Merge pull request sympy#26358 from smichr/26338

maintain ordering in heurisch mapping

sympy/integrals/heurisch.py

@@ -1,7 +1,8 @@
 from __future__ import annotations
 
-from itertools import permutations
+from collections import defaultdict
 from functools import reduce
+from itertools import permutations
 
 from sympy.core.add import Add
 from sympy.core.basic import Basic
@@ -503,7 +504,16 @@ def heurisch(f, x, rewrite=False, hints=None, mappings=None, retries=3,
         # optimizing the number of permutations of mapping              #
         assert mapping[-1][0] == x # if not, find it and correct this comment
         unnecessary_permutations = [mapping.pop(-1)]
-        mappings = permutations(mapping)
+        # only permute types of objects and let the ordering
+        # of types take care of the order of replacement
+        types = defaultdict(list)
+        for i in mapping:
+            types[type(i)].append(i)
+        mapping = [types[i] for i in types]
+        def _iter_mappings():
+            for i in permutations(mapping):
+                yield [j for i in i for j in i]
+        mappings = _iter_mappings()
     else:
         unnecessary_permutations = unnecessary_permutations or []
 

sympy/integrals/tests/test_heurisch.py

@@ -2,7 +2,7 @@
 from sympy.core.add import Add
 from sympy.core.function import (Derivative, Function, diff)
 from sympy.core.numbers import (I, Rational, pi)
-from sympy.core.relational import Ne
+from sympy.core.relational import Eq, Ne
 from sympy.core.symbol import (Symbol, symbols)
 from sympy.functions.elementary.exponential import (LambertW, exp, log)
 from sympy.functions.elementary.hyperbolic import (asinh, cosh, sinh, tanh)
@@ -12,6 +12,8 @@
 from sympy.functions.special.bessel import (besselj, besselk, bessely, jn)
 from sympy.functions.special.error_functions import erf
 from sympy.integrals.integrals import Integral
+from sympy.logic.boolalg import And
+from sympy.matrices import Matrix
 from sympy.simplify.ratsimp import ratsimp
 from sympy.simplify.simplify import simplify
 from sympy.integrals.heurisch import components, heurisch, heurisch_wrapper
@@ -365,3 +367,33 @@ def f(x):
     Uz = integrate(f(z), z)
     Ut = integrate(f(t), t)
     assert Ut == Uz.subs(z, t)
+
+
+def test_heurisch_complex_erf_issue_26338():
+    r = symbols('r', real=True)
+    a = exp(-r**2/(2*(2 - I)**2))
+    assert heurisch(a, r, hints=[]) is None  # None, not a wrong soln
+    a = sqrt(pi)*erf((1 + I)/2)/2
+    assert integrate(exp(-I*r**2/2), (r, 0, 1)) == a - I*a
+
+    a = exp(-x**2/(2*(2 - I)**2))
+    assert heurisch(a, x, hints=[]) is None  # None, not a wrong soln
+    a = sqrt(pi)*erf((1 + I)/2)/2
+    assert integrate(exp(-I*x**2/2), (x, 0, 1)) == a - I*a
+
+
+def test_issue_15498():
+    Z0 = Function('Z0')
+    k01, k10, t, s= symbols('k01 k10 t s', real=True, positive=True)
+    m = Matrix([[exp(-k10*t)]])
+    _83 = Rational(83, 100)  # 0.83 works, too
+    [a, b, c, d, e, f, g] = [100, 0.5, _83, 50, 0.6, 2, 120]
+    AIF_btf = a*(d*e*(1 - exp(-(t - b)/e)) + f*g*(1 - exp(-(t - b)/g)))
+    AIF_atf = a*(d*e*exp(-(t - b)/e)*(exp((c - b)/e) - 1
+        ) + f*g*exp(-(t - b)/g)*(exp((c - b)/g) - 1))
+    AIF_sym = Piecewise((0, t < b), (AIF_btf, And(b <= t, t < c)), (AIF_atf, c <= t))
+    aif_eq = Eq(Z0(t), AIF_sym)
+    f_vec = Matrix([[k01*Z0(t)]])
+    integrand = m*m.subs(t, s)**-1*f_vec.subs(aif_eq.lhs, aif_eq.rhs).subs(t, s)
+    solution = integrate(integrand[0], (s, 0, t))
+    assert solution is not None  # does not hang and takes less than 10 s

sympy/integrals/tests/test_integrals.py

@@ -1148,7 +1148,7 @@ def test_issue_3940():
     assert integrate(exp(-x**2 + I*c*x), x) == \
         -sqrt(pi)*exp(-c**2/4)*erf(I*c/2 - x)/2
     assert integrate(exp(a*x**2 + b*x + c), x) == \
-        sqrt(pi)*exp(c)*exp(-b**2/(4*a))*erfi(sqrt(a)*x + b/(2*sqrt(a)))/(2*sqrt(a))
+        sqrt(pi)*exp(c - b**2/(4*a))*erfi((2*a*x + b)/(2*sqrt(a)))/(2*sqrt(a))
 
     from sympy.core.function import expand_mul
     from sympy.abc import k