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Print matrices with variable column widths #41151

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1dd889a
use variable column widths for matrices with wide entries
mezzarobba Oct 10, 2025
d3b2768
update doctests after change in matrix formatting
mezzarobba Nov 8, 2025
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4 changes: 2 additions & 2 deletions src/sage/algebras/askey_wilson.py
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Expand Up @@ -700,8 +700,8 @@ def loop_representation(self):
sage: pi = AW.loop_representation()
sage: A,B,C,a,b,g = [pi(gen) for gen in AW.algebra_generators()]
sage: A
[ 1/q*lambda^-1 + q*lambda ((-q^2 + 1)/q)*lambda^-1 + ((q^2 - 1)/q)]
[ 0 q*lambda^-1 + 1/q*lambda]
[1/q*lambda^-1 + q*lambda ((-q^2 + 1)/q)*lambda^-1 + ((q^2 - 1)/q)]
[ 0 q*lambda^-1 + 1/q*lambda]
sage: B
[ q*lambda^-1 + 1/q*lambda 0]
[((-q^2 + 1)/q) + ((q^2 - 1)/q)*lambda 1/q*lambda^-1 + q*lambda]
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24 changes: 12 additions & 12 deletions src/sage/algebras/hecke_algebras/cubic_hecke_matrix_rep.py
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Expand Up @@ -937,18 +937,18 @@ def _image_on_basis(self, basis_element):
sage: CHA3.<c1, c2> = algebras.CubicHecke(3)
sage: MS = chmr.CubicHeckeMatrixSpace(CHA3, original=True)
sage: MS._image_on_basis(c1)
[ a 0 0 0 0 0 0 0 0 0 0 0]
[ 0 c 0 0 0 0 0 0 0 0 0 0]
[ 0 0 b 0 0 0 0 0 0 0 0 0]
[ 0 0 0 b 0 0 0 0 0 0 0 0]
[ 0 0 0 b*c c 0 0 0 0 0 0 0]
[ 0 0 0 0 0 a 0 0 0 0 0 0]
[ 0 0 0 0 0 a*b b 0 0 0 0 0]
[ 0 0 0 0 0 0 0 a 0 0 0 0]
[ 0 0 0 0 0 0 0 a*c c 0 0 0]
[ 0 0 0 0 0 0 0 0 0 c 0 0]
[ 0 0 0 0 0 0 0 0 0 b^2 + a*c b 0]
[ 0 0 0 0 0 0 0 0 0 b 1 a]
[a 0 0 0 0 0 0 0 0 0 0 0]
[0 c 0 0 0 0 0 0 0 0 0 0]
[0 0 b 0 0 0 0 0 0 0 0 0]
[0 0 0 b 0 0 0 0 0 0 0 0]
[0 0 0 b*c c 0 0 0 0 0 0 0]
[0 0 0 0 0 a 0 0 0 0 0 0]
[0 0 0 0 0 a*b b 0 0 0 0 0]
[0 0 0 0 0 0 0 a 0 0 0 0]
[0 0 0 0 0 0 0 a*c c 0 0 0]
[0 0 0 0 0 0 0 0 0 c 0 0]
[0 0 0 0 0 0 0 0 0 b^2 + a*c b 0]
[0 0 0 0 0 0 0 0 0 b 1 a]
"""
representation_type = self._representation_type
ch_algebra = self._cubic_hecke_algebra
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6 changes: 3 additions & 3 deletions src/sage/algebras/quantum_oscillator.py
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Expand Up @@ -111,9 +111,9 @@ class QuantumOscillatorAlgebra(CombinatorialFreeModule):
sage: quantum_det(pi121)
1 # 1 # 1
sage: pi212 = build_repr([2,1,2], [pi1, pi2]); pi212
[ 1 # a- # 1 1 # k # a- 1 # k # k]
[ -q*a- # k # 1 a- # a+ # a- - q*k # 1 # k a- # a+ # k + k # 1 # a+]
[ q^2*k # k # 1 -q*k # a+ # a- - q*a+ # 1 # k -q*k # a+ # k + a+ # 1 # a+]
[ 1 # a- # 1 1 # k # a- 1 # k # k]
[-q*a- # k # 1 a- # a+ # a- - q*k # 1 # k a- # a+ # k + k # 1 # a+]
[q^2*k # k # 1 -q*k # a+ # a- - q*a+ # 1 # k -q*k # a+ # k + a+ # 1 # a+]
sage: quantum_det(pi212)
1 # 1 # 1

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4 changes: 2 additions & 2 deletions src/sage/calculus/calculus.py
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Expand Up @@ -133,8 +133,8 @@
[x^2 + x 2*x^3]
[ 2 x^2 + x]
sage: e^M
[ 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x)) 1/2*(x*e^(2*sqrt(x)) - x)*sqrt(x)*e^(x - sqrt(x))]
[ 1/2*(e^(2*sqrt(x)) - 1)*e^(x - sqrt(x))/x^(3/2) 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x))]
[ 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x)) 1/2*(x*e^(2*sqrt(x)) - x)*sqrt(x)*e^(x - sqrt(x))]
[1/2*(e^(2*sqrt(x)) - 1)*e^(x - sqrt(x))/x^(3/2) 1/2*(e^(2*sqrt(x)) + 1)*e^(x - sqrt(x))]

Complex exponentiation works, but may require a patched version of
maxima (:issue:`32898`) for now::
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8 changes: 4 additions & 4 deletions src/sage/categories/discrete_valuation.py
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Expand Up @@ -288,10 +288,10 @@ def _matrix_hessenbergize(self, H):
[t^3 + O(t^10) t^4 + O(t^10) t^5 + O(t^10) t^6 + O(t^10)]
sage: H.hessenbergize()
sage: H
[ 1 + O(t^10) t + t^3 + t^5 + O(t^10) t^2 + O(t^10) t^3 + O(t^10)]
[ t + O(t^10) t^2 + t^4 + t^6 + O(t^10) t^3 + O(t^10) t^4 + O(t^10)]
[ O(t^10) O(t^10) O(t^10) O(t^10)]
[ O(t^10) O(t^10) O(t^10) O(t^10)]
[1 + O(t^10) t + t^3 + t^5 + O(t^10) t^2 + O(t^10) t^3 + O(t^10)]
[t + O(t^10) t^2 + t^4 + t^6 + O(t^10) t^3 + O(t^10) t^4 + O(t^10)]
[ O(t^10) O(t^10) O(t^10) O(t^10)]
[ O(t^10) O(t^10) O(t^10) O(t^10)]

Another example over the `p`-adics::

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6 changes: 3 additions & 3 deletions src/sage/combinat/root_system/plot.py
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Expand Up @@ -1557,9 +1557,9 @@ def barycentric_projection_matrix(n, angle=0):
Four vectors in dimension 3::

sage: m = barycentric_projection_matrix(3); m
[ 1/3*sqrt(3)*sqrt(2) -1/3*sqrt(3)*sqrt(2) 0 0]
[ 1/3*sqrt(2) 1/3*sqrt(2) -2/3*sqrt(2) 0]
[ 1/3 1/3 1/3 -1]
[1/3*sqrt(3)*sqrt(2) -1/3*sqrt(3)*sqrt(2) 0 0]
[ 1/3*sqrt(2) 1/3*sqrt(2) -2/3*sqrt(2) 0]
[ 1/3 1/3 1/3 -1]

The columns give four vectors that sum up to zero::

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6 changes: 3 additions & 3 deletions src/sage/combinat/sf/hall_littlewood.py
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Expand Up @@ -496,9 +496,9 @@ def transition_matrix(self, basis, n):
[ 0 0 0 0 1]
sage: HLQ = Sym.hall_littlewood().Q()
sage: HLQ.transition_matrix(s,3)
[ -t + 1 t^2 - t -t^3 + t^2]
[ 0 t^2 - 2*t + 1 -t^4 + t^3 + t^2 - t]
[ 0 0 -t^6 + t^5 + t^4 - t^2 - t + 1]
[-t + 1 t^2 - t -t^3 + t^2]
[ 0 t^2 - 2*t + 1 -t^4 + t^3 + t^2 - t]
[ 0 0 -t^6 + t^5 + t^4 - t^2 - t + 1]
sage: HLQp = Sym.hall_littlewood().Qp()
sage: HLQp.transition_matrix(s,3)
[ 1 0 0]
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14 changes: 6 additions & 8 deletions src/sage/dynamics/arithmetic_dynamics/projective_ds.py
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Expand Up @@ -5206,16 +5206,14 @@
sage: K.<w> = QuadraticField(5)
sage: P.<x,y,z> = ProjectiveSpace(K, 2)
sage: f = DynamicalSystem_projective([x^2 + w*x*y + y^2, y^2, z^2])
sage: f.multiplier_spectra(1) # long time

Check failure on line 5209 in src/sage/dynamics/arithmetic_dynamics/projective_ds.py

View workflow job for this annotation

GitHub Actions / Conda (ubuntu, Python 3.12, new)

Failed example: 

Failed example:: Got: [
[1.000000000000000? - 1.572302755514847?*I 0]  [1.000000000000000? - 1.572302755514847?*I 0.618033988749895? - 1.757887921270715?*I]
[                                        0 0], [                                        0                                         2],

[1.000000000000000? + 1.572302755514847?*I 0]  [1.000000000000000? + 1.572302755514847?*I 0.618033988749895? + 1.757887921270715?*I]
[                                        0 0], [                                        0                                         2],

[0 0]  [0 0]  [                 2 2.236067977499790?]
[0 0], [0 0], [                 0                  0]
]

Check failure on line 5209 in src/sage/dynamics/arithmetic_dynamics/projective_ds.py

View workflow job for this annotation

GitHub Actions / test-long (src/sage/[a-f]*)

Failed example: 

Failed example:: Got: [
[1.000000000000000? - 1.572302755514847?*I 0]  [1.000000000000000? - 1.572302755514847?*I 0.618033988749895? - 1.757887921270715?*I]
[                                        0 0], [                                        0                                         2],

[1.000000000000000? + 1.572302755514847?*I 0]  [1.000000000000000? + 1.572302755514847?*I 0.618033988749895? + 1.757887921270715?*I]
[                                        0 0], [                                        0                                         2],

[0 0]  [0 0]  [                 2 2.236067977499790?]
[0 0], [0 0], [                 0                  0]
]
[
[1.000000000000000? - 1.572302755514847?*I 0]
[1.000000000000000? - 1.572302755514847?*I 0.618033988749895? - 1.757887921270715?*I]
[1.000000000000000? + 1.572302755514847?*I 0]
[1.000000000000000? + 1.572302755514847?*I 0.618033988749895? + 1.757887921270715?*I]
[ 0 0],
[ 0 2],
[ 0 0],
[ 0 2],
[1.000000000000000? - 1.572302755514847?*I 0] [1.000000000000000? - 1.572302755514847?*I 0.618033988749895? - 1.757887921270715?*I]
[ 0 0], [ 0 2],

[1.000000000000000? + 1.572302755514847?*I 0] [1.000000000000000? + 1.572302755514847?*I 0.618033988749895? + 1.757887921270715?*I]
[ 0 0], [ 0 2],

[0 0] [0 0] [ 2 2.236067977499790?]
[0 0], [0 0], [ 0 0]
]
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10 changes: 5 additions & 5 deletions src/sage/functions/orthogonal_polys.py
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Expand Up @@ -2722,11 +2722,11 @@ class Func_krawtchouk(OrthogonalFunction):
....: * krawtchouk(i,m,n,p) * krawtchouk(j,m,n,p)
....: for m in range(n+1)).expand().factor()
....: for i in range(n+1)] for j in range(n+1)])
[ 1 0 0 0 0]
[ 0 -4*(p - 1)*p 0 0 0]
[ 0 0 6*(p - 1)^2*p^2 0 0]
[ 0 0 0 -4*(p - 1)^3*p^3 0]
[ 0 0 0 0 (p - 1)^4*p^4]
[1 0 0 0 0]
[0 -4*(p - 1)*p 0 0 0]
[0 0 6*(p - 1)^2*p^2 0 0]
[0 0 0 -4*(p - 1)^3*p^3 0]
[0 0 0 0 (p - 1)^4*p^4]

We verify the relationship between the Krawtchouk implementations::

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14 changes: 7 additions & 7 deletions src/sage/graphs/generic_graph.py
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Expand Up @@ -26126,13 +26126,13 @@ def katz_matrix(self, alpha, nonedgesonly=False, vertices=None):

sage: H = Graph([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(2,3),(3,4),(4,5)])
sage: H.katz_matrix(1/10) # needs sage.modules sage.rings.number_field
[ 169/2256 545/4512 25/188 605/4512 25/188 545/4512 485/4512]
[ 545/4512 7081/297792 4355/37224 229/9024 595/37224 4073/297792 109/9024]
[ 25/188 4355/37224 172/4653 45/376 125/4653 595/37224 5/376]
[ 605/4512 229/9024 45/376 337/9024 45/376 229/9024 121/9024]
[ 25/188 595/37224 125/4653 45/376 172/4653 4355/37224 5/376]
[ 545/4512 4073/297792 595/37224 229/9024 4355/37224 7081/297792 109/9024]
[ 485/4512 109/9024 5/376 121/9024 5/376 109/9024 97/9024]
[169/2256 545/4512 25/188 605/4512 25/188 545/4512 485/4512]
[545/4512 7081/297792 4355/37224 229/9024 595/37224 4073/297792 109/9024]
[ 25/188 4355/37224 172/4653 45/376 125/4653 595/37224 5/376]
[605/4512 229/9024 45/376 337/9024 45/376 229/9024 121/9024]
[ 25/188 595/37224 125/4653 45/376 172/4653 4355/37224 5/376]
[545/4512 4073/297792 595/37224 229/9024 4355/37224 7081/297792 109/9024]
[485/4512 109/9024 5/376 121/9024 5/376 109/9024 97/9024]

.. SEEALSO::

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7 changes: 4 additions & 3 deletions src/sage/groups/braid.py
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Expand Up @@ -2101,9 +2101,10 @@ def deformed_burau_matrix(self, variab='q'):
sage: B = BraidGroup(4)
sage: b = B([1, 2, -3, -2, 3, 1])
sage: db = b.deformed_burau_matrix(); db
[ ap_0*ap_5 ... bp_0*ap_1*cm_3*bp_4]
...
[ bm_2*bm_3*cp_5 ... bm_2*am_3*bp_4]
[ ap_0*ap_5 ap_0*bp_5 bp_0*bp_1*cm_2*cp_4 + bp_0*ap_1*cm_3*ap_4 bp_0*ap_1*cm_3*bp_4]
[ cp_0*ap_5 cp_0*bp_5 0 0]
[ 0 0 cp_1*cm_3*ap_4 cp_1*cm_3*bp_4]
[bm_2*bm_3*cp_5 0 am_2*cp_4 + bm_2*am_3*ap_4 bm_2*am_3*bp_4]

We check how this relates to the nondeformed Burau matrix::

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10 changes: 5 additions & 5 deletions src/sage/groups/finitely_presented.py
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Expand Up @@ -1644,11 +1644,11 @@ def alexander_matrix(self, im_gens=None):
sage: G.<a,b,c,d,e> = FreeGroup()
sage: H = G.quotient([a*b/a/b, a*c/a/c, a*d/a/d, b*c*d/(c*d*b), b*c*d/(d*b*c)])
sage: H.alexander_matrix()
[ 1 - a*b*a^-1 a - a*b*a^-1*b^-1 0 0 0]
[ 1 - a*c*a^-1 0 a - a*c*a^-1*c^-1 0 0]
[ 1 - a*d*a^-1 0 0 a - a*d*a^-1*d^-1 0]
[ 0 1 - b*c*d*b^-1 b - b*c*d*b^-1*d^-1*c^-1 b*c - b*c*d*b^-1*d^-1 0]
[ 0 1 - b*c*d*c^-1*b^-1 b - b*c*d*c^-1 b*c - b*c*d*c^-1*b^-1*d^-1 0]
[1 - a*b*a^-1 a - a*b*a^-1*b^-1 0 0 0]
[1 - a*c*a^-1 0 a - a*c*a^-1*c^-1 0 0]
[1 - a*d*a^-1 0 0 a - a*d*a^-1*d^-1 0]
[ 0 1 - b*c*d*b^-1 b - b*c*d*b^-1*d^-1*c^-1 b*c - b*c*d*b^-1*d^-1 0]
[ 0 1 - b*c*d*c^-1*b^-1 b - b*c*d*c^-1 b*c - b*c*d*c^-1*b^-1*d^-1 0]
sage: R.<t1,t2,t3,t4> = LaurentPolynomialRing(ZZ)
sage: H.alexander_matrix([t1,t2,t3,t4])
[ -t2 + 1 t1 - 1 0 0 0]
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4 changes: 2 additions & 2 deletions src/sage/manifolds/differentiable/automorphismfield.py
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Expand Up @@ -850,8 +850,8 @@ def restrict(self, subdomain, dest_map=None):
Field of tangent-space automorphisms a on the Open subset V of the
2-dimensional differentiable manifold S^2
sage: a.restrict(V)[eS,:]
[ (u^4 + 10*u^2*v^2 + v^4 + 2*(u^3*v - u*v^3)*arctan(1/(u^2 + v^2)))/(u^4 + 2*u^2*v^2 + v^4) -(4*u^3*v - 4*u*v^3 + (u^4 - 2*u^2*v^2 + v^4)*arctan(1/(u^2 + v^2)))/(u^4 + 2*u^2*v^2 + v^4)]
[ 4*(u^2*v^2*arctan(1/(u^2 + v^2)) - u^3*v + u*v^3)/(u^4 + 2*u^2*v^2 + v^4) (3*u^4 - 2*u^2*v^2 + 3*v^4 - 2*(u^3*v - u*v^3)*arctan(1/(u^2 + v^2)))/(u^4 + 2*u^2*v^2 + v^4)]
[(u^4 + 10*u^2*v^2 + v^4 + 2*(u^3*v - u*v^3)*arctan(1/(u^2 + v^2)))/(u^4 + 2*u^2*v^2 + v^4) -(4*u^3*v - 4*u*v^3 + (u^4 - 2*u^2*v^2 + v^4)*arctan(1/(u^2 + v^2)))/(u^4 + 2*u^2*v^2 + v^4)]
[ 4*(u^2*v^2*arctan(1/(u^2 + v^2)) - u^3*v + u*v^3)/(u^4 + 2*u^2*v^2 + v^4) (3*u^4 - 2*u^2*v^2 + 3*v^4 - 2*(u^3*v - u*v^3)*arctan(1/(u^2 + v^2)))/(u^4 + 2*u^2*v^2 + v^4)]
sage: a.restrict(W)
Field of tangent-space automorphisms a on the Open subset W of the
2-dimensional differentiable manifold S^2
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6 changes: 3 additions & 3 deletions src/sage/manifolds/differentiable/pseudo_riemannian_submanifold.py
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Expand Up @@ -155,9 +155,9 @@
ambient manifold::

sage: N.ambient_extrinsic_curvature()[:] # long time
[ -(x^2 + y^2)/b^3 (b^2*x + x^3 + x*y^2)/(sqrt(b^2 + x^2 + y^2)*b^3) (y^3 + (b^2 + x^2)*y)/(sqrt(b^2 + x^2 + y^2)*b^3)]
[ sqrt(b^2 + x^2 + y^2)*x/b^3 -(b^2 + x^2)/b^3 -x*y/b^3]
[ sqrt(b^2 + x^2 + y^2)*y/b^3 -x*y/b^3 -(b^2 + y^2)/b^3]
[ -(x^2 + y^2)/b^3 (b^2*x + x^3 + x*y^2)/(sqrt(b^2 + x^2 + y^2)*b^3) (y^3 + (b^2 + x^2)*y)/(sqrt(b^2 + x^2 + y^2)*b^3)]
[sqrt(b^2 + x^2 + y^2)*x/b^3 -(b^2 + x^2)/b^3 -x*y/b^3]
[sqrt(b^2 + x^2 + y^2)*y/b^3 -x*y/b^3 -(b^2 + y^2)/b^3]

The extrinsic curvature as a tensor field on the submanifold::

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4 changes: 2 additions & 2 deletions src/sage/manifolds/differentiable/tensorfield.py
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Expand Up @@ -3766,8 +3766,8 @@ def up(
Tensor field of type (1,1) on the 2-dimensional differentiable
manifold M
sage: tu0[:]
[ ((3*x + 1)*y - 1)/(x^2*y^2 + (x + 1)*y - x - 1) 2*((2*x + 1)*y - 1)/(x^2*y^2 + (x + 1)*y - x - 1)]
[ (x*y - 3*x - 3)/(x^2*y^2 + (x + 1)*y - x - 1) 2*(x*y - 2*x - 2)/(x^2*y^2 + (x + 1)*y - x - 1)]
[((3*x + 1)*y - 1)/(x^2*y^2 + (x + 1)*y - x - 1) 2*((2*x + 1)*y - 1)/(x^2*y^2 + (x + 1)*y - x - 1)]
[ (x*y - 3*x - 3)/(x^2*y^2 + (x + 1)*y - x - 1) 2*(x*y - 2*x - 2)/(x^2*y^2 + (x + 1)*y - x - 1)]
sage: tu0 == ig['^ac']*t['_cb'] # the same operation in index notation
True
sage: tuu0 = tu0.up(g) ; tuu0 # the two indices have been raised, starting from the first one
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