_map import PoorManMap
sage: f = PoorManMap(lambda x: x+1, domain = (1,2,3), codomain = (2,3,4))
sage: g = PoorManMap(lambda x: -x, domain = (2,3,4), codomain = (-2,-3,-4))
sage: g*f
A map from (1, 2, 3) to (-2, -3, -4)
Note that the compatibility of the domains and codomains is for performance
reasons only checked for proper parents. For example, the incompatibility
is not detected here::
sage: f*g
A map from (2, 3, 4) to (2, 3, 4)
But it is detected here::
sage: g = PoorManMap(factorial, domain = ZZ, codomain = ZZ)
sage: h = PoorManMap(sqrt, domain = RR, codomain = CC)
sage: g*h
Traceback (most recent call last):
...
ValueError: the codomain Complex Field with 53 bits of precision does not coerce into the domain Integer Ring
sage: h*g
A map from Integer Ring to Complex Field with 53 bits of precision
"""
self_domain = self.domain()
try:
other_codomain = other.codomain()
except AttributeError:
other_codomain = None
if self_domain is not None and other_codomain is not None:
from sage.structure.parent import is_Parent
if is_Parent(self_domain) and is_Parent(other_codomain):
if not self_domain.has_coerce_map_from(other_codomain):
raise ValueError(
"the codomain %r does not coerce into the domain %r" %
(other_codomain, self_domain))
codomain = self.codomain()
try:
domain = other.domain()
except AttributeError:
domain = None
if isinstance(other, PoorManMap):
other = other._functions
else:
other = (other, )
return PoorManMap(self._functions + other,
domain=domain,
codomain=codomain)
def __mul__(self, other):
"""
Composition
INPUT:
- ``self`` -- a map `f`
- ``other`` -- a map `g`
Returns the composition map `f\circ g` of `f`` and `g`
EXAMPLES::
sage: from sage.categories.poor_man_map import PoorManMap
sage: f = PoorManMap(lambda x: x+1, domain = (1,2,3), codomain = (2,3,4))
sage: g = PoorManMap(lambda x: -x, domain = (2,3,4), codomain = (-2,-3,-4))
sage: g*f
A map from (1, 2, 3) to (-2, -3, -4)
Note that the compatibility of the domains and codomains is for performance
reasons only checked for proper parents. For example, the incompatibility
is not detected here::
sage: f*g
A map from (2, 3, 4) to (2, 3, 4)
But it is detected here::
sage: g = PoorManMap(factorial, domain = ZZ, codomain = ZZ)
sage: h = PoorManMap(sqrt, domain = RR, codomain = CC)
sage: g*h
Traceback (most recent call last):
...
ValueError: the codomain Complex Field with 53 bits of precision does not coerce into the domain Integer Ring
sage: h*g
A map from Integer Ring to Complex Field with 53 bits of precision
"""
self_domain = self.domain()
try:
other_codomain = other.codomain()
except AttributeError:
other_codomain = None
if self_domain is not None and other_codomain is not None:
from sage.structure.parent import is_Parent
if is_Parent(self_domain) and is_Parent(other_codomain):
if not self_domain.has_coerce_map_from(other_codomain):
raise ValueError("the codomain %r does not coerce into the domain %r"%(other_codomain, self_domain))
codomain = self.codomain()
try:
domain = other.domain()
except AttributeError:
domain = None
if isinstance(other, PoorManMap):
other = other._functions
else:
other = (other,)
return PoorManMap(self._functions + other, domain=domain, codomain=codomain)
def repr_short_to_parent(s):
r"""
Helper method for the growth group factory, which converts a short
representation string to a parent.
INPUT:
- ``s`` -- a string, short representation of a parent.
OUTPUT:
A parent.
The possible short representations are shown in the examples below.
EXAMPLES::
sage: from sage.rings.asymptotic.misc import repr_short_to_parent
sage: repr_short_to_parent('ZZ')
Integer Ring
sage: repr_short_to_parent('QQ')
Rational Field
sage: repr_short_to_parent('SR')
Symbolic Ring
sage: repr_short_to_parent('NN')
Non negative integer semiring
sage: repr_short_to_parent('UU')
Group of Roots of Unity
TESTS::
sage: repr_short_to_parent('abcdef')
Traceback (most recent call last):
...
ValueError: Cannot create a parent out of 'abcdef'.
> *previous* ValueError: unknown specification abcdef
> *and* NameError: name 'abcdef' is not defined
"""
from sage.groups.misc_gps.argument_groups import ArgumentGroup
from sage.misc.sage_eval import sage_eval
def extract(s):
try:
return ArgumentGroup(specification=s)
except Exception as e:
e_ag = e
e_ag.__traceback__ = None
try:
return sage_eval(s)
except Exception as e:
e_se = e
e_se.__traceback__ = None
raise combine_exceptions(
ValueError("Cannot create a parent out of '%s'." % (s,)),
e_ag, e_se)
P = extract(s)
from sage.misc.lazy_import import LazyImport
if type(P) is LazyImport:
P = P._get_object()
from sage.structure.parent import is_Parent
if not is_Parent(P):
raise ValueError("'%s' does not describe a parent." % (s,))
return P