def __init__(self, parent, im_gen, base_morphism):
"""
EXAMPLES::
sage: R.<x> = FunctionField(GF(7)); S.<y> = R[]
sage: L.<y> = R.extension(y^3 + 6*x^3 + x); f = L.hom(y*2); f
Morphism of function fields defined by y |--> 2*y
sage: type(f)
<class 'sage.rings.function_field.maps.FunctionFieldMorphism'>
sage: factor(L.polynomial())
y^3 + 6*x^3 + x
sage: f(y).charpoly('y')
y^3 + 6*x^3 + x
"""
self._im_gen = im_gen
self._base_morphism = base_morphism
Map.__init__(self, parent)
# Verify that the morphism is valid:
R = self.codomain()['X']
v = parent.domain().polynomial().list()
if base_morphism is not None:
v = [base_morphism(a) for a in v]
f = R(v)
if f(im_gen):
raise ValueError, "invalid morphism"
def __init__(self, B, Bp, normalization=0):
"""
Initialize ``self``.
EXAMPLES::
sage: K = crystals.KirillovReshetikhin(['A',7,2], 1,2)
sage: K2 = crystals.KirillovReshetikhin(['A',7,2], 2,1)
sage: H = K.local_energy_function(K2)
sage: TestSuite(H).run(skip=['_test_category', '_test_pickling'])
TESTS:
Check that :trac:`23014` is fixed::
sage: La = RootSystem(['G',2,1]).weight_space().fundamental_weights()
sage: K = crystals.ProjectedLevelZeroLSPaths(La[1])
sage: H = K.local_energy_function(K)
sage: hw = H.domain().classically_highest_weight_vectors()
sage: [H(x) for x in hw]
[0, 1, 2, 1]
"""
self._B = B
self._Bp = Bp
self._R_matrix = self._B.R_matrix(self._Bp)
T = B.tensor(Bp)
self._known_values = {
T(*[K.maximal_vector() for K in T.crystals]): ZZ(normalization)
}
self._I0 = T.cartan_type().classical().index_set()
from sage.categories.homset import Hom
Map.__init__(self, Hom(T, ZZ))
def __init__(self, B, Bp, normalization=0):
"""
Initialize ``self``.
EXAMPLES::
sage: K = crystals.KirillovReshetikhin(['A',7,2], 1,2)
sage: K2 = crystals.KirillovReshetikhin(['A',7,2], 2,1)
sage: H = K.local_energy_function(K2)
sage: TestSuite(H).run(skip=['_test_category', '_test_pickling'])
TESTS:
Check that :trac:`23014` is fixed::
sage: La = RootSystem(['G',2,1]).weight_space().fundamental_weights()
sage: K = crystals.ProjectedLevelZeroLSPaths(La[1])
sage: H = K.local_energy_function(K)
sage: hw = H.domain().classically_highest_weight_vectors()
sage: [H(x) for x in hw]
[0, 1, 2, 1]
"""
self._B = B
self._Bp = Bp
self._R_matrix = self._B.R_matrix(self._Bp)
T = B.tensor(Bp)
self._known_values = {T(*[K.maximal_vector() for K in T.crystals]):
ZZ(normalization)}
self._I0 = T.cartan_type().classical().index_set()
from sage.categories.homset import Hom
Map.__init__(self, Hom(T, ZZ))
def __init__(self, K):
r"""
Initialize a derivation from `K` to `K`.
INPUT:
- ``K`` -- function field
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: d = K.derivation()
sage: TestSuite(d).run(skip=['_test_category', '_test_pickling'])
.. TODO::
Make the caching done at the map by subclassing
``UniqueRepresentation``, which will then implement a
valid equality check. Then this will pass the pickling test.
"""
from .function_field import is_FunctionField
if not is_FunctionField(K):
raise ValueError("K must be a function field")
self.__field = K
from sage.categories.homset import Hom
from sage.categories.sets_cat import Sets
Map.__init__(self, Hom(K,K,Sets()))
def __init__(self, parent, im_gen, base_morphism):
"""
EXAMPLES::
sage: R.<x> = FunctionField(GF(7)); S.<y> = R[]
sage: L.<y> = R.extension(y^3 + 6*x^3 + x); f = L.hom(y*2); f
Morphism of function fields defined by y |--> 2*y
sage: type(f)
<class 'sage.rings.function_field.maps.FunctionFieldMorphism'>
sage: factor(L.polynomial())
y^3 + 6*x^3 + x
sage: f(y).charpoly('y')
y^3 + 6*x^3 + x
"""
self._im_gen = im_gen
self._base_morphism = base_morphism
Map.__init__(self, parent)
# Verify that the morphism is valid:
R = self.codomain()['X']
v = parent.domain().polynomial().list()
if base_morphism is not None:
v = [base_morphism(a) for a in v]
f = R(v)
if f(im_gen):
raise ValueError, "invalid morphism"
def __init__(self, parent):
r"""
TESTS::
sage: K.<x> = FunctionField(QQ)
sage: f = QQ.convert_map_from(K)
sage: from sage.rings.function_field.maps import FunctionFieldConversionToConstantBaseField
sage: isinstance(f, FunctionFieldConversionToConstantBaseField)
True
"""
Map.__init__(self, parent)
def __init__(self, parent):
r"""
TESTS::
sage: K.<x> = FunctionField(QQ)
sage: f = QQ.convert_map_from(K)
sage: from sage.rings.function_field.maps import FunctionFieldConversionToConstantBaseField
sage: isinstance(f, FunctionFieldConversionToConstantBaseField)
True
"""
Map.__init__(self, parent)
def __init__(self, parent, im_gen):
"""
EXAMPLES::
sage: R.<x> = FunctionField(GF(7)); f = R.hom(1/x); f
Morphism of function fields defined by x |--> 1/x
sage: type(f)
<class 'sage.rings.function_field.maps.FunctionFieldMorphism_rational'>
"""
Map.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = None
def __init__(self, parent, im_gen):
"""
EXAMPLES::
sage: R.<x> = FunctionField(GF(7)); f = R.hom(1/x); f
Morphism of function fields defined by x |--> 1/x
sage: type(f)
<class 'sage.rings.function_field.maps.FunctionFieldMorphism_rational'>
"""
Map.__init__(self, parent)
self._im_gen = im_gen
self._base_morphism = None
def __init__(self, K):
r"""
Initialize a derivation from ``K`` to ``K``.
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: d = K.derivation() # indirect doctest
"""
from .function_field import is_FunctionField
if not is_FunctionField(K):
raise ValueError("K must be a function field")
self.__field = K
from sage.categories.homset import Hom
from sage.categories.sets_cat import Sets
Map.__init__(self, Hom(K,K,Sets()))
def __init__(self, K):
r"""
Initialize a derivation from ``K`` to ``K``.
EXAMPLES::
sage: K.<x> = FunctionField(QQ)
sage: d = K.derivation() # indirect doctest
"""
from .function_field import is_FunctionField
if not is_FunctionField(K):
raise ValueError("K must be a function field")
self.__field = K
from sage.categories.homset import Hom
from sage.categories.sets_cat import Sets
Map.__init__(self, Hom(K, K, Sets()))
