Conclusion of things done on weekend regarding learning word2vec.

• word2vec is one of the really good ways to solve the problem of “word-embedding”. , developed by researchers at google (Tomas Mikolov and colleagues)

• GloVe (Global Vectors for Word Representation) is another really good way to compute word embeddings, developed at Stanford.

• The original research papers (by Tomas Mikolov and colleagues) on word2vec [1]. Efficient Estimation of Word Representation in Vector Spaces [2]. Distributed Representation of words and phrases and their composotionality

  these two papers on reading sucked the hell out of me (probably because I don’t have much background in Neural networks).

  Rather I found myself having to go through the paper [3]. word2vec explained: Deriving Mikolo et al’s negative sampling word embedding method

• I’d a go through the lecture 7 (skipped the lectures 4, 5 and 6), to get an idea of what are deep learning frameworks like Tensorflow (lecuture 7 is an introduction to it). It gives a basic idea of why to use Tensorflow and performing basic operations with it.

• All in all this weekend was all focused on things related to NLP stuff. I am hopeful that in the next year I might be able to take a few more step towards learning the NLP stuff.

Today’s day started with receiving an email from Google. Here is a snapshot:

This left a big smile on my face 😄

The past 3-4 months have been amazing and I have learnt a lot during the course of time. I would like to thank Aaron, Ondrej and the SymPy team for providing me with this opportunity, my mentor Amit Kumar for guiding me all through the phases and a special thanks to Chris who was not officially my mentor but was present all the time for reviweing my work and helping me complete the project successfully.

Here is what Amit has to say:

Though GSoC is completed I will be continuing my contribution in the developement of the software.

This post summarizes the work done on the Group Theory part of the combinatorics module during 2018 summers as a part of the GSoC programme

This post summarises the work that I have done during GSoC for SymPy. The links to the Pull Requests are in chronological order under each header. For following the progress made during GSoC, see my weekly posts.

This summer has been a great learning experience and has helped me get a good exposure of test-driven development. I plan to actively review the work that has went into this project and continue contributing to SymPy. I am grateful to my mentors, Kalevi and Aaron for reviewing my work, giving me valuable suggestions, and being readily available for discussions.

Pull Requests

This is the list of merged Pull Requests.

Major Additions

• sympy/sympy#14725: Add discrete module, and transforms sub-module including Fast Fourier Transform, Number Theoretic Transform, and include docstring, doctests, unit-tests.
• sympy/sympy#14745: Add convolution sub-module including convolution_fft, convolution_ntt and a general method convolution for identifying the type of convolution and handling the cyclic convolution case, and include docstring, doctests, unit-tests.
• sympy/sympy#14765: Implement Walsh Hadamard Transform and include doctests, unit-tests, docstring for the same.
• sympy/sympy#14783: Implement convolution_fwht and add support for keyword dyadic in the general convolution method, and include docstring, doctests, unit-tests.
• sympy/sympy#14816: Add a method linrec which allows evaluation of linear recurrences without obtaining closed form expressions, and include tests for the same.
• sympy/sympy#14853: Implement Möbius Transform using Yate’s Dynamic Programming method while having subset keyword for flexibility of the implementation, and include docstring, doctests, unit-tests.
• sympy/sympy#14878: Implement subset convolution and include docstring, doctests, unit-tests.
• sympy/sympy#14928: Add covering product in convolutions sub-module and include docstring, doctests, unit-tests.
• sympy/sympy#14954: Add intersecting product in convolutions sub-module and include docstring, doctests, unit-tests.

Documentation and Code Refinements

• sympy/sympy#14969: Improve Sphinx docs for SymPy, use plural module names - convolutions and recurrences, refine the documentation for discrete module.
• sympy/sympy#14994: Add reStructuredText file for discrete module for inclusion in Sphinx docs, which can be referred here.
• sympy/sympy#15025: Refine discrete module to fix tests using floats instead of Rationals, adding warning about sequence size for fft and other improvements.

Additional Improvements

• sympy/sympy#14712: Add .rewrite(exp) capability for instances of Pow and fix bugs in solvers module.
• sympy/sympy#14907: Fix exception handling for factorial modulo and refine the signature for general convolution method.
• sympy/sympy-bot#18: Fix the issue of incorrect links being referred in wiki by explicitly specifying the links instead of using relative paths.

Future Work

• Adding a user-facing public method that internally calls discrete.recurrences.linrec and possibly extending it for different types of recurrences as well.
• Making methods fft and convolution_fft efficient for both symbolic and numeric variants, as some discussion and benchmarking has been done for it and there is some work done by Colin for implementing a ComplexFloat class in sympy/sympy#12192 which would be very helpful for the same.

About Me:

I am Nikhil Pappu, an undergraduate Computer Science student at the International Institute of Information Technology, Bangalore.

About the Project:

Autolev (now superseded by MotionGenesis) is a domain specific language used for symbolic multibody dynamics. The SymPy mechanics module now has enough power and functionality to be a fully featured symbolic dynamics module. The parser parses Autolev (version 4.1) code to SymPy code by making use of SymPy’s math libraries and the mechanics module.

The parser has been built using the ANTLR framework and its main purpose is to help former users of Autolev to get familiarized with multibody dynamics in SymPy.

The Plan:

The plan was to build a parser using ANTLR that could parse Autolev code to SymPy code.  Overall,  I think I was able to achieve most of what I had hoped for. I had faced some difficulties in some areas of the parser due to the very different nature of Autolev and Python. The parser has some issues as a result. I have specified all the details in the documentation I have written.

Work Done:

I made a parser for the Autolev language which is now a part of SymPy in the parsing module. I have written the code for the parser using the ANTLR framework. I have also included a bunch of tests for testing the rules of the parser code.

The majority of the work was a part of PR #14758. I made a second PR #15006 for the changes I had made after the main PR.

I have written documentation for the parser which is a part of these PRs: #15046, #15066 and #15067.

I have also written a PyDy for Autolev Users guide which is a part of PR #15077. This guide is meant to be a quick reference for looking up Autolev-PyDy equivalents.

Future Work:

1. The parser has been built by referring to and parsing codes from the Autolev Tutorial and the book Dynamics Online: Theory and Implementation Using Autolev. Basically, the process involved going through each of these codes, validating the parser results and improving the rules if required to make sure the codes parsed well.

   As of now, a large number of codes of Dynamics Online have been parsed. Completing all the remaining codes of the book would make the parser more complete.

2. There are some limitations and issues with the parser and these have been discussed in the documentation. The plan is to fix these in order of priority.
3. The parser is currently built using a kind of Concrete Syntax Tree (CST) using the ANTLR framework. It would be ideal to switch from a CST to an Abstract Syntax Tree (AST). This way, the parser code will be independent of the ANTLR grammar which makes it a lot more flexible. It would also be easier to make changes to the grammar and the rules of the parser.

I would like to keep contributing to SymPy. I would be doing a lot of math in college especially related to data science so I would love to contribute in areas like Probability and Algebra among others. I would also like to help newcomers feel comfortable with the environment.

Conclusion:

I would like to thank my mentors Ondřej Čertík and Jason Moore for believing in me and taking time out from their busy schedules to guide me throughout the project. I would also like to thank Aaron Meurer for looking over GSoC as the org admin and making sure that we all had a great experience working with SymPy.

Links:

Main PR: #14758

Updated parser code PR: #15006 and #15013

Documentation PRs: #15046, #15066 and #15067

PyDy for Autolev Users guide PR: #15077

Weekly Blog link: https://nkhlpappu.wordpress.com/

This week I continued the work with log solver and lambert solver. The log solver implementation is almost done with just few check for assumptions. Symbolic logarithmic equations should be dealt with proper assumptions. Such equations would give unsolved instance of ConditionSet otherwise.

>>> a, b, x = symbols('a, b, x')
>>> solveset(a**x - b**(x + 1), x, S.Reals)
ConditionSet(x, Eq(a**x - b**(x + 1), 0), S.Reals)
# because the bases (here, `a and b`) should have a positive value > 0)

>>> a, b = symbols('a b', positive=True)
>>> solveset(a**x - b**(x + 1), x, S.Reals)
{log(b)/(log(a) - log(b))}

Discussions with Amit and Chris suggested that there should be some other way to handle vanilla symbols. There should be atleast a ValueError or something else that would tell the user why this cannot be solved. Chris suggested of returning a Piecewise as object for this scenario. Something like:

cond = True if fuzzy_and([a > 0, b > 0, Eq(im(f), 0), Eq(im(g), 0)]) else False
Piecewise((solutions, cond), ConditionSet(........),  True))

Using Piecewise was not the greatest of the option as:

• Though the assumptions were checked but it didn’t provided information to the user that why did it not solved.

• Also using Piecewise had some problem causing recursion error, though it could be solved but it would make things unncessarily complicated.

• Also solveset is not made to return objects other than Sets.

So we switched to a completely different approach. We tried using a different type of ConditionSet: providing the information within it that is necessary for the equation to be solved. The approach was: Force the equation to get solved but return a ConditionSet (a different than ususal) with the required assumptions, like: ConditionSet(x, And(a_base>0, b_base>0, Eq(im(a_exp), 0), Eq((im(b_exp), 0))), {solutions}). So now the above equation would return solutions something like: ConditionSet(x, (a > 0) & (b > 0), Intersection(Reals, {log(b)/(log(a) - log(b))}))

So this approach has been applied in the PR as of now, only a few minor changes needs to be done. I will try to finish this by the end of the week.

Apart from this some work has been done in lambert solver:

• Used _is_lambert to identify lambert type equations.
• Implemented bivariate solver (I will add a commit for this soon).
• Ran solve’s tests, to get an idea of the extent to which solveset would handle such equations.

What’s next:

I will try to wrap up the work of both the PR’s. Lambert solver PR would need a bit more time for reviewing but nevertheless I will be continuing its work post GSoC. Implementing these two solvers will make solveset fully functional to handle transcendental equations which is a major part of my GSoC propsal. There will be a few minor things left that I will try to finish post GSoC. Also since this is the last week for the coding period, I will be needing to submit a final report of my work, I will complete and submit it before the deadline.

The final week of Coding Period has completed.

This week, the work was mainly concerned with the documentation and refinements in the discrete module. I started by opening PR #14994 to update Sphinx docs for SymPy. Kalevi and Aaron were kind enough to review the PR and help refine it for the final merge. The documentation for discrete module is now part of the SymPy docs and can be referred here.

Late this week, I opened PR #15025 for improvements in the discrete module. Colin helped fix accidental floats in unit tests (which should have been Rationals). After the review, the PR was merged successfully.

Future work would include - addition of a user-facing public method for linrec and making methods fft and convolution_fft efficient for both symbolic and numeric variants, as some discussion and benchmarking has been done for it and there is some work done by Colin for ComplexFloat class in PR #12192 which would be helpful for the same.

Looking forward to the concluding phase, where I will be wrapping up GSoC and preparing the report for the final evaluation.

I have made some changes to the parser code to parse more files since #14758 has been merged. I have also made the changes suggested in that PR after it had been merged. I have opened a new PR #15006 for the updated parser code. I have also opened #15013 to include tests for physics functions which I didn’t do in the initial PR. The GitLab repo autolev-test-examples is in good shape now and is part of the sympy user.

I am currently writing the documentation in which I shall include how to use the parser, gotchas, limitations, issues and future improvements. I shall also include a rewritten version of the PyDy for Autolev Users guide in it.

I shall then write the output tests (Tests to compare the outputs of Autolev against those of SymPy) for most of the test examples in the GitLab repo (I shall include these in a directory called output-tests in the GitLab repo). I think its good to put them here as I don’t see the need to test these on Travis as changing the parser code won’t affect these. Plus, they will be in a place where the test examples are which are what they will be based on. We could still test these on Travis if required even from here I suppose.

Finally, I shall wrap things up with the Final Report and Submission.

Last week, I created #14967 for implementation of plotting methods. Soon after pushing my commits, many of the jobs failed on Travis. It was strange as I was not able to reciprocate the errors locally.

After discussing it on Gitter, I got to know that it was due to the printing of plots using TextBackend in the doctest in absence of matplotlib. As matplotlib was present in my system,  doctest used matplotlib backend instead of TextBackend locally, hence passing all tests. Kalevi suggested using unset_show to stop the printing of plots during doctest but apparently, unset_show didn’t work for TextBackend. This was fixed by #14984 later that day and #14967 passed all the tests after former one was merged.

This week, I also started editing #14453 for documentation. It included a few beam problems along with their ascii diagrams.

Next Week

• Make sure #14967 and#14453 gets merged.
•  Add more beam problems for documentation.

So this week I started up with implementing and sending a PR for lambert solver #14972. Solving these equations can be achieved by _solve_lambert routine of bivariate.py. It is really powerful and can solve a varied type of equations having a general form. Another routine comes into action, the bivariate_type to solve majorly lambert type of equations when the former is unable to solve. These two routines can be handy for implementing such equations. As of now I have added _solve_lambert() in the PR. I will add bivariate_type once the log solver PR gets finalised. There are few equations that can be solved by posifying the variable that needs to be solved. A bit discussion is needed on this part.

Apart from this, a lot of work was done in the log solver PR

• _term_factors() is used again.

• Logic for exponential identifying is modified to not identify lambert type equations

• Few mores tests were added.

• Chris advised to make identification helpers such that they identify their class even if they won’t get solved by their respective solvers, the equation should not be passed to any of the other helpers for further solving. This wasn’t the case before, the identifying helpers were implemented only for equations that their helpers could solve. So now this idea is implemented for both the exponential and logarithmic solver. Equations that these identifiers can’t identify will be further solved as lambert type.

Almost all the work of the log solver PR is done. I will be finishing the work on lambert solver PR and complete in coming week. I hope both the PR’s gets merged before the GSoC period ends.

This week, I started working on adding the final method to convolution module for Intersecting Product. PR #14954 dealt with the addition of intersection_product method. Intersecting Product was implemented using Möbius Transform with superset enumeration (mobius_transform(..., subset=False) and inverse_mobius_transform(..., subset=False)). After minor documentation improvements, the PR was merged successfully. The proposed transforms and convolutions are now part of sympy.discrete. The basic usage for the method is:

>>> from sympy import symbols, S, I, intersecting_product
>>> u, v, x, y, z = symbols('u v x y z')

>>> intersecting_product([u, v], [x, y])
[u*x + u*y + v*x, v*y]
>>> intersecting_product([u, v, x], [y, z])
[u*y + u*z + v*y + x*y + x*z, v*z, 0, 0]

Late this week, I started working on improving the documentation for SymPy’s Sphinx docs (http://docs.sympy.org/dev/index.html) and other minor changes in the PR #14969. Also, issue #14964 was opened to discuss the possibility of using LaTeX in docstrings for SymPy documentation. The following changes were part of the PR:

• Use LaTeX for docstrings in functions.combinatorial (reference to #14964)
• Include genocchi and partition numbers in sphinx docs
• Improve docstrings with single and double backticks for sphinx docs
• Use plural module names under discrete (discrete.convolutions and discrete.recurrences)
• Add graphviz as a prerequisite in sympy/doc/README.rst for Debian/Ubuntu
• Fix links in references containing rounded braces and unicode chars for sphinx docs
• Miscellaneous improvements to documentation

Successive reviews and discussions were helpful in finalizing the Pull Requests.

Looking forward to the final week of Coding Period.

Hello Everyone. I have been working on getting the PR #14758 into shape and now it is finally merged. I have written my own tests for the PR so as to not include copyrighted files that belong to the creators of Autolev.

I am now working on a test-examples repo which serves as a showcase of the parser and also as a source of additional tests. The repo is private on GitLab as it contains copyrighted files. You can request access at the repo link above. Files from this repo can be copied over to the test_examples folder of parsing/autolev to use them as tests. From now, I will be working on adding more examples from the PyDy example repo, Autolev Tutorial, and Dynamics Online to this repo while improving the code of the parser to parse all these codes. I am also making note of things like errors, inaccuracies etc to include them in the Documentation.

I will open another PR once I have made enough number of changes to the parser code.

Here is my plan for the future of this project:

Till the end of GSoC:

1. Work on getting the test-examples repo in good shape.
2. Write extensive Documentation (explaining what the parser can do, how to use it,  limitations, issues, future improvements etc).
3. Work on as many Dynamics Online codes (which I shall include in the repo) as possible (Wrap up Ch4 and hoping to get half of Ch5 done (as it is quite big)).

Post GSoC:

1. Finish the rest of the Dynamics Online Book (Whatever is left of Ch5 and also Ch6 which I think is less important).
2. Work on the issues that I will be listing down in the documentation one by one after discussing the possible fixes (Some of these might require changes in the parser while some others require changes in the SymPy code while I do not have much of an idea about the fixes of some other ones).

Thanks,

Nikhil

This week I started working on implementing methods to plot Shear force, bending moment, slope and deflection diagrams. #14967 was created for it.

Mainly four methods were added to the Beam class:

• plot_shear_force: This method returns a plot for Shear force present in the Beam object.
• plot_bending_moment: This method returns a plot for Bending moment present in the Beam object.
• plot_slope: This method returns a plot for slope of the elastic curve of the Beam.
• plot_delfection: This method returns a plot for the deflection curve of the Beam object.
• plot_loading_results: This method returns fig object containing subplots of Shear Force, Bending Moment, Slope and Deflection of the Beam object.

Here is a sample notebook demonstrating how to use these plotting methods.

Next Week

• Make sure #14967 gets merged.
• Add more beam problems to the documentation.

GSoC'18 Week 9 & 10

This week started with the merge of the PR #14736. Yehhhh!!!!!. So now solveset will be able to solve a varied type of exponential equations. Next work is going on to build the logarithmic and lambert solver.

A lot of discussion has been taken place over the implementation of the logarithmic solver, there were mainly two points to consider:

• How the logarithmic equation gets evaluated, i.e., should we consider solutions that would make the log term negative.

Take for instance a logarithmic equation log(x - 3) + log(x + 3) = 0, when solved the solutions would be -sqrt(10) and sqrt(10), but -sqrt(10) make the log term negative. So the question was what should we do for such a scenario? Should we add a check to remove these solution or just accept. it.

As of now as suggested by Kalevi and Aaron we should focus on the liberal interpratation for evaluating equations: if an expression can be written in its equivalent form and makes sense then we can consider solutions of this equivalent form. Therefore both the above solutions are acceptable.

• How the identification of the logarithmic equations would take place.

The identification of logarithmic type is another question and is still yet to be agreed upon. At first the implementation was done by extracting each term of the expression and see if it has log terms in it, this wasn’t the best of the method as we are trying to identify a large class of logarithmic equation while solving is done only for a subset of those equations (only those that can be reduced by logcombine). So Amit and Chris stressed upon making the logarithmic identification for equations that its solver would solve. So as of now I have made changes accordingly.

Another problem that this PR is facing is of the infinite recursion. The equations that both exponential and logarithmic can’t solve but still their respective solver try to handle gets into infinite recursion. One way (though not appropriate) is to use flags like in solve, using this would remove the infinite recursion but is not the best way to handle, therefore I am looking into ways on how to get this fixed.

Apart from the work on log solver, I did some work on lambert solver- how the implementation would go, ran all the tests of solve, differentiated the tests that _solve_lambert could solve and that bivariate_type would. I will be adding a PR for this in a day or so.

Next week goals:

• Finish things with logarithmic solver

• Sending a PR for lambert solver and try to finish its work as quickly as possible.

This week SymPy 1.2 was released, which included the discrete module. The complete changelog for the SymPy 1.2 is here. I started the week by cleaning up discrete module, improving the API of public convolution method by attending to reviews by Aaron and Kalevi and fixing issue #14901 reported by Aaron in PR #14907.

The PR #14907 has been merged successfully and will be part of SymPy 1.2.1.

Late this week, I started working on the convolution module for inclusion of covering_product. The PR #14298 included the same with documentation, doctests and unit tests. The implementation of covering_product uses Möbius Transform with subset enumeration (mobius_transform(..., subset=True) and inverse_mobius_transform(..., subset=True)). As included in the PR, the usage for the same is:

>>> from sympy import symbols, covering_product
>>> u, v, x, y, z = symbols('u v x y z')

>>> covering_product([u, v], [x, y])
[u*x, u*y + v*x + v*y]

>>> covering_product([u, v, x], [y, z])
[u*y, u*z + v*y + v*z, x*y, x*z]

Looking forward to the next week, where I will be implementing intersecting_product as the final method for the convolution module.

I have been working on improving the parser by parsing Dynamics online codes, planning out how to go about writing tests and other aspects of the project and getting the PR into shape.

I am currently working on writing tests to cover all the rules of the parser. I should be done with this in 2 days.

This is the plan I have for the third phase:

1. Make the PR merge ready:
   1. Finish the tests for the parser rules and get the PR merged.
   2. open a new PR to work on further improvements.
2. additional_tests (will be added in a private BitBucket repo). Here I shall go through many codes from these sources and improve the parser to parse most of these. I shall take notes on little details and errors so that I can include them in the documentation.
   1. PyDy example repo (mass spring damper, double pendulum, chaos pendulum examples)
   2. Dynamics Online Chapters 1 – 4
   3. Autolev Tutorial Examples (5.1 – 5.7)
3. Documentation (What the parser can do, How it should be used, Limitations, Future improvements etc)
4. Make the parser parse Dynamics Online Chapter 5 codes and the Bicycle Model.
5. Final Report

I started implementing Beam_3d class which can be used to find Shear force, Bending moment, Slope, Deflection and other few things for the Beam object.  PR #14883 was created for this.

I implemented Beam_3d class using  this paper as a reference. Actually, like Beam class, it uses a few sets of equations to find certain quantities:

• To find Shear force and Bending moment
  
  where [N, Q_y, Q_z] and [M_x, M_y, M_z] are the shear force and bending moment along x-y-z-axes respectively (q and m are applied load and moment).
• To find Slope and Deflection:
  
  
  where [w_x, w_y, w_z] and [θ_x, θ_y, θ_z] are deflection and slope along three axes respectively.

Example for the API:

There is a beam of l meters long. A constant distributed load of magnitude q
is applied along the y-axis from start till the end of the beam. A constant distributed
moment of magnitude m is also applied along the z-axis from start till the end of the beam. Beam is fixed at both of its end. So, deflection of the beam at the both ends
is restricted.

>>> from sympy.physics.continuum_mechanics.beam import Beam_3d
>>> from sympy import symbols
>>> l, E, G, I, A = symbols('l, E, G, I, A')
>>> b = Beam_3d(l, E, G, I, A)
>>> b.apply_support(0, "fixed")
>>> b.apply_support(l, "fixed")
>>> q, m = symbols('q, m')
>>> b.apply_load(q, dir="y")
>>> b.apply_moment_load(m, dir="z")
>>> b.shear_force()
[0, -q*x, 0]
>>> b.bending_moment()
[0, 0, -m*x + q*x**2/2]
>>> b.solve_slope_deflection()
>>> b.slope()
[0, 0, l*x*(-l*q + 3*l*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q)/(2*(A*G*l**2 + 12*E*I)) + 3*m)/(6*E*I)
+ q*x**3/(6*E*I) + x**2*(-l*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q)/(2*(A*G*l**2 + 12*E*I))
- m)/(2*E*I)]
>>> b.deflection()
[0, -l**2*q*x**2/(12*E*I) + l**2*x**2*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q)/(8*E*I*(A*G*l**2 + 12*E*I))
+ l*m*x**2/(4*E*I) - l*x**3*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q)/(12*E*I*(A*G*l**2 + 12*E*I)) - m*x**3/(6*E*I)
+ q*x**4/(24*E*I) + l*x*(A*G*l**2*q - 2*A*G*l*m + 12*E*I*q)/(2*A*G*(A*G*l**2 + 12*E*I)) - q*x**2/(2*A*G), 0]

As this class is relatively new, it would require a few improvements in the future:

• As Beam_3d doesn’t use SingularityFunction, I was unable to find a way to represent point load/moments. So for now Beam_3d  only supports continous load (applied over the whole span length of beam).
• Also, This class assumes that any kind of distributed load/moment is
  applied throughout the span of a beam.

For now, after discussing it with Arihant, we decided to raise NotImplementedError in such cases.

Next Week

• Make sure PR #14883 gets merge by the end of next week.
• Start implementing plotting methods for Beam class.

The second phase of Coding Period has concluded.

This week I worked on implementing Subset Convolution for discrete module. PR #14878 was opened for the same. The PR included unit tests, documentation, and correspondingly subset keyword was added for public convolution method.

After discussing the implementation details and references with Kalevi, the approach was finalized. The PR has been merged successfully. The usage for the same is:

>>> from sympy.discrete.convolutions import (convolution, convolution_subset)
>>> u, v, x, y, z = symbols('u v x y z')

>>> convolution_subset([u, v], [x, y])
[u*x, u*y + v*x]

>>> convolution([u, v, x], [y, z], subset=True)
[u*y, u*z + v*y, x*y, x*z]

>>> convolution([u, v, x], [y, z], subset=True, cycle=3)
[u*y + x*z, u*z + v*y, x*y]

Plan for this phase has executed well, and the second evaluation has been successful.

Looking forward to the final phase of Coding Period.

At the start of the week I worked on the leftovers of week 8:

• added log_singularities() that will help in determining logarithmic singularities,
• improved documentation of all helpers as suggested by Amit to maintain consistency

Status of the PR’s:

PR #14736 is ready to be merged.

PR #14792 is being worked on. Major tasks has been completed, just review and refining has to be done.

Apart from this I started working on the way Lambert type equations can be solved through _transolve(). I looked into _tsolve's way of handling such equations. For solving Lambert type equations _tsolve() largely depends on bivariate.py. It takes help of the different utility functions implemented there. Of them two important are _solve_lambert() and bivariate_type(). These two helpers help in getting the equations evaluated.

Equations that can be written in the standard form as: A + B*x + C*log(D + E*x) = 0 has the solutions in terms of Lambert function as:

D/E + C*B*W(t) with (B/C*E)*exp((BD - AE)/CE)

This is what _solve_lambert() determines and accordingly returns the solutions, otherwise returns a NotImplementedError

If _solve_lambert() is unable to handle bivariate_type() is tried. This function first tries to identify the type of composite bivariate and then substitutes Dummy in place of them. For eq: (x + y)**2 - 3 would become _u**2 - 3 where _u is the dummy variable. The idea is that solving the latter equation for u and then equating the solutions to the former equation is equivalent for solving the original one.

While implementing in _transolve this philosophy needs to be applied. As of now I have looked into different tests on how they behave. I will start implementing it next.

Next week’s plan:

• Finishing with the logsolver

• Implementing lambert solver.

GSoC'18 Week 7 & 8

Before the start of the week Amit and I discussed on a few points on:

Note: is_logarithmic() is an identifier helper for _transolve to determine whether the expression is logarithmic or not. and _solve_log() is a solving helper that returns the equation in a tractable form for solveset to better handle.

• What should is_logarithmic() return?

While designing the method at first it returned a logcombined equation if found to be logarithmic, but we agreed upon having consistency among all the identifying helpers to return either True or False.

• How _is_logarithmic() should work?

Next question was how it should work. We can implement it in two ways either to make the logcombined equation, if the expression reduces, it is obviously a logarithmic equation otherwise not. We also need to check whether the equation reduced has the variable to be solved in its free_symbols But logcombine possessed a problem that it unknowingly manipulates the equation, like log(x) - log(2*x) would reduce to log(1/2) for which the routine would return False as there are no symbol involved. So a more better way needs to be implemented.

• How _solve_log() will handle removing unwanted solutions?

Simply reducing the logarithmic equation to a tractable form for solveset to handle would cause spurious solutions in the result. Therefore it becomes necessary to remove them. Take for example: solveset gives the result of log(x - 3) + log(x + 3) as {-sqrt(10), sqrt(10)}, but -sqrt(10) is not the solution in Real domain. Therefore one way to remove it was using checksol. Amit suggested on to have a look over the singularities and try incorporating the check in _solveset.

Things that I did during the week:

• improved is_logarithmic()

Removed the logcombine way of checking the equation. As of now the _is_logarithm checks for every term to be logarithmic in terms of the variable to be solved, if so it returns True otherwise False

• improved the _solve_log()

As per the current documentation of _transolve this routine is improved to return a modified form of the equation that solveset could better handle. Checking of the spurious solutions will take place in solveset itself.

• Way to remove spurious solutions

To handle this scenario I have added a check in _solveset specifically for logarithmic equations to remove spurious solutions. The idea is based on the fact that natural log in undefined for negative and zero value, therefore this method gets each term of the expression, substitutes each solution to every term one by one and if for any term the value isn’t real that solution will not be included.

Why checksol() is not the appropriate way?

At first I thought of using the checksol(), but it possessed a problem. checksol unintensionally allows wrong solution to creep in. Take for example log(3*x) - log(-x + 1) - log(4*x + 1), solveset would give -1/2 and 1/2 as the solutions but the former isn’t a solution in real domain. Using checksol would not remove this as I*pi gets cancelled out during evaluating the expression therefore it returns True, which is not correct.

• Addressing comments

Apart from this few changes have been done in the _transolve PR:

• I have added a method that would return all the terms present in the expression: make_expr_args()

• Made the expresssion remain unevaluated when doing lhs - rhs within _transolve.

Read this blog for better understanding of logarithmic solving.

This week I mainly focused on finding and solving a bug due to which continuum_mechanics gave ValueError on using units with the quantities passed. Initially, I created #14856, which included a workaround in the Beam class itself to handle that error. But Arihant suggested opening a separate PR as the error was occurring due to a bug in the separate module.

So, #14865 was created. is_commutative attribute was added in the Prefix class  (setting Prefix.is_commutative to True removed PolynomialError). While doing changes in the PR, another bug appeared:

>>> from sympy.physics.units import meter, newton, kilo
>>> from sympy.physics.units.util import quantity_simplify
>>> quantity_simplify(x*(8*newton + y))
x*(8*newton + y, 1)

This bug was solved with few changes. After #14865 gets merged, continuum_mechanics should work with quantities involving units.

Next Week

• Make sure #14865 gets merged.
• Open a Pull Request and start working on 3dbeam class.

This week I started working on adding Möbius Transform to the discrete module using Yate’s DP (Dynamic Programming) method for implementation as part of PR #14853. The proposed transforms are part of sympy.discrete.transforms module.

After discussing with Kalevi, the methods implementing this transform were added with appropriate names. The keyword subset is used as a boolean to choose whether enumeration is done over subsets or supersets. The usage for the transform is:

>>> from sympy import mobius_transform, inverse_mobius_transform
>>> seq = list(symbols('w x y z'))
>>> mobius_transform(seq)
[w, w + x, w + y, w + x + y + z]
>>> inverse_mobius_transform(_)
[w, x, y, z]
>>> inverse_mobius_transform(seq, subset=False)
[w - x - y + z, x - z, y - z, z]
>>> mobius_transform(_, subset=False)
[w, x, y, z]

The PR was merged successfully, after inclusion of docstring and unit tests for the transform.

Looking forward to another exciting week.

I have a PR for a working parser now with some test cases. The Travis errors I had previously have been fixed.

I am currently going through the chapters of the book Dynamics Online: Theory and Implementation with Autolev and parsing most of the Autolev codes I come across. I feel this would help to make the parser more complete. After getting the desired parsed code I am also running the code and checking that the results are same/similar to the Autolev responses in the .ALL files.

I have parsed the codes of Chapter 1 and 2 of the book and am currently working on Chapter 3. There are 6 Chapters overall and the bulk of the stuff is concentrated in Chapters 4 and 5.

After parsing the codes of this book, I shall update the parser code and the tests in the PR. I will add more test cases as well. I will also send in a file containing all the parsed codes of Dynamics Online.

A lot of the codes are parsing completely fine. A few I feel are quite difficult to parse to SymPy code using a parser and they wouldn’t even be in the spirit of SymPy/Python if parsed exactly. I have marked these for later. A few of them are producing slightly altered expressions or in some cases errors in SymPy. I am classifying all the codes appropriately based on criteria like this.

After parsing the book I plan on finishing up the leftover parts of the Autolev Tutorial examples and making sure the Bicycle Model Autolev code is parsed.

I will then go on to do a complete code cleanup (general cleanup, using standard conventions and better variable names, adding more comments etc).

Finally, I will wrap things up by writing the Documentation and a Final Report. In these I shall discuss: what the parser can do, how it should be used (there are some minor things in some cases that the user should note to get a proper SymPy parse), limitations and future improvements.