Updates:
Status: Started
Comment #2 on issue 2606 by asmeurer: Add degree_offset argument to
heurisch()
http://code.google.com/p/sympy/issues/detail?id=2606
Here's a trivial implementation:
diff --git a/sympy/integrals/heurisch.py b/sympy/integrals/heurisch.py
index e51a070..65915c0 100644
--- a/sympy/integrals/heurisch.py
+++ b/sympy/integrals/heurisch.py
@@ -157,6 +157,7 @@ def heurisch(f, x, **kwargs):
}
rewrite = kwargs.pop('rewrite', False)
+ degree_offset = kwargs.pop('degree_offset', 0)
if rewrite:
for candidates, rule in rewritables.iteritems():
@@ -336,9 +337,9 @@ def exponent(g):
A, B = exponent(f), a + max(b, c)
if A > 1 and B > 1:
- monoms = monomials(V, A + B - 1)
+ monoms = monomials(V, A + B - 1 + degree_offset)
else:
- monoms = monomials(V, A + B)
+ monoms = monomials(V, A + B + degree_offset)
poly_coeffs = _symbols('A', len(monoms))
I already noticed that one of the simplest integrals that heurisch() cannot
do, log(x)/x, can be done if you increase the degree by one:
In [1]: from sympy.integrals.heurisch import heurisch
In [2]: heurisch(log(x)/x, x, degree_offset=0)
In [3]: heurisch(log(x)/x, x, degree_offset=1)
Out[3]:
2
log (x)
───────
2
On the other hand, the very rapid increase in the number of monomials of a
degree means that even this small change can slow down the function by
quite a bit in the general case.
In [16]: heurisch(diff(log(x)**2*exp(x), x), x)
Out[16]:
x 2
ℯ ⋅log (x)
In [18]: %timeit heurisch(diff(log(x)**2*exp(x), x), x)
1 loops, best of 3: 1.72 s per loop
In [19]: %timeit heurisch(diff(log(x)**2*exp(x), x), x, degree_offset=1)
1 loops, best of 3: 3.67 s per loop
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