Adjust tests for slight changes in sympy 1.15

Author: cbm755

inst/@sym/dsolve.m

@@ -1,4 +1,4 @@
-%% Copyright (C) 2014-2016, 2018-2019, 2022, 2025 Colin B. Macdonald
+%% Copyright (C) 2014-2016, 2018-2019, 2022, 2025-2026 Colin B. Macdonald
 %% Copyright (C) 2014-2015 Andrés Prieto
 %% Copyright (C) 2020 Rafael Laboissière
 %% Copyright (C) 2020 Jing-Chen Peng
@@ -306,17 +306,22 @@
 %! ode1 = diff(x(t),t) == 2*y(t);
 %! ode2 = diff(y(t),t) == 2*x(t);
 %! soln = dsolve([ode1, ode2]);
+%! X = soln.x;
+%! Y = soln.y;
 %! soln = [soln.x, soln.y];
+%! % check its a soln
+%! assert (isequal (simplify (diff (X, t) - 2*Y), sym(0)))
 %! g1 = [C1*exp(-2*t) + C2*exp(2*t), -C1*exp(-2*t) + C2*exp(2*t)];
 %! g2 = [C1*exp(2*t) + C2*exp(-2*t), C1*exp(2*t) - C2*exp(-2*t)];
 %! g3 = [-C1*exp(-2*t) + C2*exp(2*t), C1*exp(-2*t) + C2*exp(2*t)];
 %! g4 = [C1*exp(2*t) - C2*exp(-2*t), C1*exp(2*t) + C2*exp(-2*t)];
 %! % old SymPy <= 1.5.1 had some extra twos
-%! g5 = [2*C1*exp(-2*t) + 2*C2*exp(2*t), -2*C1*exp(-2*t) + 2*C2*exp(2*t)];
-%! g6 = [2*C1*exp(2*t) + 2*C2*exp(-2*t), 2*C1*exp(2*t) - 2*C2*exp(-2*t)];
+%! % new SymPy >= 1.15.0 also has extra twos
+%! % so also try dividing by two
 %! assert (isequal (soln, g1) || isequal (soln, g2) || ...
 %!         isequal (soln, g3) || isequal (soln, g4) || ...
-%!         isequal (soln, g5) || isequal (soln, g6))
+%!         isequal (soln/2, g1) || isequal (soln/2, g2) ||
+%!         isequal (soln/2, g3) || isequal (soln/2, g4))
 
 %!test
 %! % System of ODEs (initial-value problem)

inst/@sym/jordan.m

@@ -1,5 +1,5 @@
 %% Copyright (C) 2016 Alex Vong
-%% Copyright (C) 2017-2019 Colin B. Macdonald
+%% Copyright (C) 2017-2019, 2026 Colin B. Macdonald
 %%
 %% This file is part of OctSymPy.
 %%
@@ -135,13 +135,24 @@
 %! A = sym ([2 1 0 0; 0 2 1 0; 0 0 3 0; 0 1 -1 3]);
 %! [V, J] = jordan (A);
 %! assert (isequal (inv (V) * A * V, J));
-%! assert (isequal (J, sym ([2 1 0 0; 0 2 0 0; 0 0 3 0; 0 0 0 3])))
-%! % the first 2 generalized eigenvectors form a cycle
-%! assert (isequal ((A - J(1, 1) * eye (4)) * V(:, 1), zeros (4, 1)));
-%! assert (isequal ((A - J(2, 2) * eye (4)) * V(:, 2), V(:, 1)));
-%! % the last 2 generalized eigenvectors are eigenvectors
-%! assert (isequal ((A - J(3, 3) * eye (4)) * V(:, 3), zeros (4, 1)));
-%! assert (isequal ((A - J(4, 4) * eye (4)) * V(:, 4), zeros (4, 1)));
+%! % it might give J1 or J2: either answer is ok.
+%! J1 = sym ([2 1 0 0; 0 2 0 0; 0 0 3 0; 0 0 0 3]);
+%! J2 = sym ([3 0 0 0; 0 3 0 0; 0 0 2 1; 0 0 0 2]);
+%! assert (isequal (J, J1) | isequal (J, J2))
+%! if (isequal (J, J1))
+%!   % the first 2 generalized eigenvectors form a cycle
+%!   assert (isequal ((A - J(1, 1) * eye (4)) * V(:, 1), zeros (4, 1)));
+%!   assert (isequal ((A - J(2, 2) * eye (4)) * V(:, 2), V(:, 1)));
+%!   % the last 2 generalized eigenvectors are eigenvectors
+%!   assert (isequal ((A - J(3, 3) * eye (4)) * V(:, 3), zeros (4, 1)));
+%!   assert (isequal ((A - J(4, 4) * eye (4)) * V(:, 4), zeros (4, 1)));
+%! else
+%!   % opposite order as above
+%!   assert (isequal ((A - J(1, 1) * eye (4)) * V(:, 1), zeros (4, 1)));
+%!   assert (isequal ((A - J(2, 2) * eye (4)) * V(:, 2), zeros (4, 1)));
+%!   assert (isequal ((A - J(3, 3) * eye (4)) * V(:, 3), zeros (4, 1)));
+%!   assert (isequal ((A - J(4, 4) * eye (4)) * V(:, 4), V(:, 3)));
+%! end
 
 %!test
 %! % scalars
@@ -153,8 +164,10 @@
 %! A = diag (sym ([6 6 7]));
 %! [V1, D] = eig (A);
 %! [V2, J] = jordan (A);
-%! assert (isequal (V1, V2));
-%! assert (isequal (D, J));
+%! assert (isequal (A*V2, V2*J));
+%! assert (isequal (V1 * V1', sym (eye (3))))
+%! assert (isequal (V2 * V2', sym (eye (3))))
+%! assert (isempty (setdiff (diag (D), diag (J))))
 
 %!test
 %! % matrices of unknown entries