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Fix Singular polynomial comparison #39018

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merged 16 commits into from
Jan 27, 2025
Merged

Fix Singular polynomial comparison #39018

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e21672b
Fix Singular polynomial comparison
user202729 Nov 21, 2024
0d85f6f
Make polynomial comparison more robust
user202729 Nov 22, 2024
c489f3d
Fix tests
user202729 Nov 22, 2024
47c6fcf
Actually fix test
user202729 Nov 22, 2024
f5aec98
Actually actually fix tests
user202729 Nov 29, 2024
cca2d2b
Forget to fix long tests
user202729 Nov 29, 2024
58c0dce
Apparently line continuation makes fixdoctests fail, fixed now
user202729 Nov 29, 2024
5c8248a
Merge remote-tracking branch 'upstream/develop' into singular-cmp-fix
user202729 Dec 23, 2024
a8cd3b3
Merge branch 'develop' into singular-cmp-fix
user202729 Jan 5, 2025
8d8ba8f
Merge remote-tracking branch 'upstream/develop' into singular-cmp-fix
user202729 Jan 22, 2025
d66d021
Fix broken merge conflict resolution
user202729 Jan 23, 2025
723f5c1
Wrap long lines
user202729 Jan 23, 2025
5427ce1
Recover manual formatting
kwankyu Jan 23, 2025
4bac201
Add another doctest
user202729 Jan 23, 2025
66f0083
Lines in doctest output cannot be broken at non-whitespaces
user202729 Jan 23, 2025
f18e9fc
Fix style issue
user202729 Jan 23, 2025
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6 changes: 3 additions & 3 deletions src/doc/de/tutorial/tour_advanced.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -35,11 +35,11 @@ wir diese schneiden und dann die irreduziblen Komponenten berechnen.
sage: V = C2.intersection(C3)
sage: V.irreducible_components()
[Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y - 1,
x,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x + y + 2,
2*y^2 + 4*y + 3]
Expand Down
6 changes: 3 additions & 3 deletions src/doc/en/tutorial/tour_advanced.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -35,11 +35,11 @@ intersecting them and computing the irreducible components.
sage: V = C2.intersection(C3)
sage: V.irreducible_components()
[Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y - 1,
x,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x + y + 2,
2*y^2 + 4*y + 3]
Expand Down
6 changes: 3 additions & 3 deletions src/doc/fr/tutorial/tour_advanced.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -36,11 +36,11 @@ irréductibles.
sage: V = C2.intersection(C3)
sage: V.irreducible_components()
[Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y - 1,
x,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x + y + 2,
2*y^2 + 4*y + 3]
Expand Down
6 changes: 3 additions & 3 deletions src/doc/ja/tutorial/tour_advanced.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -35,11 +35,11 @@ Sageでは，任意の代数多様体を定義することができるが，そ
sage: V = C2.intersection(C3)
sage: V.irreducible_components()
[Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y - 1,
x,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x + y + 2,
2*y^2 + 4*y + 3]
Expand Down
6 changes: 3 additions & 3 deletions src/doc/pt/tutorial/tour_advanced.rst
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -36,11 +36,11 @@ irredutíveis.
sage: V = C2.intersection(C3)
sage: V.irreducible_components()
[Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y - 1,
x,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x + y + 2,
2*y^2 + 4*y + 3]
Expand Down
6 changes: 3 additions & 3 deletions src/doc/ru/tutorial/tour_advanced.rst
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Original file line number Diff line number Diff line change
Expand Up @@ -33,11 +33,11 @@ Sage позволяет создавать любые алгебраически
sage: V = C2.intersection(C3)
sage: V.irreducible_components()
[Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y - 1,
x,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
y,
x - 1,
Closed subscheme of Affine Space of dimension 2 over Rational Field defined by:
x + y + 2,
2*y^2 + 4*y + 3]
Expand Down
87 changes: 42 additions & 45 deletions src/sage/algebras/hecke_algebras/ariki_koike_algebra.py
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Original file line number Diff line number Diff line change
Expand Up @@ -212,14 +212,14 @@ class ArikiKoikeAlgebra(Parent, UniqueRepresentation):
sage: T1 * L1 * T2 * L3 * T1 * T2
-(q-q^2)*L2*L3*T[2] + q*L1*L2*T[2,1] - (1-q)*L1*L2*T[2,1,2]
sage: L1^3
u0*u1*u2 + ((-u0*u1-u0*u2-u1*u2))*L1 + ((u0+u1+u2))*L1^2
u0*u1*u2 - ((u0*u1+u0*u2+u1*u2))*L1 + ((u0+u1+u2))*L1^2
sage: L3 * L2 * L1
L1*L2*L3
sage: u = LT.u()
sage: q = LT.q()
sage: (q + 2*u[0]) * (T1 * T2) * L3
(-2*u0+(2*u0-1)*q+q^2)*L3*T[1] + (-2*u0+(2*u0-1)*q+q^2)*L2*T[2]
+ (2*u0+q)*L1*T[1,2]
-(2*u0+(-2*u0+1)*q-q^2)*L3*T[1] - (2*u0+(-2*u0+1)*q-q^2)*L2*T[2]
+ (2*u0+q)*L1*T[1,2]

We check the defining relations::

Expand Down Expand Up @@ -789,11 +789,11 @@ def L(self, i=None):

sage: LT = algebras.ArikiKoike(1, 3).LT()
sage: LT.L(2)
u + (-u*q^-1+u)*T[1]
u - (u*q^-1-u)*T[1]
sage: LT.L()
[u,
u + (-u*q^-1+u)*T[1],
u + (-u*q^-1+u)*T[2] + (-u*q^-2+u*q^-1)*T[2,1,2]]
u - (u*q^-1-u)*T[1],
u - (u*q^-1-u)*T[2] - (u*q^-2-u*q^-1)*T[2,1,2]]
"""
G = self.algebra_generators()
if i is None:
Expand Down Expand Up @@ -824,18 +824,18 @@ def product_on_basis(self, m1, m2):
sage: L1^2 * T1 * L1^2 * T1
q*L1^2*L2^2 + (1-q)*L1^3*L2*T[1]
sage: L1^3 * T1 * L1^2 * T1
(-u0*u1*u2*u3+u0*u1*u2*u3*q)*L2*T[1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3)+(-u0*u1*u2-u0*u1*u3-u0*u2*u3-u1*u2*u3)*q)*L1*L2*T[1]
+ ((-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3)+(u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3)*q)*L1^2*L2*T[1]
+ ((u0+u1+u2+u3)+(-u0-u1-u2-u3)*q)*L1^3*L2*T[1] + q*L1^3*L2^2
-(u0*u1*u2*u3-u0*u1*u2*u3*q)*L2*T[1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3)+(-u0*u1*u2-u0*u1*u3-u0*u2*u3-u1*u2*u3)*q)*L1*L2*T[1]
- ((u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3)+(-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3)*q)*L1^2*L2*T[1]
+ ((u0+u1+u2+u3)+(-u0-u1-u2-u3)*q)*L1^3*L2*T[1] + q*L1^3*L2^2

sage: L1^2 * T1 * L1^3 * T1
(-u0*u1*u2*u3+u0*u1*u2*u3*q)*L2*T[1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3)+(-u0*u1*u2-u0*u1*u3-u0*u2*u3-u1*u2*u3)*q)*L1*L2*T[1]
+ ((-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3)+(u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3)*q)*L1^2*L2*T[1]
+ q*L1^2*L2^3
+ ((u0+u1+u2+u3)+(-u0-u1-u2-u3)*q)*L1^3*L2*T[1]
+ (1-q)*L1^3*L2^2*T[1]
-(u0*u1*u2*u3-u0*u1*u2*u3*q)*L2*T[1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3)+(-u0*u1*u2-u0*u1*u3-u0*u2*u3-u1*u2*u3)*q)*L1*L2*T[1]
- ((u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3)+(-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3)*q)*L1^2*L2*T[1]
+ q*L1^2*L2^3
+ ((u0+u1+u2+u3)+(-u0-u1-u2-u3)*q)*L1^3*L2*T[1]
+ (1-q)*L1^3*L2^2*T[1]

sage: L1^2 * T1*T2*T1 * L2 * L3 * T2
(q-2*q^2+q^3)*L1^2*L2*L3 - (1-2*q+2*q^2-q^3)*L1^2*L2*L3*T[2]
Expand Down Expand Up @@ -1061,7 +1061,7 @@ def _Li_power(self, i, m):
sage: H = algebras.ArikiKoike(3, 2).LT()
sage: L2 = H.L(2)
sage: H._Li_power(2, 4)
((u0^2*u1*u2+u0*u1^2*u2+u0*u1*u2^2)) + ...
((u0^2*u1*u2+u0*u1^2*u2+u0*u1*u2^2)) ...
- (q^-1-1)*L1*L2^3*T[1] ...
- (q^-1-1)*L1^3*L2*T[1]
sage: H._Li_power(2, 4) == L2^4
Expand All @@ -1078,20 +1078,20 @@ def _Li_power(self, i, m):
L_1^0 = 1
L_1^1 = L1
L_1^2 = L1^2
L_1^3 = u0*u1*u2 + ((-u0*u1-u0*u2-u1*u2))*L1 + ((u0+u1+u2))*L1^2
L_1^3 = u0*u1*u2 - ((u0*u1+u0*u2+u1*u2))*L1 + ((u0+u1+u2))*L1^2
L_2^0 = 1
L_2^1 = L2
L_2^2 = L2^2
L_2^3 = u0*u1*u2 + (-u0*u1*u2*q^-1+u0*u1*u2)*T[1]
+ ((-u0*u1-u0*u2-u1*u2))*L2 + ((u0+u1+u2))*L2^2
L_2^3 = u0*u1*u2 - (u0*u1*u2*q^-1-u0*u1*u2)*T[1]
- ((u0*u1+u0*u2+u1*u2))*L2 + ((u0+u1+u2))*L2^2
+ ((u0+u1+u2)*q^-1+(-u0-u1-u2))*L1*L2*T[1]
- (q^-1-1)*L1*L2^2*T[1] - (q^-1-1)*L1^2*L2*T[1]
L_3^0 = 1
L_3^1 = L3
L_3^2 = L3^2
L_3^3 = u0*u1*u2 + (-u0*u1*u2*q^-1+u0*u1*u2)*T[2]
+ (-u0*u1*u2*q^-2+u0*u1*u2*q^-1)*T[2,1,2]
+ ((-u0*u1-u0*u2-u1*u2))*L3 + ((u0+u1+u2))*L3^2
L_3^3 = u0*u1*u2 - (u0*u1*u2*q^-1-u0*u1*u2)*T[2]
- (u0*u1*u2*q^-2-u0*u1*u2*q^-1)*T[2,1,2]
- ((u0*u1+u0*u2+u1*u2))*L3 + ((u0+u1+u2))*L3^2
+ ((u0+u1+u2)*q^-1+(-u0-u1-u2))*L2*L3*T[2]
- (q^-1-1)*L2*L3^2*T[2] - (q^-1-1)*L2^2*L3*T[2]
+ ((u0+u1+u2)*q^-2+(-2*u0-2*u1-2*u2)*q^-1+(u0+u1+u2))*L1*L3*T[1,2]
Expand Down Expand Up @@ -1376,11 +1376,11 @@ def L(self, i=None):

sage: T = algebras.ArikiKoike(1, 3).T()
sage: T.L(2)
u + (-u*q^-1+u)*T[1]
u - (u*q^-1-u)*T[1]
sage: T.L()
[u,
u + (-u*q^-1+u)*T[1],
u + (-u*q^-1+u)*T[2] + (-u*q^-2+u*q^-1)*T[2,1,2]]
u - (u*q^-1-u)*T[1],
u - (u*q^-1-u)*T[2] - (u*q^-2-u*q^-1)*T[2,1,2]]

TESTS:

Expand Down Expand Up @@ -1432,10 +1432,10 @@ def product_on_basis(self, m1, m2):
sage: T2 * (T2 * T1 * T0)
-(1-q)*T[2,1,0] + q*T[1,0]
sage: (T1 * T0 * T1 * T0) * T0
(-u0*u1)*T[1,0,1] + ((u0+u1))*T[0,1,0,1]
-u0*u1*T[1,0,1] + ((u0+u1))*T[0,1,0,1]
sage: (T0 * T1 * T0 * T1) * (T0 * T1)
(-u0*u1*q)*T[1,0] + (u0*u1-u0*u1*q)*T[1,0,1]
+ ((u0+u1)*q)*T[0,1,0] + ((-u0-u1)+(u0+u1)*q)*T[0,1,0,1]
-u0*u1*q*T[1,0] + (u0*u1-u0*u1*q)*T[1,0,1]
+ ((u0+u1)*q)*T[0,1,0] - ((u0+u1)+(-u0-u1)*q)*T[0,1,0,1]
sage: T1 * (T0 * T2 * T1 * T0)
T[1,0,2,1,0]
sage: (T1 * T2) * (T2 * T1 * T0)
Expand All @@ -1462,7 +1462,7 @@ def product_on_basis(self, m1, m2):
sage: T = algebras.ArikiKoike(2, 3).T()
sage: T0, T1, T2 = T.T()
sage: (T1 * T0 * T1) * (T0 * T0)
(-u0*u1)*T[1,0,1] + ((u0+u1))*T[0,1,0,1]
-u0*u1*T[1,0,1] + ((u0+u1))*T[0,1,0,1]
sage: T1 * T.L(3) * T2 * T1 * T0 - T1 * (T.L(3) * T2 * T1 * T0)
0

Expand Down Expand Up @@ -1674,42 +1674,39 @@ def _product_TT(self, kp, a, k, b):
sage: T._product_TT(1, 2, 0, 1)
T[1,0,0,0]
sage: T._product_TT(1, 3, 0, 1)
(-u0*u1*u2*u3)*T[1]
-u0*u1*u2*u3*T[1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3))*T[1,0]
+ ((-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3))*T[1,0,0]
- ((u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3))*T[1,0,0]
+ ((u0+u1+u2+u3))*T[1,0,0,0]
sage: T._product_TT(1, 2, 0, 2)
(-u0*u1*u2*u3)*T[1]
-u0*u1*u2*u3*T[1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3))*T[1,0]
+ ((-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3))*T[1,0,0]
- ((u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3))*T[1,0,0]
+ ((u0+u1+u2+u3))*T[1,0,0,0]
sage: T._product_TT(2, 1, 0, 3)
(-u0*u1*u2*u3)*T[2,1]
-u0*u1*u2*u3*T[2,1]
+ ((u0*u1*u2+u0*u1*u3+u0*u2*u3+u1*u2*u3))*T[2,1,0]
+ ((-u0*u1-u0*u2-u1*u2-u0*u3-u1*u3-u2*u3))*T[2,1,0,0]
- ((u0*u1+u0*u2+u1*u2+u0*u3+u1*u3+u2*u3))*T[2,1,0,0]
+ ((u0+u1+u2+u3))*T[2,1,0,0,0]

TESTS::

sage: H = algebras.ArikiKoike(3, 4)
sage: T = H.T()
sage: T._product_TT(1, 2, 1, 2)
(-u0*u1*u2+u0*u1*u2*q)*T[1,0]
+ (u0*u1*u2-u0*u1*u2*q)*T[0,1]
-(u0*u1*u2-u0*u1*u2*q)*T[1,0] + (u0*u1*u2-u0*u1*u2*q)*T[0,1]
+ ((u0+u1+u2)+(-u0-u1-u2)*q)*T[0,1,0,0]
+ ((-u0-u1-u2)+(u0+u1+u2)*q)*T[0,0,1,0]
+ T[0,0,1,0,0,1]
- ((u0+u1+u2)+(-u0-u1-u2)*q)*T[0,0,1,0] + T[0,0,1,0,0,1]
sage: T._product_TT(2,2,2,2)
(-u0*u1*u2+u0*u1*u2*q)*T[2,1,0,2]
-(u0*u1*u2-u0*u1*u2*q)*T[2,1,0,2]
+ (u0*u1*u2-u0*u1*u2*q)*T[1,0,2,1]
+ ((u0+u1+u2)+(-u0-u1-u2)*q)*T[1,0,2,1,0,0]
+ ((-u0-u1-u2)+(u0+u1+u2)*q)*T[1,0,0,2,1,0]
+ T[1,0,0,2,1,0,0,1]
- ((u0+u1+u2)+(-u0-u1-u2)*q)*T[1,0,0,2,1,0] + T[1,0,0,2,1,0,0,1]
sage: T._product_TT(3,2,3,2)
(-u0*u1*u2+u0*u1*u2*q)*T[3,2,1,0,3,2]
-(u0*u1*u2-u0*u1*u2*q)*T[3,2,1,0,3,2]
+ (u0*u1*u2-u0*u1*u2*q)*T[2,1,0,3,2,1]
+ ((u0+u1+u2)+(-u0-u1-u2)*q)*T[2,1,0,3,2,1,0,0]
+ ((-u0-u1-u2)+(u0+u1+u2)*q)*T[2,1,0,0,3,2,1,0]
- ((u0+u1+u2)+(-u0-u1-u2)*q)*T[2,1,0,0,3,2,1,0]
+ T[2,1,0,0,3,2,1,0,0,1]
"""
# Quadratic relation: S_i^2 - (q - 1) S_i - q == 0
Expand Down
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