def __init__(self, parent, partition):
r"""
An irreducible representation of the symmetric group corresponding
to ``partition``.
For more information, see the documentation for
:func:`SymmetricGroupRepresentation`.
EXAMPLES::
sage: spc = SymmetricGroupRepresentation([3])
sage: spc([3,2,1])
[1]
sage: spc == loads(dumps(spc))
True
sage: spc = SymmetricGroupRepresentation([3], cache_matrices=False)
sage: spc([3,2,1])
[1]
sage: spc == loads(dumps(spc))
True
"""
self._partition = Partition(partition)
self._n = parent._n
self._ring = parent._ring
if not parent._cache_matrices:
self.representation_matrix = self._representation_matrix_uncached
Element.__init__(self, parent)
def __init__(self, parent, component_dict, name="sheaf morpism"):
Element.__init__(self, parent)
self._parent = parent
self._components = component_dict
self._base_ring = self._parent._base_ring
self._domain_poset = self._parent._domain_poset
self._name = name
def __init__(self, parent, blocks):
self._blocks = blocks
self._number_of_blocks = len(blocks)
self._n = parent._n
if not SetPartitions(self._n)(self._blocks).is_noncrossing():
raise ValueError("{} is not noncrossing".format(blocks))
Element.__init__(self, parent)
def __init__(self, model, coordinates, is_boundary, check=True, **graphics_options):
r"""
See ``HyperbolicPoint`` for full documentation.
EXAMPLES::
sage: p = HyperbolicPlane().UHP().get_point(I)
sage: TestSuite(p).run()
"""
if is_boundary:
if not model.is_bounded():
raise NotImplementedError("boundary points are not implemented in the {0} model".format(model.short_name()))
if check and not model.boundary_point_in_model(coordinates):
raise ValueError(
"{0} is not a valid".format(coordinates) +
" boundary point in the {0} model".format(model.short_name()))
elif check and not model.point_in_model(coordinates):
raise ValueError(
"{0} is not a valid".format(coordinates) +
" point in the {0} model".format(model.short_name()))
if isinstance(coordinates, tuple):
coordinates = vector(coordinates)
self._coordinates = coordinates
self._bdry = is_boundary
self._graphics_options = graphics_options
Element.__init__(self, model)
def __init__(self, domain, coords=None, chart=None, name=None,
latex_name=None):
Element.__init__(self, domain)
self.manifold = domain.manifold
self.domain = domain
self.coordinates = {}
if coords is not None:
if len(coords) != self.manifold.dim:
raise ValueError("The number of coordinates must be equal" +
" to the manifold dimension.")
if chart is None:
chart = self.domain.def_chart
else:
if chart not in self.domain.atlas:
raise ValueError("The " + str(chart) +
" has not been defined on the " + str(self.domain))
#!# The following check is not performed for it would fail with
# symbolic coordinates:
# if not chart.valid_coordinates(*coords):
# raise ValueError("The coordinates " + str(coords) +
# " are not valid on the " + str(chart))
for schart in chart.supercharts:
self.coordinates[schart] = tuple(coords)
for schart in chart.subcharts:
if schart != chart:
if schart.valid_coordinates(*coords):
self.coordinates[schart] = tuple(coords)
self.name = name
if latex_name is None:
self.latex_name = self.name
else:
self.latex_name = latex_name
def __init__(self, parent, series):
Element.__init__(self, parent)
if isinstance(series,ContinuousGeneralizedSeriesMult):
series=series.get_summands()
m=parent.get_monoid()
if not type(series) is list:
series=[series]
series=[i for i in series if i!=0]
if len(series)==0:
series=[parent.get_monoid().zero()]
for i in range(len(series)):
if isinstance(series[i],FractionFieldElement_1poly_field):
var=series[0].parent().gen()
expansion=padic_expansion(series[i],var,parent.prec())
series[i]=m(sum([lift(expansion[1][j])*var**j for j in range(len(expansion[1]))]),expansion[0])
series=[*map(m,series)]
self.__summands=[series[0]]
series=series[1:]
for i in series:
found=False
for j in range(len(self.__summands)):
if self.__summands[j].similar(i):
self.__summands[j]=self.__summands[j]+i
found=True
if not found:
self.__summands.append(i)
def __init__(self, data, check=True):
"""
Initialize ``self``.
TESTS::
sage: B = BraidGroup(8)
sage: K = Knot(B([1, -2, 1, -2]))
sage: TestSuite(K).run()
sage: K = Knot([[1, 1, 2, 2]])
sage: TestSuite(K).run()
The following is not a knot: it has two components. ::
sage: Knot([[[1, 2], [-2, -1]], [1, -1]])
Traceback (most recent call last):
...
ValueError: the input has more than 1 connected component
sage: Knot([[[1, 2], [-2, -1]], [1, -1]], check=False)
Knot represented by 2 crossings
"""
Element.__init__(self, Knots())
Link.__init__(self, data)
if check:
if self.number_of_components() != 1:
raise ValueError("the input has more than 1 connected "
"component")
def __init__(self, parent, Vrep, Hrep, polymake_polytope=None, **kwds):
"""
Initializes the polyhedron.
See :class:`Polyhedron_polymake` for a description of the input
data.
TESTS:
We skip the pickling test because pickling is currently
not implemented::
sage: p = Polyhedron(backend='polymake') # optional - polymake
sage: TestSuite(p).run(skip="_test_pickling") # optional - polymake
sage: p = Polyhedron(vertices=[(1, 1)], rays=[(0, 1)], # optional - polymake
....: backend='polymake')
sage: TestSuite(p).run(skip="_test_pickling") # optional - polymake
sage: p = Polyhedron(vertices=[(-1,-1), (1,0), (1,1), (0,1)], # optional - polymake
....: backend='polymake')
sage: TestSuite(p).run(skip="_test_pickling") # optional - polymake
"""
if polymake_polytope:
if Hrep is not None or Vrep is not None:
raise ValueError("only one of Vrep, Hrep, or polymake_polytope can be different from None")
Element.__init__(self, parent=parent)
self._init_from_polymake_polytope(polymake_polytope)
else:
Polyhedron_base.__init__(self, parent, Vrep, Hrep, **kwds)
def __init__(self, core, parent):
"""
TESTS::
sage: C = Cores(4,3)
sage: c = C([2,1]); c
[2, 1]
sage: type(c)
<class 'sage.combinat.core.Cores_length_with_category.element_class'>
sage: c.parent()
4-Cores of length 3
sage: TestSuite(c).run()
sage: C = Cores(3,3)
sage: C([2,1])
Traceback (most recent call last):
...
ValueError: [2, 1] is not a 3-core
"""
k = parent.k
part = Partition(core)
if not part.is_core(k):
raise ValueError, "%s is not a %s-core" % (part, k)
CombinatorialObject.__init__(self, core)
Element.__init__(self, parent)
def __init__(self, core, parent):
"""
TESTS::
sage: C = Cores(4,3)
sage: c = C([2,1]); c
[2, 1]
sage: type(c)
<class 'sage.combinat.core.Cores_length_with_category.element_class'>
sage: c.parent()
4-Cores of length 3
sage: TestSuite(c).run()
sage: C = Cores(3,3)
sage: C([2,1])
Traceback (most recent call last):
...
ValueError: [2, 1] is not a 3-core
"""
k = parent.k
part = Partition(core)
if not part.is_core(k):
raise ValueError, "%s is not a %s-core"%(part, k)
CombinatorialObject.__init__(self, core)
Element.__init__(self, parent)
def __init__(self, parent, Vrep, Hrep, normaliz_cone=None, **kwds):
"""
Initializes the polyhedron.
See :class:`Polyhedron_normaliz` for a description of the input
data.
TESTS:
We skip the pickling test because pickling is currently
not implemented::
sage: p = Polyhedron(backend='normaliz') # optional - pynormaliz
sage: TestSuite(p).run(skip="_test_pickling") # optional - pynormaliz
sage: p = Polyhedron(vertices=[(1, 1)], rays=[(0, 1)], # optional - pynormaliz
....: backend='normaliz')
sage: TestSuite(p).run(skip="_test_pickling") # optional - pynormaliz
sage: p = Polyhedron(vertices=[(-1,-1), (1,0), (1,1), (0,1)], # optional - pynormaliz
....: backend='normaliz')
sage: TestSuite(p).run(skip="_test_pickling") # optional - pynormaliz
"""
if normaliz_cone:
if Hrep is not None or Vrep is not None:
raise ValueError(
"only one of Vrep, Hrep, or normaliz_cone can be different from None"
)
Element.__init__(self, parent=parent)
self._init_from_normaliz_cone(normaliz_cone)
else:
Polyhedron_base.__init__(self, parent, Vrep, Hrep, **kwds)
def __init__(self, poset, element, vertex):
r"""
Establishes the parent-child relationship between ``poset``
and ``element``, where ``element`` is associated to the
vertex ``vertex`` of the Hasse diagram of the poset.
INPUT:
- ``poset`` - a poset object
- ``element`` - any object
- ``vertex`` - a vertex of the Hasse diagram of the poset
TESTS::
sage: from sage.combinat.posets.elements import PosetElement
sage: P = Poset([[1,2],[4],[3],[4],[]], facade = False)
sage: e = P(0)
sage: e.parent() is P
True
sage: TestSuite(e).run()
"""
Element.__init__(self, poset)
if isinstance(element, self.parent().element_class):
self.element = element.element
else:
self.element = element
self.vertex = vertex
def __init__(self,
model,
coordinates,
is_boundary,
check=True,
**graphics_options):
r"""
See ``HyperbolicPoint`` for full documentation.
EXAMPLES::
sage: p = HyperbolicPlane().UHP().get_point(I)
sage: TestSuite(p).run()
"""
if is_boundary:
if not model.is_bounded():
raise NotImplementedError(
"boundary points are not implemented in the {0} model".
format(model.short_name()))
if check and not model.boundary_point_in_model(coordinates):
raise ValueError("{0} is not a valid".format(coordinates) +
" boundary point in the {0} model".format(
model.short_name()))
elif check and not model.point_in_model(coordinates):
raise ValueError(
"{0} is not a valid".format(coordinates) +
" point in the {0} model".format(model.short_name()))
if isinstance(coordinates, tuple):
coordinates = vector(coordinates)
self._coordinates = coordinates
self._bdry = is_boundary
self._graphics_options = graphics_options
Element.__init__(self, model)
def __init__(self, parent, blocks):
self._blocks = blocks
self._number_of_blocks = len(blocks)
self._n = parent._n
if not SetPartitions(self._n)(self._blocks).is_noncrossing():
raise ValueError("{} is not noncrossing".format(blocks))
Element.__init__(self, parent)
def __init__(self,
parent,
coords=None,
chart=None,
name=None,
latex_name=None,
check_coords=True):
r"""
Construct a manifold point.
TESTS::
sage: M = Manifold(2, 'M', structure='topological')
sage: X.<x,y> = M.chart()
sage: p = M((2,3), name='p'); p
Point p on the 2-dimensional topological manifold M
sage: TestSuite(p).run()
sage: U = M.open_subset('U', coord_def={X: x<0})
sage: q = U((-1,2), name='q'); q
Point q on the 2-dimensional topological manifold M
sage: TestSuite(q).run()
"""
if parent.is_empty():
raise TypeError(
f'cannot define a point on the {parent} because it has been declared empty'
)
Element.__init__(self, parent)
parent._has_defined_points = True
self._manifold = parent.manifold() # a useful shortcut
self._coordinates = {
} # dictionary of the point coordinates in various
# charts, with the charts as keys
if coords is not None:
if len(coords) != parent.manifold().dimension():
raise ValueError("the number of coordinates must be equal " +
"to the manifold's dimension")
from sage.manifolds.manifold import TopologicalManifold
if chart is None:
chart = parent._def_chart
elif isinstance(parent, TopologicalManifold):
if chart not in parent._atlas:
raise ValueError("the {} has not been".format(chart) +
"defined on the {}".format(parent))
if check_coords:
if not chart.valid_coordinates(*coords):
raise ValueError("the coordinates {}".format(coords) +
" are not valid on the {}".format(chart))
for schart in chart._supercharts:
self._coordinates[schart] = tuple(coords)
for schart in chart._subcharts:
if schart != chart:
if schart.valid_coordinates(*coords):
self._coordinates[schart] = tuple(coords)
self._name = name
if latex_name is None:
self._latex_name = self._name
else:
self._latex_name = latex_name
def __init__(self, parent, t):
r"""
Initialize a composition tableau.
TESTS::
sage: t = CompositionTableaux()([[1],[2,2]])
sage: s = CompositionTableaux(3)([[1],[2,2]])
sage: s==t
True
sage: t.parent()
Composition Tableaux
sage: s.parent()
Composition Tableaux of size 3 and maximum entry 3
sage: r = CompositionTableaux()(s)
sage: r.parent()
Composition Tableaux
"""
if isinstance(t, CompositionTableau):
Element.__init__(self, parent)
CombinatorialObject.__init__(self, t._list)
return
# CombinatorialObject verifies that t is a list
# We must verify t is a list of lists
if not all(isinstance(row, list) for row in t):
raise ValueError("A composition tableau must be a list of lists.")
if not map(len, t) in Compositions():
raise ValueError(
"A composition tableau must be a list of non-empty lists.")
# Verify rows weakly decrease from left to right
for row in t:
if any(row[i] < row[i + 1] for i in range(len(row) - 1)):
raise ValueError(
"Rows must weakly decrease from left to right.")
# Verify leftmost column strictly increases from top to bottom
first_col = [row[0] for row in t if t != [[]]]
if any(first_col[i] >= first_col[i + 1] for i in range(len(t) - 1)):
raise ValueError(
"Leftmost column must strictly increase from top to bottom.")
# Verify triple condition
l = len(t)
m = max(map(len, t) + [0])
TT = [row + [0] * (m - len(row)) for row in t]
for i in range(l):
for j in range(i + 1, l):
for k in range(1, m):
if TT[j][k] != 0 and TT[j][k] >= TT[i][k] and TT[j][
k] <= TT[i][k - 1]:
raise ValueError("Triple condition must be satisfied.")
Element.__init__(self, parent)
CombinatorialObject.__init__(self, t)
def __init__(self, parent, data):
r"""
TESTS::
sage: T = TotallyOrderedFiniteSet([3,2,1],facade=False)
sage: TestSuite(T.an_element()).run()
"""
Element.__init__(self, parent)
self.value = data
def __init__(self, parent, data):
r"""
TESTS::
sage: T = TotallyOrderedFiniteSet([3,2,1],facade=False)
sage: TestSuite(T.an_element()).run()
"""
Element.__init__(self, parent)
self.value = data
def __init__(self, parent, key):
"""
Create a cipher.
INPUT: Parent and key
EXAMPLES: None yet
"""
Element.__init__(self, parent)
self._key = key
def __init__(self, instance, workprec=None):
if isinstance(instance, LazyApproximationWrapper):
raise TypeError
Element.__init__(self, instance.parent())
self._instance = instance
ref = weakref.ref(self, delete_max_workprec)
wrappers[ref] = instance
self._ref = ref
if workprec is not None:
instance.update_max_workprec(workprec, wrapper=ref)
def __init__(self, parent, m):
r"""
EXAMPLES::
sage: B = crystals.elementary.Elementary(['B',7],7)
sage: elt = B(17); elt
17
"""
self._m = m
Element.__init__(self, parent)
def __init__(self, parent, m):
r"""
EXAMPLES::
sage: B = crystals.elementary.Elementary(['B',7],7)
sage: elt = B(17); elt
17
"""
self._m = m
Element.__init__(self, parent)
def __init__(self, parent, key):
"""
Create a cipher.
INPUT: Parent and key
EXAMPLES: None yet
"""
Element.__init__(self, parent)
self._key = key
def __init__(self,
subset,
coords=None,
chart=None,
name=None,
latex_name=None,
check_coords=True):
r"""
Construct a manifold point.
TESTS::
sage: Manifold._clear_cache_() # for doctests only
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: p = M((2,3), name='p') ; p
point 'p' on 2-dimensional manifold 'M'
sage: TestSuite(p).run()
sage: U = M.open_subset('U', coord_def={X: x<0})
sage: q = U((-1,2), name='q') ; q
point 'q' on 2-dimensional manifold 'M'
sage: TestSuite(q).run()
"""
Element.__init__(self, subset._manifold)
self._manifold = subset._manifold
self._subset = subset
self._coordinates = {}
if coords is not None:
if len(coords) != self._manifold._dim:
raise ValueError("The number of coordinates must be equal" +
" to the manifold dimension.")
if chart is None:
chart = self._subset._def_chart
else:
if chart not in self._subset._atlas:
raise ValueError("The " + str(chart) +
" has not been defined on the " +
str(self._subset))
if check_coords:
if not chart.valid_coordinates(*coords):
raise ValueError("The coordinates " + str(coords) +
" are not valid on the " + str(chart))
for schart in chart._supercharts:
self._coordinates[schart] = tuple(coords)
for schart in chart._subcharts:
if schart != chart:
if schart.valid_coordinates(*coords):
self._coordinates[schart] = tuple(coords)
self._name = name
if latex_name is None:
self._latex_name = self._name
else:
self._latex_name = latex_name
self._tangent_space = None # tangent vector space at the point (not
def __init__(self, parent, rdict):
r"""
Create an eta product object. Usually called implicitly via
EtaGroup_class.__call__ or the EtaProduct factory function.
EXAMPLES::
sage: EtaProduct(8, {1:24, 2:-24})
Eta product of level 8 : (eta_1)^24 (eta_2)^-24
sage: g = _; g == loads(dumps(g))
True
sage: TestSuite(g).run()
"""
self._N = parent._N
N = self._N
if isinstance(rdict, EtaGroupElement):
rdict = rdict._rdict
# Note: This is needed because the "x in G" test tries to call G(x)
# and see if it returns an error. So sometimes this will be getting
# called with rdict being an eta product, not a dictionary.
if rdict == 1:
rdict = {}
# Check Ligozat criteria
sumR = sumDR = sumNoverDr = 0
prod = 1
for d in list(rdict):
if N % d:
raise ValueError("%s does not divide %s" % (d, N))
if rdict[d] == 0:
del rdict[d]
continue
sumR += rdict[d]
sumDR += rdict[d] * d
sumNoverDr += rdict[d] * N / d
prod *= (N // d)**rdict[d]
if sumR != 0:
raise ValueError("sum r_d (=%s) is not 0" % sumR)
if sumDR % 24:
raise ValueError("sum d r_d (=%s) is not 0 mod 24" % sumDR)
if sumNoverDr % 24:
raise ValueError("sum (N/d) r_d (=%s) is not 0 mod 24" %
sumNoverDr)
if not is_square(prod):
raise ValueError("product (N/d)^(r_d) (=%s) is not a square" %
prod)
self._sumDR = ZZ(sumDR) # this is useful to have around
self._rdict = rdict
Element.__init__(self, parent)
def __init__(self, parent, lst):
"""
Initialize ``self``.
EXAMPLES::
sage: C = Composition([3,1,2])
sage: TestSuite(C).run()
"""
CombinatorialObject.__init__(self, lst)
Element.__init__(self, parent)
def __init__(self, parent):
r"""
Initialisation function.
EXAMPLES::
sage: pAdicWeightSpace(17)(0)
0
"""
Element.__init__(self, parent)
self._p = self.parent().prime()
def __init__(self, parent, tau):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = SimilarityClassType([[3, [3, 2, 1]], [2, [2, 1]]])
sage: TestSuite(elt).run()
"""
CombinatorialObject.__init__(self, sorted(tau, key=lambda PT: (PT.degree(), PT.partition())))
Element.__init__(self, parent)
def __init__(self, parent, lst):
"""
Initialize ``self``.
EXAMPLES::
sage: C = Composition([3,1,2])
sage: TestSuite(C).run()
"""
CombinatorialObject.__init__(self, lst)
Element.__init__(self, parent)
def __init__(self, parent, vecpar):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = VectorPartition([[3, 2, 1], [2, 2, 1]])
sage: TestSuite(elt).run()
"""
CombinatorialObject.__init__(self, sorted(vecpar))
Element.__init__(self, parent)
def __init__(self, parent, vecpar):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = VectorPartition([[3, 2, 1], [2, 2, 1]])
sage: TestSuite(elt).run()
"""
CombinatorialObject.__init__(self, sorted(vecpar))
Element.__init__(self, parent)
def __init__(self, parent, x):
"""
Initialize ``self``.
EXAMPLES::
sage: mst = MultiSkewTableau([ [[None,1],[2,3]], [[1,2],[2]] ])
sage: TestSuite(mst).run()
"""
CombinatorialObject.__init__(self, x)
Element.__init__(self, parent)
def __init__(self, parent, x):
"""
Initialize ``self``.
EXAMPLES::
sage: mst = MultiSkewTableau([ [[None,1],[2,3]], [[1,2],[2]] ])
sage: TestSuite(mst).run()
"""
CombinatorialObject.__init__(self, x)
Element.__init__(self, parent)
def __init__(self, parent, t):
r"""
Initialize a composition tableau.
TESTS::
sage: t = CompositionTableaux()([[1],[2,2]])
sage: s = CompositionTableaux(3)([[1],[2,2]])
sage: s==t
True
sage: t.parent()
Composition Tableaux
sage: s.parent()
Composition Tableaux of size 3 and maximum entry 3
sage: r = CompositionTableaux()(s)
sage: r.parent()
Composition Tableaux
"""
if isinstance(t, CompositionTableau):
Element.__init__(self, parent)
CombinatorialObject.__init__(self, t._list)
return
# CombinatorialObject verifies that t is a list
# We must verify t is a list of lists
if not all(isinstance(row, list) for row in t):
raise ValueError("A composition tableau must be a list of lists.")
if not map(len,t) in Compositions():
raise ValueError("A composition tableau must be a list of non-empty lists.")
# Verify rows weakly decrease from left to right
for row in t:
if any(row[i] < row[i+1] for i in range(len(row)-1)):
raise ValueError("Rows must weakly decrease from left to right.")
# Verify leftmost column strictly increases from top to bottom
first_col = [row[0] for row in t if t!=[[]]]
if any(first_col[i] >= first_col[i+1] for i in range(len(t)-1)):
raise ValueError("Leftmost column must strictly increase from top to bottom.")
# Verify triple condition
l = len(t)
m = max(map(len,t)+[0])
TT = [row+[0]*(m-len(row)) for row in t]
for i in range(l):
for j in range(i+1,l):
for k in range(1,m):
if TT[j][k] != 0 and TT[j][k] >= TT[i][k] and TT[j][k] <= TT[i][k-1]:
raise ValueError("Triple condition must be satisfied.")
Element.__init__(self, parent)
CombinatorialObject.__init__(self, t)
def __init__(self, parent, deg, par):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = PrimarySimilarityClassType(2, [3, 2, 1])
sage: TestSuite(elt).run()
"""
self._deg = deg
self._par = par
Element.__init__(self, parent)
def __init__(self, parent, gap_handle):
"""
Initialize an element of ``parent``
.. TODO:: make this more robust
"""
#from sage.libs.gap.element import GapElement
#if not isinstance(gap_handle, GapElement):
# raise ValueError("Input not a GAP handle")
Element.__init__(self, parent)
GAPObject.__init__(self, gap_handle)
def __init__(self, parent, tau):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = SimilarityClassType([[3, [3, 2, 1]], [2, [2, 1]]])
sage: TestSuite(elt).run()
"""
CombinatorialObject.__init__(
self, sorted(tau, key=lambda PT: (PT.degree(), PT.partition())))
Element.__init__(self, parent)
def __init__(self, lst):
"""
TESTS::
sage: NonDecreasingParkingFunction([1, 1, 2, 2, 5, 6])
[1, 1, 2, 2, 5, 6]
"""
if not is_a(lst):
raise ValueError('%s is not a non-decreasing parking function' % lst)
parent = NonDecreasingParkingFunctions_n(len(lst))
Element.__init__(self, parent)
self._list = lst
def __init__(self, parent, asm):
"""
Initialize ``self``.
EXAMPLES:
sage: A = AlternatingSignMatrices(3)
sage: elt = A([[1, 0, 0],[0, 1, 0],[0, 0, 1]])
sage: TestSuite(elt).run()
"""
self._matrix = asm
Element.__init__(self, parent)
def __init__(self, lst):
"""
TESTS::
sage: NonDecreasingParkingFunction([1, 1, 2, 2, 5, 6])
[1, 1, 2, 2, 5, 6]
"""
if not is_a(lst):
raise ValueError('%s is not a non-decreasing parking function' % lst)
parent = NonDecreasingParkingFunctions_n(len(lst))
Element.__init__(self, parent)
self._list = lst
def __init__(self, parent, lst):
"""
Initialize ``self``.
EXAMPLES::
sage: D = Derangements(4)
sage: elt = D([4,3,2,1])
sage: TestSuite(elt).run()
"""
CombinatorialObject.__init__(self, lst)
Element.__init__(self, parent)
def __init__(self, parent, gap_handle):
"""
Initialize an element of ``parent``
.. TODO:: make this more robust
"""
#from sage.libs.gap.element import GapElement
#if not isinstance(gap_handle, GapElement):
# raise ValueError("Input not a GAP handle")
Element.__init__(self, parent)
GAPObject.__init__(self, gap_handle)
def __init__(self, parent):
r"""
Initialisation function.
EXAMPLE::
sage: pAdicWeightSpace(17)(0)
0
"""
Element.__init__(self, parent)
self._p = self.parent().prime()
def __init__(self, parent, lst):
"""
Initialize ``self``.
EXAMPLES::
sage: D = Derangements(4)
sage: elt = D([4,3,2,1])
sage: TestSuite(elt).run()
"""
CombinatorialObject.__init__(self, lst)
Element.__init__(self, parent)
def __init__(self, parent, deg, par):
"""
Initialize ``self``.
EXAMPLES::
sage: elt = PrimarySimilarityClassType(2, [3, 2, 1])
sage: TestSuite(elt).run()
"""
self._deg = deg
self._par = par
Element.__init__(self, parent)
def __init__(self, parent, asm):
"""
Initialize ``self``.
EXAMPLES:
sage: A = AlternatingSignMatrices(3)
sage: elt = A([[1, 0, 0],[0, 1, 0],[0, 0, 1]])
sage: TestSuite(elt).run()
"""
self._matrix = asm
Element.__init__(self, parent)
def __init__(self, parent, b, m):
"""
Initialize ``self``.
EXAMPLES::
sage: A = crystals.KirillovReshetikhin(['A',2,1], 2, 2).affinization()
sage: mg = A.module_generators[0]
sage: TestSuite(mg).run()
"""
self._b = b
self._m = m
Element.__init__(self, parent)
def __init__(self,parent,data):
i = len(data)-1
while i >= 0 and len(data[i]) == 0:
data.pop()
i -= 1
self.rows = len(data)
if data == []:
self.cols = 0
else:
self.cols = max([len(r) for r in data])
self.data = data
CombinatorialObject.__init__(self, data)
Element.__init__(self, parent)
def __init__(self, parent, b, m):
"""
Initialize ``self``.
EXAMPLES::
sage: A = crystals.KirillovReshetikhin(['A',2,1], 2, 2).affinization()
sage: mg = A.module_generators[0]
sage: TestSuite(mg).run()
"""
self._b = b
self._m = m
Element.__init__(self, parent)
def __init__(self, triangulation, parent, check=True):
"""
The constructor of a ``Triangulation`` object. Note that an
internal reference to the underlying ``PointConfiguration`` is
kept.
INPUT:
- ``parent`` -- a
:class:`~sage.geometry.triangulation.point_configuration.PointConfiguration`
- ``triangulation`` -- an iterable of integers or iterable of
iterables (e.g. a list of lists). In the first case, the
integers specify simplices via
:meth:`PointConfiguration.simplex_to_int`. In the second
case, the point indices of the maximal simplices of the
triangulation.
- ``check`` -- boolean. Whether to perform checks that the
triangulation is, indeed, a triangulation of the point
configuration.
NOTE:
Passing ``check=False`` allows you to create triangulations of
subsets of the points of the configuration, see
:meth:`~sage.geometry.triangulation.point_configuration.PointConfiguration.bistellar_flips`.
EXAMPLES::
sage: p = [[0,1],[0,0],[1,0]]
sage: points = PointConfiguration(p)
sage: from sage.geometry.triangulation.point_configuration import Triangulation
sage: Triangulation([(0,1,2)], points)
(<0,1,2>)
sage: Triangulation([1], points)
(<0,1,2>)
"""
Element.__init__(self, parent=parent)
self._point_configuration = parent
try:
triangulation = tuple(
sorted(tuple(sorted(t)) for t in triangulation))
except TypeError:
triangulation = tuple(self.point_configuration().int_to_simplex(i)
for i in triangulation)
assert not check or all(
len(t) == self.point_configuration().dim() + 1
for t in triangulation)
self._triangulation = triangulation
def __init__(self, parent, value, format):
"""
EXAMPLES::
sage: C = crystals.FastRankTwo(['A',2],shape=[2,1])
sage: c = C(0); c
[0, 0, 0]
sage: C[0].parent()
The fast crystal for A2 with shape [2,1]
sage: TestSuite(c).run()
"""
Element.__init__(self, parent)
self.value = value
self.format = format
def __init__(self, parent, dim, name):
"""
Initialize ``self``.
EXAMPLES::
sage: from sage.categories.cw_complexes import CWComplexes
sage: X = CWComplexes().example()
sage: f = X.an_element()
sage: TestSuite(f).run()
"""
Element.__init__(self, parent)
self._dim = dim
self._name = name
def __init__(self, parent, dim, name):
"""
Initialize ``self``.
EXAMPLES::
sage: from sage.categories.cw_complexes import CWComplexes
sage: X = CWComplexes().example()
sage: f = X.an_element()
sage: TestSuite(f).run()
"""
Element.__init__(self, parent)
self._dim = dim
self._name = name
def __init__(self, parent, dict):
r"""
INPUT:
- ``dict`` -- a dictionary of with pairs of the form ``{(i,k):y}``
EXAMPLES::
sage: M = crystals.infinity.NakajimaMonomials("C5")
sage: mg = M.module_generators[0]
sage: TestSuite(mg).run()
"""
self._dict = dict
Element.__init__(self, parent)
def __init__(self, parent, list):
"""
EXAMPLES::
sage: from sage.combinat.crystals.tensor_product import ImmutableListWithParent, TestParent
sage: l = ImmutableListWithParent(TestParent(), [1,2,3])
sage: l.parent()
A parent for tests
sage: parent(l)
A parent for tests
sage: TestSuite(l).run(skip = "_test_category")
"""
Element.__init__(self, parent)
CombinatorialObject.__init__(self, list)
def __init__(self, triangulation, parent, check=True):
"""
The constructor of a ``Triangulation`` object. Note that an
internal reference to the underlying ``PointConfiguration`` is
kept.
INPUT:
- ``parent`` -- a
:class:`~sage.geometry.triangulation.point_configuration.PointConfiguration`
- ``triangulation`` -- an iterable of integers or iterable of
iterables (e.g. a list of lists). In the first case, the
integers specify simplices via
:meth:`PointConfiguration.simplex_to_int`. In the second
case, the point indices of the maximal simplices of the
triangulation.
- ``check`` -- boolean. Whether to perform checks that the
triangulation is, indeed, a triangulation of the point
configuration.
NOTE:
Passing ``check=False`` allows you to create triangulations of
subsets of the points of the configuration, see
:meth:`~sage.geometry.triangulation.point_configuration.PointConfiguration.bistellar_flips`.
EXAMPLES::
sage: p = [[0,1],[0,0],[1,0]]
sage: points = PointConfiguration(p)
sage: from sage.geometry.triangulation.point_configuration import Triangulation
sage: Triangulation([(0,1,2)], points)
(<0,1,2>)
sage: Triangulation([1], points)
(<0,1,2>)
"""
Element.__init__(self, parent=parent)
self._point_configuration = parent
try:
triangulation = tuple(sorted( tuple(sorted(t)) for t in triangulation))
except TypeError:
triangulation = tuple( self.point_configuration().int_to_simplex(i)
for i in triangulation )
assert not check or all( len(t)==self.point_configuration().dim()+1
for t in triangulation)
self._triangulation = triangulation
def __init__(self, subset, coords=None, chart=None, name=None,
latex_name=None, check_coords=True):
r"""
Construct a manifold point.
TESTS::
sage: Manifold._clear_cache_() # for doctests only
sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: p = M((2,3), name='p') ; p
point 'p' on 2-dimensional manifold 'M'
sage: TestSuite(p).run()
sage: U = M.open_subset('U', coord_def={X: x<0})
sage: q = U((-1,2), name='q') ; q
point 'q' on 2-dimensional manifold 'M'
sage: TestSuite(q).run()
"""
Element.__init__(self, subset._manifold)
self._manifold = subset._manifold
self._subset = subset
self._coordinates = {}
if coords is not None:
if len(coords) != self._manifold._dim:
raise ValueError("The number of coordinates must be equal" +
" to the manifold dimension.")
if chart is None:
chart = self._subset._def_chart
else:
if chart not in self._subset._atlas:
raise ValueError("The " + str(chart) +
" has not been defined on the " + str(self._subset))
if check_coords:
if not chart.valid_coordinates(*coords):
raise ValueError("The coordinates " + str(coords) +
" are not valid on the " + str(chart))
for schart in chart._supercharts:
self._coordinates[schart] = tuple(coords)
for schart in chart._subcharts:
if schart != chart:
if schart.valid_coordinates(*coords):
self._coordinates[schart] = tuple(coords)
self._name = name
if latex_name is None:
self._latex_name = self._name
else:
self._latex_name = latex_name
self._tangent_space = None # tangent vector space at the point (not
def __init__(self, parent, value, is_name=False, name=None):
Element.__init__(self, parent)
self._create = value
if parent is None: return # means "invalid element"
# idea: Joe Wetherell -- try to find out if the output
# is too long and if so get it using file, otherwise
# don't.
if is_name:
self._name = value
else:
try:
self._name = parent._create(value, name=name)
except (TypeError, RuntimeError, ValueError) as x:
raise TypeError(x)