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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,124 @@ | ||
| r""" | ||
| Linear family of coordinates on a veering triangulation | ||
| """ | ||
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| if sage is not None: | ||
| from sage.structure.element import get_coercion_model | ||
| cm = get_coercion_model() | ||
| else: | ||
| cm = None | ||
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| def subspace_are_equal(subspace1, subspace2): | ||
| if subspace1.ncols() != subspace2.ncols(): | ||
| raise ValueError | ||
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| n = subspace1.nrows() | ||
| if n != subspace2.nrows(): | ||
| return False | ||
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| base_ring = cm.common_parent(subspace1.base_ring(), subspace2.base_ring()) | ||
| mat = matrix(base_ring, n + 1, subspace1.ncols()) | ||
| mat[:n] = subspace1 | ||
| for v in subspace2.rows(): | ||
| mat[n] = v | ||
| r = mat.rank() | ||
| if r < n: | ||
| raise RuntimeError('matrices where expected to be full rank') | ||
| if r > n: | ||
| return False | ||
| return True | ||
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| class VeeringTriangulationLinearFamily(VeeringTriangulation): | ||
| __slots__ = ['_equations'] | ||
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| def __init__(self, triangulation, colouring, subspace, check=True): | ||
| VeeringTriangulation.__init__(triangulation, colouring) | ||
| self._subspace = subspace | ||
| if check: | ||
| self._check(ValueError) | ||
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| def __str__(self): | ||
| return "LinearFamily\n {}\n{}".format(self._vt, self._Gx) | ||
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| def __repr__(self): | ||
| return str(self) | ||
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| def _check(self, error=ValueError): | ||
| subspace = self._subspace | ||
| if subspace.ncols() != self.num_edges(): | ||
| raise error('subspace matrix has wrong dimension') | ||
| if subspace.rank() != subspace.nrows(): | ||
| raise error('subspace matrix is not of full rank') | ||
| # test that elements satisfy the switch condition | ||
| for v in subspace.rows(): | ||
| self._set_switch_conditions(self._tt_check, v, VERTICAL) | ||
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| def __eq__(self, other): | ||
| if type(self) is not type(other): | ||
| raise TypeError | ||
| test = (VeeringTriangulation.__eq__(self, other) and | ||
| self._subspace.nrows() != other._subspace.nrows()) | ||
| if not test: | ||
| return False | ||
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| return subspace_are_equal(self._subspace, other._subspace) | ||
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| def __ne__(self, other): | ||
| if type(self) is not type(other): | ||
| raise TypeError | ||
| test = (VeeringTriangulation.__eq__(self, other) and | ||
| self._subspace.nrows() != other._subspace.nrows()) | ||
| if not test: | ||
| return True | ||
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| return not subspace_are_equal(self._subspace, other._subspace) | ||
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| def dimension(self): | ||
| r""" | ||
| Return the dimension of the linear family. | ||
| """ | ||
| return self._subspace.nrows() | ||
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| def is_core(self): | ||
| r""" | ||
| Test whether this linear family is core. | ||
| It is core, if the dimension of the polytope given by the train-track | ||
| and non-negativity conditions is full dimensional in the subspace. | ||
| """ | ||
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| def relabel(self, p): | ||
| pass | ||
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| def iso_sig(self): | ||
| pass | ||
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| # TODO: change to canonicalize ? Since we also need to canonicalize the subspace | ||
| # it is not only about labels | ||
| def set_canonical_labels(self): | ||
| pass | ||
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| def is_isomorphic_to(self, other, certificate=False): | ||
| pass | ||
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| def flip(self, e, col, check=True): | ||
| pass | ||
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| def geometric_polytope(self, x_low_bound=0, y_low_bound=0, hw_bound=0): | ||
| pass | ||
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| def geometric_flips(self): | ||
| pass | ||
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| class VeeringTriangulationLinearFamilies: | ||
| r""" | ||
| A collection of linear families. | ||
| """ | ||
| @staticmethod | ||
| def L_shaped_surface(a1, a2, b1, b2, t1=0, t2=0): | ||
| vt, s, t = VeeringTriangulations.L_shaped_surface(a1, a2, b1, b2, t1, t2) | ||
| return VeeringTriangulationLinearFamily(vt, matrix([s, t])) |
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