matrices: set the default value for dotprodsimp to None

oscarbenjamin · oscarbenjamin · commit cab61718013a · 2020-10-11T01:02:49.000+01:00
Simplify excessively complicated ODE system test. This test has a
solution that is too complicated to write out explicitly in the code. It
also takes too long for checkodesol to verify the solution. Instead we
check that the solution holds for t=1.
diff --git a/sympy/solvers/ode/tests/test_systems.py b/sympy/solvers/ode/tests/test_systems.py
@@ -13,6 +13,7 @@
                                        _eqs2dict, _dict2graph)
 from sympy.functions import airyai, airybi
 from sympy.integrals.integrals import Integral
+from sympy.simplify.ratsimp import ratsimp
 from sympy.testing.pytest import ON_TRAVIS, raises, slow, skip, XFAIL
 
 
@@ -2173,60 +2174,22 @@ def test_dsolve():
         dsolve(eqs)
 
 
-def _higher_order_slow1():
+@slow
+def test_higher_order1_slow1():
     x, y = symbols("x y", cls=Function)
     t = symbols("t")
 
-    eq = (Eq(diff(x(t),t,t), (log(t)+t**2)*diff(x(t),t)+(log(t)+t**2)*3*diff(y(t),t)), Eq(diff(y(t),t,t), \
-    (log(t)+t**2)*2*diff(x(t),t)+(log(t)+t**2)*9*diff(y(t),t)))
-    _x1 = log(t)**2
-    _x2 = sqrt(22)
-    _x3 = sqrt(9*_x1 + t**4 + 6*t**2*log(t) - 6*t**2 - 18*log(t) + 9)
-    _x4 = 1/(-_x2*_x3*t/3 - 4*t**3/3 - 4*t*log(t) + 4*t)
-    _x5 = 1/(_x2*_x3*t/3 - 4*t**3/3 - 4*t*log(t) + 4*t)
-    _x6 = 1/(-_x4*t**3 - 3*_x4*t*log(t) + 3*_x4*t + _x5*t**3 + 3*_x5*t*log(t) - 3*_x5*t)
-    _x7 = exp(-_x2*_x3*t/3 + 5*t**3/3 + 5*t*log(t) - 5*t)
-    _x8 = exp(_x2*_x3*t/3 + 5*t**3/3 + 5*t*log(t) - 5*t)
-    _x9 = 1/(18*_x1*_x4*t**5 - 54*_x1*_x4*t**3 - 18*_x1*_x5*t**5 + 54*_x1*_x5*t**3 + 2*_x4*t**9/3 + 6*_x4*t**7*log(t) -
-             6*_x4*t**7 - 36*_x4*t**5*log(t) + 18*_x4*t**5 + 18*_x4*t**3*log(t)**3 + 54*_x4*t**3*log(t) - 18*_x4*t**3 -
-             2*_x5*t**9/3 - 6*_x5*t**7*log(t) + 6*_x5*t**7 + 36*_x5*t**5*log(t) - 18*_x5*t**5 - 18*_x5*t**3*log(t)**3 -
-             54*_x5*t**3*log(t) + 18*_x5*t**3)
-    _x10 = -12*_x1*_x5*t**2
-    _x11 = 24*_x5*t**2*log(t)
-    _x12 = 8*_x4*t**4*log(t)
-    _x13 = -24*_x4*t**2*log(t)
-    _x14 = -8*_x5*t**4*log(t)
-    _x15 = 1/(12*_x1*_x4*t**2 + _x10 + _x11 + _x12 + _x13 + _x14 + _x2*_x3*_x4*t**4/3 + _x2*_x3*_x4*t**2*log(t) -
-              _x2*_x3*_x4*t**2 - _x2*_x3*_x5*t**4/3 - _x2*_x3*_x5*t**2*log(t) + _x2*_x3*_x5*t**2 + 4*_x4*t**6/3 -
-              8*_x4*t**4 + 12*_x4*t**2 - 4*_x5*t**6/3 + 8*_x5*t**4 - 12*_x5*t**2)
-    _x16 = 1/(12*_x1*_x4*t**2 + _x10 + _x11 + _x12 + _x13 + _x14 - _x2*_x3*_x4*t**4/3 - _x2*_x3*_x4*t**2*log(t) +
-              _x2*_x3*_x4*t**2 + _x2*_x3*_x5*t**4/3 + _x2*_x3*_x5*t**2*log(t) - _x2*_x3*_x5*t**2 + 4*_x4*t**6/3 -
-              8*_x4*t**4 + 12*_x4*t**2 - 4*_x5*t**6/3 + 8*_x5*t**4 - 12*_x5*t**2)
-    _x17 = (t**3 + 3*t*log(t) - 3*t)**2
-    sol = [
-        Eq(x(t), C1 + Integral(-C2*_x15*_x8*t**3 - 3*C2*_x15*_x8*t*log(t) + 3*C2*_x15*_x8*t + C2*_x16*_x7*t**3 +
-            3*C2*_x16*_x7*t*log(t) - 3*C2*_x16*_x7*t + C3*_x17*_x7*_x9 - C3*_x17*_x8*_x9, t)),
-        Eq(y(t), C4 + Integral(-C2*_x6*_x7 + C2*_x6*_x8 - C3*_x15*_x7*t**3 - 3*C3*_x15*_x7*t*log(t) + 3*C3*_x15*_x7*t +
-            C3*_x16*_x8*t**3 + 3*C3*_x16*_x8*t*log(t) - 3*C3*_x16*_x8*t, t)),
+    eq = [
+        Eq(diff(x(t),t,t), (log(t)+t**2)*diff(x(t),t)+(log(t)+t**2)*3*diff(y(t),t)),
+        Eq(diff(y(t),t,t), (log(t)+t**2)*2*diff(x(t),t)+(log(t)+t**2)*9*diff(y(t),t))
     ]
-
-    return eq, sol
-
-
-@slow
-def test_higher_order_slow1():
-    eq, sol = _higher_order_slow1()
-
-    assert dsolve_system(eq, simplify=False, doit=False) == [sol]
-
-
-@slow
-def test_higher_order1_slow1_check():
-    if ON_TRAVIS:
-        skip("Too slow for travis.")
-
-    eq, sol = _higher_order_slow1()
-    assert checksysodesol(eq, sol) == (True, [0, 0])
+    sol, = dsolve_system(eq, simplify=False, doit=False)
+    # The solution is too long to write out explicitly and checkodesol is too
+    # slow so we test for particular values of t:
+    for e in eq:
+        res = (e.lhs - e.rhs).subs({sol[0].lhs:sol[0].rhs, sol[1].lhs:sol[1].rhs})
+        res = res.subs({d: d.doit(deep=False) for d in res.atoms(Derivative)})
+        assert ratsimp(res.subs(t, 1)) == 0
 
 
 @slow
