integrals and algorithms

[Enrique Artal]

I was prepairing some exercises and I got some errors using differente algorithms for integral, using version 8.0. Integrating with mathematica_free, I got this error:

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

  File "_sage_input_4.py", line 10, in <module>

    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("aW50ZWdyYWwoeCx4LGFsZ29yaXRobT0nbWF0aGVtYXRpY2FfZnJlZScp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))

  File "", line 1, in <module>

    

  File "/tmp/tmpfvk1XJ/___code___.py", line 2, in <module>

    exec compile(u"integral(x,x,algorithm='mathematica_free')" + '\n', '', 'single')

  File "", line 1, in <module>

    

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sage/misc/functional.py", line 721, in integral

    return x.integral(*args, **kwds)

  File "sage/symbolic/expression.pyx", line 12275, in sage.symbolic.expression.Expression.integral (/usr/local/sage-8.0/src/build/cythonized/sage/symbolic/expression.cpp:69945)

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 795, in integrate

    return integrator(expression, v, a, b)

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sage/symbolic/integration/external.py", line 97, in mma_free_integrator

    page = page[page.index('"inputForm"'):page.index('"outputForm"')]

ValueError: substring not found

  

If I try  integral(sin(x^2),x,algorithm='sympy') I get:

Traceback (most recent call last):

  File "<stdin>", line 1, in <module>

  File "_sage_input_20.py", line 10, in <module>

    exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("aD1pbnRlZ3JhbChzaW4oeF4yKSx4LGFsZ29yaXRobT0nc3ltcHknKQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))

  File "", line 1, in <module>

    

  File "/tmp/tmpK8eQi1/___code___.py", line 3, in <module>

    exec compile(u"h=integral(sin(x**_sage_const_2 ),x,algorithm='sympy')" + '\n', '', 'single')

  File "", line 1, in <module>

    

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sage/misc/functional.py", line 721, in integral

    return x.integral(*args, **kwds)

  File "sage/symbolic/expression.pyx", line 12275, in sage.symbolic.expression.Expression.integral (/usr/local/sage-8.0/src/build/cythonized/sage/symbolic/expression.cpp:69945)

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sage/symbolic/integration/integral.py", line 795, in integrate

    return integrator(expression, v, a, b)

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sage/symbolic/integration/external.py", line 56, in sympy_integrator

    return result._sage_()

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sympy/core/mul.py", line 1572, in _sage_

    s *= x._sage_()

  File "/usr/local/sage-8.0/local/lib/python2.7/site-packages/sympy/core/function.py", line 707, in _sage_

    func = getattr(sage, fname)

AttributeError: 'module' object has no attribute 'fresnels'

It seems that fresnels is defined in sympy but not in sagemath, Is it possible to correct these errors? Thanks, Enrique.

[Vincent Delecroix]

You should give the command that leads you to the error.

Concerning sympy, note that you can use it directly within Sage

sage: import sympy
sage: x = sympy.Symbol('x')
sage: sympy.integrate(sympy.sin(x^2), x)
3*sqrt(2)*sqrt(pi)*fresnels(sqrt(2)*x/sqrt(pi))*gamma(3/4)/(8*gamma(7/4))

[Enrique Artal]

Sorry. 

For the first one

integral(x,x,algorithm='mathematica_free')

You can replace the first x by any function; a previous problem was solved in #22641 but now I does not work. For the the second one the problem is with

integral(sin(x^2),x,algorithm='mathematica_free')

and I presume it is due to the non-existence of Fresnel integrals in sage. It works for other integrals, and it works also importing sympy as you did.

[Enrique Artal]

Sorry. 

For the first one

integral(x,x,algorithm='mathematica_free')

You can replace the first x by any function; a previous problem was solved in #22641 but now I does not work. For the the second one the problem is with

integral(sin(x^2),x,algorithm='mathematica_free')

and I presume it is due to the non-existence of Fresnel integrals in sage. It works for other integrals, and it works also importing sympy as you did.

El domingo, 12 de noviembre de 2017, 11:57:06 (UTC+1), vdelecroix escribió:

[Ralf Stephan]

On Sunday, November 12, 2017 at 11:30:51 AM UTC+1, Enrique Artal wrote:

It seems that fresnels is defined in sympy but not in sagemath, Is it possible to correct these errors? Thanks, Enrique.

 I opened https://trac.sagemath.org/ticket/24212

Thanks for the report,

[Enrique Artal]

Thanks to you for your work!

[kcrisman]

On Monday, November 13, 2017 at 4:12:36 PM UTC-5, Enrique Artal wrote:

Thanks to you for your work!

Yes, indeed!