def __iter__(self):
"""
Iterate through ``self``.
EXAMPLES::
sage: FPLs = FullyPackedLoops(2)
sage: len(FPLs)
2
"""
for X in SixVertexModel(self._n, boundary_conditions='ice'):
yield self.element_class(self, X)
def _an_element_(self):
"""
Return an element of ``self``.
EXAMPLES::
sage: FPLs = FullyPackedLoops(3)
sage: FPLs.an_element()
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+ + -- +
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-- + + + --
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+ -- + +
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"""
#ASM = AlternatingSignMatrix(matrix.identity(self._n))
#SVM = ASM.to_six_vertex_model()
SVM = SixVertexModel(self._n,boundary_conditions='ice').an_element()
return self.element_class(self, SVM)
def __classcall_private__(cls, generator):
"""
Create a FPL.
EXAMPLES::
sage: A = AlternatingSignMatrix([[1, 0, 0],[0, 1, 0],[0, 0, 1]])
sage: FullyPackedLoop(A)
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+ + -- +
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-- + + + --
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+ -- + +
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sage: SVM = SixVertexModel(4, boundary_conditions='ice')[0]
sage: FullyPackedLoop(SVM)
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+ + -- + + --
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-- + + + -- +
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+ -- + + + --
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-- + + -- + +
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"""
if isinstance(generator, AlternatingSignMatrix):
SVM = generator.to_six_vertex_model()
elif isinstance(generator, SquareIceModel.Element):
SVM = generator
elif isinstance(generator, SixVertexConfiguration):
# Check that this is an ice square model
generator = SixVertexModel(generator.parent()._nrows, \
boundary_conditions='ice')(generator)
M = generator.to_alternating_sign_matrix().to_matrix()
M = AlternatingSignMatrix(M)
SVM = generator
else: # Not ASM nor SVM
try:
SVM = AlternatingSignMatrix(generator).to_six_vertex_model()
except (TypeError, ValueError):
generator = matrix(generator)
generator = SixVertexModel(generator.nrows(), boundary_conditions='ice')(generator)
# Check that this is an ice square model
M = generator.to_alternating_sign_matrix()
SVM = generator
if not SVM:
raise TypeError('generator for FullyPackedLoop must either be an \
AlternatingSignMatrix or a SquareIceModel.Element')
FPLs = FullyPackedLoops(len(SVM))
return FPLs(generator)
def _element_constructor_(self, generator):
"""
Construct an element of ``self``.
EXAMPLES::
sage: FPLs = FullyPackedLoops(4)
sage: M = [[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]
sage: A = AlternatingSignMatrix(M)
sage: elt = FullyPackedLoop(A)
sage: FPL = FPLs(elt); FPL
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+ + -- + + --
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-- + + + -- +
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+ -- + + + --
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-- + + -- + +
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sage: FPLs(A) == FPL
True
sage: FPLs(M) == FPL
True
sage: FPLs(FPL._six_vertex_model) == FPL
True
sage: FPL.parent() is FPLs
True
sage: FPL = FullyPackedLoops(2)
sage: FPL([[3,1],[5,3]])
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+ + --
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-- + +
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"""
if isinstance(generator, AlternatingSignMatrix):
SVM = generator.to_six_vertex_model()
elif isinstance(generator, SquareIceModel.Element) or \
isinstance(generator, SixVertexConfiguration):
SVM = generator
else: # Not ASM nor SVM
try:
SVM = AlternatingSignMatrix(generator).to_six_vertex_model()
except (TypeError, ValueError):
SVM = SixVertexModel(self._n, boundary_conditions='ice')(generator)
SVM.to_alternating_sign_matrix()
if len(SVM) != self._n:
raise ValueError("invalid size")
return self.element_class(self, SVM)
