Improvement to the beam sphinx docs

[moorepants]

References to other Issues or PRs

#15304 needs to be merged before this one.

Brief description of what is fixed or changed

I added the matplotlib sphinx directive to the sphinx config file so that we can use the plot directive to display plots from sympy.plot() or matplotlib directly. I made use of it to improve the first beam bending example. The following screenshot shows the results:

Other comments

• Figure out doctest outputs for matplotlib plot directives.
• Add matplotlib to the doc build on travis.

Release Notes

• physics.continuum_mechanics
  • Added text and plots to the beam sphinx docs.

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• physics.continuum_mechanics
  • Added text and plots to the beam sphinx docs. (#15310 by @moorepants)

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#### References to other Issues or PRs
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#15304  needs to be merged before this one.

#### Brief description of what is fixed or changed

I added the matplotlib sphinx directive to the sphinx config file so that we can use the plot directive to display plots from sympy.plot() or matplotlib directly. I made use of it to improve the first beam bending example. The following screenshot shows the results:
![screenshot_2018-09-29 solving beam bending problems using singularity functions sympy 1 4 dev documentation](https://user-images.githubusercontent.com/276007/46239818-021da800-c353-11e8-8ea2-861ab51ae0af.png)

#### Other comments

- [x] Figure out doctest outputs for matplotlib plot directives.
- [x] Add matplotlib to the doc build on travis.

#### Release Notes

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<!-- BEGIN RELEASE NOTES -->
* physics.continuum_mechanics
  * Added text and plots to the beam sphinx docs.
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Update

The release notes on the wiki have been updated.

[moorepants]

The matplolib plot directive seems to create an output on Travis that I don't see locally. I thought the trailing semicolon would suppress that:

**********************************************************************
File "/home/travis/build/sympy/sympy/doc/src/modules/physics/continuum_mechanics/beam_problems.rst", line 199, in beam_problems.rst
Failed example:
    b.plot_shear_force();
Expected nothing
Got:
                                                                                                                   Plot object containing:                                                                                                                
    [0]: cartesian line: -258*SingularityFunction(x, 0, -1) + 52*SingularityFunction(x, 0, 0) - 8*SingularityFunction(x, 0, 1) + 50*SingularityFunction(x, 5, -1) + 8*SingularityFunction(x, 5, 1) - 12*SingularityFunction(x, 9, 0) for x over (0.0, 9.0)
**********************************************************************
File "/home/travis/build/sympy/sympy/doc/src/modules/physics/continuum_mechanics/beam_problems.rst", line 200, in beam_problems.rst
Failed example:
    b.plot_bending_moment();
Expected nothing
Got:
                                                                                                                  Plot object containing:                                                                                                               
    [0]: cartesian line: -258*SingularityFunction(x, 0, 0) + 52*SingularityFunction(x, 0, 1) - 4*SingularityFunction(x, 0, 2) + 50*SingularityFunction(x, 5, 0) + 4*SingularityFunction(x, 5, 2) - 12*SingularityFunction(x, 9, 1) for x over (0.0, 9.0)
**********************************************************************
File "/home/travis/build/sympy/sympy/doc/src/modules/physics/continuum_mechanics/beam_problems.rst", line 233, in beam_problems.rst
Failed example:
    b.plot_slope(subs={E: 20E9, I: 3.25E-6});
Expected nothing
Got:
                                                                                                                                                                Plot object containing:                                                                                                                                                            
    [0]: cartesian line: -0.00396923076923077*SingularityFunction(x, 0, 1) + 0.0004*SingularityFunction(x, 0, 2) - 2.05128205128205e-5*SingularityFunction(x, 0, 3) + 0.000769230769230769*SingularityFunction(x, 5, 1) + 2.05128205128205e-5*SingularityFunction(x, 5, 3) - 9.23076923076923e-5*SingularityFunction(x, 9, 2) for x over (0.0, 9.0)
**********************************************************************
File "/home/travis/build/sympy/sympy/doc/src/modules/physics/continuum_mechanics/beam_problems.rst", line 234, in beam_problems.rst
Failed example:
    b.plot_deflection(subs={E: 20E9, I: 3.25E-6});
Expected nothing
Got:
                                                                                                                                                                       Plot object containing:                                                                                                                                                                   
    [0]: cartesian line: -0.00198461538461538*SingularityFunction(x, 0, 2) + 0.000133333333333333*SingularityFunction(x, 0, 3) - 5.12820512820513e-6*SingularityFunction(x, 0, 4) + 0.000384615384615385*SingularityFunction(x, 5, 2) + 5.12820512820513e-6*SingularityFunction(x, 5, 4) - 3.07692307692308e-5*SingularityFunction(x, 9, 3) for x over (0.0, 9.0)
**********************************************************************
File "/home/travis/build/sympy/sympy/doc/src/modules/physics/continuum_mechanics/beam_problems.rst", line 243, in beam_problems.rst
Failed example:
    b.plot_loading_results(subs={E: 20E9, I: 3.25E-6});
Exception raised:
    Traceback (most recent call last):
      File "/opt/python/3.6.3/lib/python3.6/doctest.py", line 1330, in __run
        compileflags, 1), test.globs)
      File "<doctest beam_problems.rst[27]>", line 1, in <module>
        b.plot_loading_results(subs={E: 20E9, I: 3.25E-6});
      File "/home/travis/build/sympy/sympy/sympy/physics/continuum_mechanics/beam.py", line 1432, in plot_loading_results
        plt = matplotlib.pyplot
    AttributeError: 'NoneType' object has no attribute 'pyplot'
**********************************************************************
File "/home/travis/build/sympy/sympy/doc/src/modules/physics/continuum_mechanics/beam_problems.rst", line 884, in beam_problems.rst
Failed example:
    plot(b.load, (x, 0, 10*n))
Expected nothing
Got:
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                Plot object containing:                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            
    [0]: cartesian line: 1.0*SingularityFunction(x, 5, 0) - 1.0*SingularityFunction(x, 10, 0) + 0.2*SingularityFunction(x, 15, 1) - 1.0*SingularityFunction(x, 20, 0) - 0.2*SingularityFunction(x, 20, 1) + 0.04*SingularityFunction(x, 25, 2) - 1.0*SingularityFunction(x, 30, 0) - 0.4*SingularityFunction(x, 30, 1) - 0.04*SingularityFunction(x, 30, 2) + 0.008*SingularityFunction(x, 35, 3) - 1.0*SingularityFunction(x, 40, 0) - 0.6*SingularityFunction(x, 40, 1) - 0.12*SingularityFunction(x, 40, 2) - 0.008*SingularityFunction(x, 40, 3) + 0.0016*SingularityFunction(x, 45, 4) - 1.0*SingularityFunction(x, 50, 0) - 0.8*SingularityFunction(x, 50, 1) - 0.24*SingularityFunction(x, 50, 2) - 0.032*SingularityFunction(x, 50, 3) - 0.0016*SingularityFunction(x, 50, 4) + 0.00032*SingularityFunction(x, 55, 5) - 1.0*SingularityFunction(x, 60, 0) - 1.0*SingularityFunction(x, 60, 1) - 0.4*SingularityFunction(x, 60, 2) - 0.08*SingularityFunction(x, 60, 3) - 0.008*SingularityFunction(x, 60, 4) - 0.00032*SingularityFunction(x, 60, 5) for x over (0.0, 60.0)
**********************************************************************

[moorepants]

@asmeurer Curious if you are fine adding the matplotlib sphinx directive extension so that we can show plots in the sympy docs? (before I do more work on this)

[jashan498]

I am getting errors locally. Just writing the Plot object under the plotting functions(like below) got rid of error.

>>> b.plot_shear_force()
   Plot object containing:                                                                                                                
   [0]: cartesian line: -258*SingularityFunction(x, 0, -1) + 52*SingularityFunction(x, 0, 0) - 8*SingularityFunction(x, 0, 1) + 50*SingularityFunction(x, 5, -1) + 8*SingularityFunction(x, 5, 1) - 12*SingularityFunction(x, 9, 0) for x over (0.0, 9.0)

[moorepants]

This is ready for a review. Tests seem to be passing.

[moorepants]

@jashan498 Can you review?

[jashan498]

Shouldn't deflection and slope curves also be added for truncated polynomial load example?
Rest looks good to me.

[moorepants]

Yes, more can always be added. I think that it is sufficient as is to demonstrate that the loading work correctly (from fixes in #15304). All of the examples can be improved. Just wanted to get matplotlib extension working and have at least one example showing that off. Gonna merge for now and open issues for further improvements.

[asmeurer]

This looks nice. I would suggest replacing the ASCII art with an SVG image (it shouldn't be too hard to recreate in Inkscape).

[asmeurer]

Worth noting that this ⭯ character doesn't render for me on my phone (it just comes out as a blank space).

[moorepants]

This looks nice. I would suggest replacing the ASCII art with an SVG image (it shouldn't be too hard to recreate in Inkscape).

Yes, it would be nice to have SVG diagrams. We can open an issue for that. Drawing them will take some time.

Worth noting that this ⭯ character doesn't render for me on my phone (it just comes out as a blank space).

I guess this is a system font thing? Not sure how to know what unicode characters are generally supported.