Integrate gives a wrong result #14991

maurogaravello · 2018-07-29T17:23:28Z

References to other Issues or PRs

Brief description of what is fixed or changed

integrate(sqrt(-x**2 + 1)*(-x**2 + x), [x, -1, 1]) gives 0 instead -pi/8.
The antiderivative works correctly, but it returns a function containing
a Piecewise() expression, defined in the open interval (-1, 1).
The function _eval_interval() does not work correctly, since the antiderivative
is not a Piecewise() expression.
Hence, separating the terms of type Piecewise() and using the _eval_interval() for
Piecewise() solves the issue.

Other comments

Added a test.

Unfortunately, a test in test_ode.py fails due to the fact that a minus sign compares
inside Piecewise() instead that outside. So I modified such a test, without changing the
final result.

Release Notes

integrals
- fixed a issue related to a wrong result in integrate

The PR fixes issue 14782. integrate(sqrt(-x**2 + 1)*(-x**2 + x), [x, -1, 1]) gives 0 instead -pi/8. The antiderivative works correctly, but it returns a function containing a Piecewise expression, defined in the open interval (-1, 1). The function _eval_interval() does not work correctly, since the antiderivative is not a Piecewise expression. Hence, separating the terms of type Piecewise and using the _eval_interval() for Piecewise() solves the issue. Added a test. Unfortunately, a test in test_ode.py fails due to the fact that a minus sign compares inside Piecewise intead that outside. So I modified such a test, without changing the final result.

sympy-bot · 2018-07-29T17:23:38Z

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#### References to other Issues or PRs
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Fixes #14782 
#### Brief description of what is fixed or changed
`integrate(sqrt(-x**2 + 1)*(-x**2 + x), [x, -1, 1])` gives `0` instead `-pi/8`.
The antiderivative works correctly, but it returns a function containing
a `Piecewise()` expression, defined in the open interval `(-1, 1)`.
The function `_eval_interval()` does not work correctly, since the antiderivative
is not a `Piecewise()` expression.
Hence, separating the terms of type `Piecewise()` and using the `_eval_interval()` for
`Piecewise()` solves the issue.
#### Other comments
Added a test.
Unfortunately, a test in `test_ode.py` fails due to the fact that a minus sign compares
inside `Piecewise()` instead that outside. So I modified such a test, without changing the
final result.
#### Release Notes
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https://github.com/sympy/sympy/wiki/Writing-Release-Notes for more information
on how to write release notes. If there is no release notes entry for this PR,
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<!-- BEGIN RELEASE NOTES -->
* integrals
    * fixed a issue related to a wrong result in integrate
<!-- END RELEASE NOTES -->

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integrals
- fixed a issue related to a wrong result in integrate (#14991 by @maurogaravello)

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Update

The release notes on the wiki have been updated.

jksuom · 2018-07-29T18:03:49Z

sympy/integrals/integrals.py

                            else:
                                others.append(f)
                        uneval = Add(*[eval_factored(f, x, a, b)
                                       for f in integrals])
                        try:
                            evalued = Add(*others)._eval_interval(x, a, b)
-                            function = uneval + evalued
+                            evalued_pw = Add(*piecewises)._eval_interval(x, a, b)


What will happen if there are several items in piecewises?

You right. It does not work, since Add(*piecewises) is an Add and not Piecewise.

evalued_pw = piecewise_fold(Add(*piecewises))._eval_interval(x, a, b) seems to work.

jksuom · 2018-07-30T05:52:35Z

sympy/solvers/tests/test_ode.py

@@ -1584,7 +1584,7 @@ def test_1st_homogeneous_coeff_ode3():
    sol = Eq(log(f(x)), C1 - Piecewise(
            (-acosh(f(x)/x), abs(f(x)**2)/x**2 > 1),
            (I*asin(f(x)/x), True)))
-    assert dsolve(eq, hint='1st_homogeneous_coeff_subs_indep_div_dep') == sol
+    assert simplify(dsolve(eq, hint='1st_homogeneous_coeff_subs_indep_div_dep') - sol) == 0


The use of simplify is discouraged as it is an expensive operation. In this case, it is better to edit sol.

jksuom · 2018-07-31T15:54:30Z

Thanks, this looks good.

jksuom reviewed Jul 29, 2018

View reviewed changes

Added piecewise_fold after Add(*piecewises)

be53939

jksuom reviewed Jul 30, 2018

View reviewed changes

Edited sol in a test in test_ode.py

be8ec18

jksuom merged commit 45e7cea into sympy:master Jul 31, 2018

maurogaravello deleted the integrate_14782 branch September 1, 2020 07:02

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maurogaravello commented Jul 29, 2018

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Release Notes

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