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Diagrams now do checks with __lt__.
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Travis Scrimshaw committed May 19, 2018
1 parent fbab6bb commit 91996a1
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112 changes: 65 additions & 47 deletions src/sage/combinat/diagram_algebras.py
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Expand Up @@ -288,6 +288,15 @@ def __eq__(self, other):
sage: pd3 = da.AbstractPartitionDiagram(pd, [[1,-2],[-1,2]])
sage: pd1 == pd3
False
Check the inherited inequality::
sage: pd1 = da.AbstractPartitionDiagram(pd, [[1,2],[-1,-2]])
sage: pd2 = da.AbstractPartitionDiagram(pd, [[1,-2],[-1,2]])
sage: pd1 != pd2
True
sage: pd1 != ((-2,-1),(2,1))
False
"""
try:
return self._base_diagram == other._base_diagram
Expand All @@ -300,22 +309,28 @@ def __eq__(self, other):
except (TypeError, ValueError, AttributeError):
return False

def __ne__(self, other):
def __lt__(self, other):
"""
Check not equals.
Compare less than.
TESTS::
EXAMPLES::
sage: import sage.combinat.diagram_algebras as da
sage: pd = da.AbstractPartitionDiagrams(2)
sage: pd1 = da.AbstractPartitionDiagram(pd, [[1,2],[-1,-2]])
sage: pd2 = da.AbstractPartitionDiagram(pd, [[1,-2],[-1,2]])
sage: pd1 != pd2
sage: pd1 < pd2
True
sage: pd1 != ((-2,-1),(2,1))
sage: pd2 < pd1
False
sage: pd2 > pd1
True
sage: pd1 > pd2
False
"""
return not self == other
if not isinstance(other, AbstractPartitionDiagram):
return False
return self._base_diagram < other._base_diagram

def base_diagram(self):
r"""
Expand Down Expand Up @@ -1552,7 +1567,7 @@ class DiagramAlgebra(CombinatorialFreeModule):
sage: import sage.combinat.diagram_algebras as da
sage: R.<x> = QQ[]
sage: D = da.DiagramAlgebra(2, x, R, 'P', da.PartitionDiagrams(2))
sage: sorted(D.basis())
sage: list(D.basis())
[P{{-2, -1, 1, 2}}, P{{-2, -1, 2}, {1}},
P{{-2, -1, 1}, {2}}, P{{-2, 1, 2}, {-1}},
P{{-2}, {-1, 1, 2}}, P{{-2, 1}, {-1, 2}},
Expand Down Expand Up @@ -2058,7 +2073,7 @@ class PartitionAlgebra(DiagramBasis, UnitDiagramMixin):
sage: E^5
x^4*P{{-2, -1}, {1, 2}}
sage: (P([[2,-2],[-1,1]]) - 2*P([[1,2],[-1,-2]]))^2
P{{-2, 2}, {-1, 1}} + (4*x-4)*P{{-2, -1}, {1, 2}}
(4*x-4)*P{{-2, -1}, {1, 2}} + P{{-2, 2}, {-1, 1}}
One can work with partition algebras using a symbol for the parameter,
leaving the base ring unspecified. This implies that the underlying
Expand Down Expand Up @@ -2214,32 +2229,32 @@ def _element_constructor_(self, x):
sage: B = BrauerAlgebra(3, x, R)
sage: O = A.orbit_basis()
sage: O2.an_element()
2*O{{-2, -1, 1, 2}} + 3*O{{-2, -1, 1}, {2}} + 2*O{{-2, -1, 2}, {1}}
3*O{{-2, -1, 1}, {2}} + 2*O{{-2, -1, 1, 2}} + 2*O{{-2, -1, 2}, {1}}
sage: A(O2.an_element())
3*P{{-3, 3}, {-2, -1, 1}, {2}} + 2*P{{-3, 3}, {-2, -1, 2}, {1}}
- 3*P{{-3, 3}, {-2, -1, 1, 2}}
3*P{{-3, 3}, {-2, -1, 1}, {2}} - 3*P{{-3, 3}, {-2, -1, 1, 2}}
+ 2*P{{-3, 3}, {-2, -1, 2}, {1}}
sage: A2.an_element()
2*P{{-2, -1, 1, 2}} + 3*P{{-2, -1, 1}, {2}} + 2*P{{-2, -1, 2}, {1}}
3*P{{-2, -1, 1}, {2}} + 2*P{{-2, -1, 1, 2}} + 2*P{{-2, -1, 2}, {1}}
sage: A(A2.an_element())
3*P{{-3, 3}, {-2, -1, 1}, {2}} + 2*P{{-3, 3}, {-2, -1, 2}, {1}}
+ 2*P{{-3, 3}, {-2, -1, 1, 2}}
3*P{{-3, 3}, {-2, -1, 1}, {2}} + 2*P{{-3, 3}, {-2, -1, 1, 2}}
+ 2*P{{-3, 3}, {-2, -1, 2}, {1}}
sage: S.an_element()
[1, 2, 3] + 2*[1, 3, 2] + 3*[2, 1, 3] + [3, 1, 2]
sage: A(S.an_element())
P{{-3, 3}, {-2, 2}, {-1, 1}} + P{{-3, 1}, {-2, 3}, {-1, 2}} + 3*P{{-3, 3}, {-2, 1}, {-1, 2}}
+ 2*P{{-3, 2}, {-2, 3}, {-1, 1}}
P{{-3, 1}, {-2, 3}, {-1, 2}} + 2*P{{-3, 2}, {-2, 3}, {-1, 1}}
+ 3*P{{-3, 3}, {-2, 1}, {-1, 2}} + P{{-3, 3}, {-2, 2}, {-1, 1}}
sage: B.an_element()
3*B{{-3, 1}, {-2, -1}, {2, 3}} + 2*B{{-3, 1}, {-2, 2}, {-1, 3}}
+ 2*B{{-3, 1}, {-2, 3}, {-1, 2}}
sage: A(B.an_element())
2*P{{-3, 1}, {-2, 2}, {-1, 3}} + 2*P{{-3, 1}, {-2, 3}, {-1, 2}}
+ 3*P{{-3, 1}, {-2, -1}, {2, 3}}
3*P{{-3, 1}, {-2, -1}, {2, 3}} + 2*P{{-3, 1}, {-2, 2}, {-1, 3}}
+ 2*P{{-3, 1}, {-2, 3}, {-1, 2}}
sage: O.an_element()
2*O{{-3, -2, -1, 2, 3}, {1}} + 3*O{{-3, -2, -1, 1, 3}, {2}}
+ 2*O{{-3, -2, -1, 1, 2, 3}}
2*O{{-3, -2, -1, 1, 2, 3}} + 3*O{{-3, -2, -1, 1, 3}, {2}}
+ 2*O{{-3, -2, -1, 2, 3}, {1}}
sage: A(O.an_element())
2*P{{-3, -2, -1, 2, 3}, {1}} + 3*P{{-3, -2, -1, 1, 3}, {2}}
- 3*P{{-3, -2, -1, 1, 2, 3}}
-3*P{{-3, -2, -1, 1, 2, 3}} + 3*P{{-3, -2, -1, 1, 3}, {2}}
+ 2*P{{-3, -2, -1, 2, 3}, {1}}
sage: A([])
P{{-3, 3}, {-2, 2}, {-1, 1}}
sage: A(4)
Expand Down Expand Up @@ -2366,10 +2381,11 @@ def _coerce_map_from_(self, R):
TESTS::
sage: elt = O3.an_element(); elt
2*O{{-3, -2, -1, 2, 3}, {1}} + 3*O{{-3, -2, -1, 1, 3}, {2}}
+ 2*O{{-3, -2, -1, 1, 2, 3}}
2*O{{-3, -2, -1, 1, 2, 3}} + 3*O{{-3, -2, -1, 1, 3}, {2}}
+ 2*O{{-3, -2, -1, 2, 3}, {1}}
sage: A._coerce_map_from_(O3)(elt)
3*P{{-4, 4}, {-3, -2, -1, 1, 3}, {2}} - 3*P{{-4, 4}, {-3, -2, -1, 1, 2, 3}}
-3*P{{-4, 4}, {-3, -2, -1, 1, 2, 3}}
+ 3*P{{-4, 4}, {-3, -2, -1, 1, 3}, {2}}
+ 2*P{{-4, 4}, {-3, -2, -1, 2, 3}, {1}}
"""
# coerce from Orbit basis.
Expand Down Expand Up @@ -2405,12 +2421,14 @@ def orbit_basis(self):
sage: pp = 7 * P2[{-1}, {-2, 1, 2}] - 2 * P2[{-2}, {-1, 1}, {2}]; pp
-2*P{{-2}, {-1, 1}, {2}} + 7*P{{-2, 1, 2}, {-1}}
sage: op = pp.to_orbit_basis(); op
5*O{{-2, -1, 1, 2}} - 2*O{{-2, 2}, {-1, 1}} - 2*O{{-2, -1, 1}, {2}}
- 2*O{{-2}, {-1, 1}, {2}} - 2*O{{-2}, {-1, 1, 2}} + 7*O{{-2, 1, 2}, {-1}}
-2*O{{-2}, {-1, 1}, {2}} - 2*O{{-2}, {-1, 1, 2}}
- 2*O{{-2, -1, 1}, {2}} + 5*O{{-2, -1, 1, 2}}
+ 7*O{{-2, 1, 2}, {-1}} - 2*O{{-2, 2}, {-1, 1}}
sage: op == O2(op)
True
sage: pp * op.leading_term()
35*P{{-2, -1, 1, 2}} - 10*P{{-2, -1, 1}, {2}}
4*P{{-2}, {-1, 1}, {2}} - 4*P{{-2, -1, 1}, {2}}
+ 14*P{{-2, -1, 1, 2}} - 14*P{{-2, 1, 2}, {-1}}
"""
return OrbitBasis(self)

Expand Down Expand Up @@ -2445,9 +2463,9 @@ def to_orbit_basis(self):
sage: R.<x> = QQ[]
sage: P = PartitionAlgebra(2, x, R)
sage: pp = P.an_element(); pp
2*P{{-2, -1, 1, 2}} + 3*P{{-2, -1, 1}, {2}} + 2*P{{-2, -1, 2}, {1}}
3*P{{-2, -1, 1}, {2}} + 2*P{{-2, -1, 1, 2}} + 2*P{{-2, -1, 2}, {1}}
sage: pp.to_orbit_basis()
7*O{{-2, -1, 1, 2}} + 3*O{{-2, -1, 1}, {2}} + 2*O{{-2, -1, 2}, {1}}
3*O{{-2, -1, 1}, {2}} + 7*O{{-2, -1, 1, 2}} + 2*O{{-2, -1, 2}, {1}}
"""
OP = self.parent().orbit_basis()
return OP(self)
Expand Down Expand Up @@ -2495,8 +2513,8 @@ class OrbitBasis(DiagramAlgebra):
We can convert between the two bases::
sage: pa = P2(oa); pa
2*P{{-2, -1, 1, 2}} - P{{-2, 1, 2}, {-1}} - P{{-2, 2}, {-1, 1}}
+ P{{-2, 2}, {-1}, {1}} - P{{-2, -1, 2}, {1}}
2*P{{-2, -1, 1, 2}} - P{{-2, -1, 2}, {1}} - P{{-2, 1, 2}, {-1}}
+ P{{-2, 2}, {-1}, {1}} - P{{-2, 2}, {-1, 1}}
sage: pa * ob
(-x+2)*P{{-2, -1, 1, 2}} + (x-2)*P{{-2, -1, 2}, {1}}
sage: _ == pa * P2(ob)
Expand Down Expand Up @@ -2678,7 +2696,7 @@ def diagram_basis(self):
Partition Algebra of rank 2 with parameter x over Univariate
Polynomial Ring in x over Rational Field
sage: P2(O2.an_element())
-3*P{{-2, -1, 1, 2}} + 3*P{{-2, -1, 1}, {2}} + 2*P{{-2, -1, 2}, {1}}
3*P{{-2, -1, 1}, {2}} - 3*P{{-2, -1, 1, 2}} + 2*P{{-2, -1, 2}, {1}}
TESTS::
Expand Down Expand Up @@ -2716,8 +2734,8 @@ def _diagram_to_orbit_on_basis(self, diag):
O{{-2, -1, 1, 2}} + O{{-2, 2}, {-1, 1}}
sage: pp = P2[{-2}, {-1, 1}, {2}]
sage: O2(pp)
O{{-2, -1, 1, 2}} + O{{-2, -1, 1}, {2}} + O{{-2}, {-1, 1}, {2}}
+ O{{-2, 2}, {-1, 1}} + O{{-2}, {-1, 1, 2}}
O{{-2}, {-1, 1}, {2}} + O{{-2}, {-1, 1, 2}} + O{{-2, -1, 1}, {2}}
+ O{{-2, -1, 1, 2}} + O{{-2, 2}, {-1, 1}}
TESTS::
Expand Down Expand Up @@ -2754,7 +2772,7 @@ def product_on_basis(self, d1, d2):
sage: o3 * o1 == o1 * o3 and o3 * o1 == o3
True
sage: o3 * o3
4*O{{-2, -1, 1, 2}} + 6*O{{-2, -1, 1}, {2}} + 4*O{{-2, -1, 2}, {1}}
6*O{{-2, -1, 1}, {2}} + 4*O{{-2, -1, 1, 2}} + 4*O{{-2, -1, 2}, {1}}
We compute Examples 4.5 in [BH2017]_::
Expand All @@ -2766,12 +2784,12 @@ def product_on_basis(self, d1, d2):
sage: P = PartitionAlgebra(4,x); O = P.orbit_basis()
sage: O[[1],[-1],[2,3],[4,-2],[-3,-4]] * O[[1],[2,-2],[3,4],[-1,-3],[-4]]
(x^2-11*x+30)*O{{-4}, {-3, -1}, {-2, 4}, {1}, {2, 3}}
+ (x^2-7*x+12)*O{{-4, 1}, {-3, -1, 2, 3}, {-2, 4}}
+ (x^2-7*x+12)*O{{-4, 2, 3}, {-3, -1, 1}, {-2, 4}}
+ (x^2-9*x+20)*O{{-4, 1}, {-3, -1}, {-2, 4}, {2, 3}}
+ (x^2-9*x+20)*O{{-4, 2, 3}, {-3, -1}, {-2, 4}, {1}}
+ (x^2-9*x+20)*O{{-4}, {-3, -1, 1}, {-2, 4}, {2, 3}}
+ (x^2-9*x+20)*O{{-4}, {-3, -1, 2, 3}, {-2, 4}, {1}}
+ (x^2-9*x+20)*O{{-4, 1}, {-3, -1}, {-2, 4}, {2, 3}}
+ (x^2-7*x+12)*O{{-4, 1}, {-3, -1, 2, 3}, {-2, 4}}
+ (x^2-9*x+20)*O{{-4, 2, 3}, {-3, -1}, {-2, 4}, {1}}
+ (x^2-7*x+12)*O{{-4, 2, 3}, {-3, -1, 1}, {-2, 4}}
sage: O[[1,-1],[2,-2],[3],[4,-3],[-4]] * O[[1,-2],[2],[3,-1],[4],[-3],[-4]]
(x-6)*O{{-4}, {-3}, {-2, 1}, {-1, 4}, {2}, {3}}
Expand Down Expand Up @@ -2853,12 +2871,12 @@ def to_diagram_basis(self):
sage: P = PartitionAlgebra(2, x, R)
sage: O = P.orbit_basis()
sage: elt = O.an_element(); elt
2*O{{-2, -1, 1, 2}} + 3*O{{-2, -1, 1}, {2}} + 2*O{{-2, -1, 2}, {1}}
3*O{{-2, -1, 1}, {2}} + 2*O{{-2, -1, 1, 2}} + 2*O{{-2, -1, 2}, {1}}
sage: elt.to_diagram_basis()
-3*P{{-2, -1, 1, 2}} + 3*P{{-2, -1, 1}, {2}} + 2*P{{-2, -1, 2}, {1}}
3*P{{-2, -1, 1}, {2}} - 3*P{{-2, -1, 1, 2}} + 2*P{{-2, -1, 2}, {1}}
sage: pp = P.an_element()
sage: op = pp.to_orbit_basis(); op
7*O{{-2, -1, 1, 2}} + 3*O{{-2, -1, 1}, {2}} + 2*O{{-2, -1, 2}, {1}}
3*O{{-2, -1, 1}, {2}} + 7*O{{-2, -1, 1, 2}} + 2*O{{-2, -1, 2}, {1}}
sage: pp == op.to_diagram_basis()
True
"""
Expand Down Expand Up @@ -2950,8 +2968,8 @@ def to_orbit_basis(self):
sage: bb = B.an_element(); bb
3*B{{-2, -1}, {1, 2}} + 2*B{{-2, 1}, {-1, 2}} + 2*B{{-2, 2}, {-1, 1}}
sage: bb.to_orbit_basis()
7*O{{-2, -1, 1, 2}} + 3*O{{-2, -1}, {1, 2}} + 2*O{{-2, 2}, {-1, 1}}
+ 2*O{{-2, 1}, {-1, 2}}
3*O{{-2, -1}, {1, 2}} + 7*O{{-2, -1, 1, 2}} + 2*O{{-2, 1}, {-1, 2}}
+ 2*O{{-2, 2}, {-1, 1}}
"""
P = self.parent().lift.codomain()
OP = P.orbit_basis()
Expand Down Expand Up @@ -3138,9 +3156,9 @@ def jucys_murphy(self, j):
sage: B.jucys_murphy(1)
(1/2*z-1/2)*B{{-3, 3}, {-2, 2}, {-1, 1}}
sage: B.jucys_murphy(3)
-B{{-3, -1}, {-2, 2}, {1, 3}} + (1/2*z-1/2)*B{{-3, 3}, {-2, 2}, {-1, 1}}
-B{{-3, -2}, {-1, 1}, {2, 3}} - B{{-3, -1}, {-2, 2}, {1, 3}}
+ B{{-3, 1}, {-2, 2}, {-1, 3}} + B{{-3, 2}, {-2, 3}, {-1, 1}}
- B{{-3, -2}, {-1, 1}, {2, 3}}
+ (1/2*z-1/2)*B{{-3, 3}, {-2, 2}, {-1, 1}}
"""
if j < 1:
raise ValueError("Jucys-Murphy index must be positive")
Expand Down
6 changes: 3 additions & 3 deletions src/sage/combinat/set_partition.py
View file
Expand Up @@ -110,7 +110,7 @@ def __eq__(self, y):
sage: A == D
False
"""
if not isinstance(y, SetPartition):
if not isinstance(y, AbstractSetPartition):
return False
return list(self) == list(y)

Expand Down Expand Up @@ -174,7 +174,7 @@ def __lt__(self, y):
sage: A < C
True
"""
if not isinstance(y, SetPartition):
if not isinstance(y, AbstractSetPartition):
return False
return [sorted(_) for _ in self] < [sorted(_) for _ in y]

Expand Down Expand Up @@ -202,7 +202,7 @@ def __gt__(self, y):
sage: A > B
False
"""
if not isinstance(y, SetPartition):
if not isinstance(y, AbstractSetPartition):
return False
return [sorted(_) for _ in self] > [sorted(_) for _ in y]

Expand Down

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