def inject_shorthands(self, shorthands = _shorthands):
"""
Imports standard shorthands into the global namespace
INPUT:
- shorthands - a list (or iterable) of strings (default: ['e', 'h', 'm', 'p', 's'])
EXAMPLES::
sage: S = SymmetricFunctions(ZZ)
sage: S.inject_shorthands()
doctest:...: RuntimeWarning: redefining global value `e`
doctest:...: RuntimeWarning: redefining global value `m`
sage: s[1] + e[2] * p[1,1] + 2*h[3] + m[2,1]
s[1] - 2*s[1, 1, 1] + s[1, 1, 1, 1] + s[2, 1] + 2*s[2, 1, 1] + s[2, 2] + 2*s[3] + s[3, 1]
sage: e
Symmetric Function Algebra over Integer Ring, Elementary symmetric functions as basis
sage: p
Symmetric Function Algebra over Integer Ring, Power symmetric functions as basis
sage: s
Symmetric Function Algebra over Integer Ring, Schur symmetric functions as basis
sage: e == S.e(), h == S.h(), m == S.m(), p == S.p(), s == S.s()
(True, True, True, True, True)
One can also just import a subset of the shorthands::
sage: S = SymmetricFunctions(QQ)
sage: S.inject_shorthands(['p', 's'])
doctest:...: RuntimeWarning: redefining global value `p`
doctest:...: RuntimeWarning: redefining global value `s`
sage: p
Symmetric Function Algebra over Rational Field, Power symmetric functions as basis
sage: s
Symmetric Function Algebra over Rational Field, Schur symmetric functions as basis
Note that ``e`` is left unchanged::
sage: e
Symmetric Function Algebra over Integer Ring, Elementary symmetric functions as basis
"""
from sage.misc.misc import inject_variable
for shorthand in shorthands:
assert shorthand in self._shorthands
inject_variable(shorthand, getattr(self, shorthand)())
def inject_shorthands(self, shorthands=_shorthands):
"""
Imports standard shorthands into the global namespace
INPUT:
- ``shorthands`` -- a list (or iterable) of strings (default: ['e', 'h', 'm', 'p', 's'])
EXAMPLES::
sage: S = SymmetricFunctions(ZZ)
sage: S.inject_shorthands()
sage: s[1] + e[2] * p[1,1] + 2*h[3] + m[2,1]
s[1] - 2*s[1, 1, 1] + s[1, 1, 1, 1] + s[2, 1] + 2*s[2, 1, 1] + s[2, 2] + 2*s[3] + s[3, 1]
sage: e
Symmetric Functions over Integer Ring in the elementary basis
sage: p
Symmetric Functions over Integer Ring in the powersum basis
sage: s
Symmetric Functions over Integer Ring in the Schur basis
sage: e == S.e(), h == S.h(), m == S.m(), p == S.p(), s == S.s()
(True, True, True, True, True)
One can also just import a subset of the shorthands::
sage: S = SymmetricFunctions(QQ)
sage: S.inject_shorthands(['p', 's'])
sage: p
Symmetric Functions over Rational Field in the powersum basis
sage: s
Symmetric Functions over Rational Field in the Schur basis
Note that ``e`` is left unchanged::
sage: e
Symmetric Functions over Integer Ring in the elementary basis
"""
from sage.misc.misc import inject_variable
for shorthand in shorthands:
assert shorthand in self._shorthands
inject_variable(shorthand, getattr(self, shorthand)())
def inject_shorthands(self, shorthands = _shorthands):
"""
Imports standard shorthands into the global namespace
INPUT:
- ``shorthands`` -- a list (or iterable) of strings (default: ['e', 'h', 'm', 'p', 's'])
EXAMPLES::
sage: S = SymmetricFunctions(ZZ)
sage: S.inject_shorthands()
sage: s[1] + e[2] * p[1,1] + 2*h[3] + m[2,1]
s[1] - 2*s[1, 1, 1] + s[1, 1, 1, 1] + s[2, 1] + 2*s[2, 1, 1] + s[2, 2] + 2*s[3] + s[3, 1]
sage: e
Symmetric Functions over Integer Ring in the elementary basis
sage: p
Symmetric Functions over Integer Ring in the powersum basis
sage: s
Symmetric Functions over Integer Ring in the Schur basis
sage: e == S.e(), h == S.h(), m == S.m(), p == S.p(), s == S.s()
(True, True, True, True, True)
One can also just import a subset of the shorthands::
sage: S = SymmetricFunctions(QQ)
sage: S.inject_shorthands(['p', 's'])
sage: p
Symmetric Functions over Rational Field in the powersum basis
sage: s
Symmetric Functions over Rational Field in the Schur basis
Note that ``e`` is left unchanged::
sage: e
Symmetric Functions over Integer Ring in the elementary basis
"""
from sage.misc.misc import inject_variable
for shorthand in shorthands:
assert shorthand in self._shorthands
inject_variable(shorthand, getattr(self, shorthand)())
def fusion_labels(self, labels=None, inject_variables=False):
r"""
Set the labels of the basis.
INPUT:
- ``labels`` -- (default: ``None``) a list of strings or string
- ``inject_variables`` -- (default: ``False``) if ``True``, then
inject the variable names into the global namespace; note that
this could override objects already defined
If ``labels`` is a list, the length of the list must equal the
number of basis elements. These become the names of
the basis elements.
If ``labels`` is a string, this is treated as a prefix and a
list of names is generated.
If ``labels`` is ``None``, then this resets the labels to the default.
EXAMPLES::
sage: A13 = FusionRing("A1", 3)
sage: A13.fusion_labels("x")
sage: fb = list(A13.basis()); fb
[x0, x1, x2, x3]
sage: Matrix([[x*y for y in A13.basis()] for x in A13.basis()])
[ x0 x1 x2 x3]
[ x1 x0 + x2 x1 + x3 x2]
[ x2 x1 + x3 x0 + x2 x1]
[ x3 x2 x1 x0]
We give an example where the variables are injected into the
global namepsace::
sage: A13.fusion_labels("y", inject_variables=True)
sage: y0
y0
sage: y0.parent() is A13
True
We reset the labels to the default::
sage: A13.fusion_labels()
sage: fb
[A13(0), A13(1), A13(2), A13(3)]
sage: y0
A13(0)
"""
if labels is None:
# Remove the fusion labels
self._fusion_labels = None
return
B = self.basis()
if isinstance(labels, str):
labels = [labels + str(k) for k in range(len(B))]
elif len(labels) != len(B):
raise ValueError('invalid data')
d = {}
ac = self.simple_coroots()
for j, b in enumerate(self.get_order()):
t = tuple([b.inner_product(x) for x in ac])
d[t] = labels[j]
if inject_variables:
inject_variable(labels[j], B[b])
self._fusion_labels = d