def to_alternating_sign_matrix(self):
"""
Return an alternating sign matrix of ``self``.
.. SEEALSO::
:meth:`~sage.combinat.six_vertex_model.SixVertexConfiguration.to_signed_matrix()`
EXAMPLES::
sage: M = SixVertexModel(4, boundary_conditions='ice')
sage: M[6].to_alternating_sign_matrix()
[1 0 0 0]
[0 0 0 1]
[0 0 1 0]
[0 1 0 0]
sage: M[7].to_alternating_sign_matrix()
[ 0 1 0 0]
[ 1 -1 1 0]
[ 0 1 -1 1]
[ 0 0 1 0]
"""
from sage.combinat.alternating_sign_matrix import AlternatingSignMatrix #AlternatingSignMatrices
#ASM = AlternatingSignMatrices(self.parent()._nrows)
#return ASM(self.to_signed_matrix())
return AlternatingSignMatrix(self.to_signed_matrix())
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)
