[sympy] Assumptions for integration (integrate over area)

[Yuxiang Wang]

Hi all,

Not sure if sympy can do this, but wondering...

I am integrating some quantities over area in Y-Z domain. In general, most 
part of the integrand is constant across the area. However, there sometimes 
are factors such as y, z, y**2, z**2. I would like to simply denote them as:

Integration of y over area A = first moment of area of y = A_y
Integration of z over area A = first moment of area of z = A_z

Integration of y**2 over area A = second moment of area of y = I_yy
Integration of z**2 over area A = second moment of area of z = I_zz


So what I was hoping for is that I can somehow tell the system that 
integrate(y, some_area) == A_y, and then when it evaluates it we will plug 
in A_y automatically. Would that be possible?

Thank you,
Shawn


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[sympy] [Discussion] Equation of Motion Generation

[Harinandan]

Being an engineering student with a passion for physics,especially 
mechanics, i think this project idea would be a great fit for me, and help 
me expanding my python skill set as well

Looking into the idea, it says there is no previous work on the topic so i 
am slightly confused here as it also says that currently Kane's and 
Lagrange's method are being used to compute the same. Hence i am going to 
assume that you want to do away with those completely as they are quite 
overkill of a treatment in most cases.

I am to assume this module is to built ground up so both statics and 
dynamics in such a way that the user doesn't need to know even the basic 
equations of motion. 

So i could broadly say this project can be divided into 3 segments :

Kinematics
Dynamics
Refactoring the existing code, improving it and merging all this together

Within these obviously, there are many different mathematical treatments 
possible depending on the physical situations to be computed. 

As such i Kindly request any of the members to give an indication of what 
the endgame for this idea is, as in what would you like the end product to 
be? If i can get an indication regarding that i can make a more detailed 
path of how i plan to get there , and timeline, and everything i plan to 
implement for the same. Please do suggest further actions to be taken . I 
hope this will be a fruitful collaboration

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Re: [sympy] Re: [Discussion] GSoC 2020: Improving and extending ODE

[Oscar Benjamin]

That sounds reasonable.

Note that we can't start raising NotImplementedError yet. You will
need to think about how to introduce the new code gradually while
still ensuring that dsolve falls back on the old code for cases not
yet handled by the new code.

On Tue, 17 Mar 2020 at 17:51, Milan Jolly  wrote:
>
> So, I have made a rough layout of the main function that will be used to 
> solve ODEs with the methods like 
> neq_nth_order_linear_constant_coeff_homogeneous/nonhomogeneous, 
> neq_nth_linear_symmetric_coeff_homogeneous/nonhomogeneous, special case 
> non-linear solvers, etc.
>
> Some notations used:
>eqs: Equations, funcs: dependent variables, t: independent variable, wcc: 
> weakly connected component, scc: strongly connected component
>
> Introduction to helper functions that will be used(these are temporary names, 
> parameters and return elements and may be changed if required):
>
> 1. match_ode:-
> Parameters: eqs, funcs, t
> Returns: dictionary which has important keys like: order(a dict that 
> has func as a key and maximum order found as value), is_linear, is_constant, 
> is_homogeneous, eqs, funcs.
>
> 2. component_division:-
> Paramters: eqs, funcs
> Returns: A 3D list where the eqs are first divided into its wccs and 
> then into its sccs.
> This function is suggested to be implemented later. So, until all the 
> other solvers are not ready(tested and working), this function will just take 
> eqs and return [[eqs]].
>
> 3. get_coeff_matrix:-
> Parameters: eqs, funcs
> Returns: coefficient matrix A(t) and f(t)
> This function takes in a first order linear ODE and returns matrix 
> A(t) and f(t) from X' = A(t) * X + f(t).
>
> 4. nth_order_to_first_order:-
> Parameters: eqs, order
> Returns: first order ODE with new introduced dependent variables.
>
> And all the first order linear solvers mentioned above.
>
> Now, besides the main function, there are two separate functions depending on 
> whether the system of ODEs is linear or not, namely _linear_ode_sol and 
> _non_linear_ode_sol.
>
> 1. _first_order_linear_ode_sol:-
> Parameters: match dict(obtained earlier and maybe modified in ode_sol)
> Returns: Dict with keys as func and value as its solution that solves 
> the ODE.
> Working: First, extracts A(t) and f(t) using get_coeff_matrix, then 
> using match dict, identify which solver is required and solve the ODE if it 
> is possible to do so. For example: Case where A(t) is not symmetric isn't 
> solved.
>
> 2. _non_linear_ode_sol has similar Parameters and Returns but the function 
> operates differently that's why it is essential to use a different function. 
> But I don't have a clear understanding
>of how to design _non_linear_ode_sol yet but here is what I have came up 
> with: First match the condition where it is possible seperate out the 
> independent variable to get a relationship
>between the dependent variables and then finally, just use the special 
> solver to solve the ODE.
>
> Now, coming to the main function ode_sol(for now, I haven't considered 
> initial values):-
>   Parameters: eqs, funcs, t
>   Returns: Solution in a dict form where func is the key and value is the 
> solution for that corresponding func.
>
>   Working:
>   The steps of its working-
>   1. Preprocess the equations.
>   2. Get the match dict using match_ode function.
>   3. Convert nth order equations to first order equations using 
> nth_order_to_first_order while storing the funcs seperately so that we can 
> later filter out the dependent variables that were introduced in this step.
>   4. Get the 3D list of equations using component_division function.
>   5. Iterate through the wccs and solve and store solutions seperately 
> but for sccs, first solve the first set of equations in a scc, then 
> substitute the solutions found in the first set of the current scc to the 
> second
>  set of current scc. Keep doing this until the all the sets for a 
> particular scc is solved.
>   6. For solving a component, choose either _linear_ode_sol or 
> _non_linear_ode_sol depending upon the set of equations to be solved.
>   7. Return a dict by taking out values from the solution obtained using 
> all the dependent variables in funcs as there may be more variables 
> introduced when we made the system into first order.
>
> For now, this is what I have came up with. Obviously the order in which we 
> will proceed is, build the basic layout of the main function and 
> component_division will just increase the number of dimensions to 3 
> rudimentarily as we
> will have to first ensure that the general solvers work well since working on 
> both of them simultaneously will make it tough to pinpoint the errors. Along 
> with that, non-linear solvers can be implemented later, we can just raise a
> NotImplementedError for now till we have completed both the general lin

[sympy] Classical equation mechanics

[vinit wadgaonkar]

dear sir,
i have read past application as per your guidance please guide me more
about classical equations module what to be done about kane's method
whether  we should  apply any alternative method or apply new Techniques to
make code  base faster , relying on the existing principle of method
solving please Guide me through this



On Fri, 13 Mar, 2020, 10:53 PM Jason Moore,  wrote:

> Vinit,
>
> I recommend reading past successful proposals on the sympy wiki to get an
> idea of what and how much your proposal should include. What you've written
> is not sufficient.
>
> Jason
> moorepants.info
> +01 530-601-9791
>
>
> On Fri, Mar 13, 2020 at 10:06 AM vinit wadgaonkar 
> wrote:
>
>> Since I am not getting pr for the same
>>
>> Get Outlook for Android 
>>
>> --
>> *From:* vinit wadgaonkar 
>> *Sent:* Friday, March 13, 2020 10:33:47 PM
>> *To:* sympy@googlegroups.com ; asmeu...@gmail.com
>> 
>> *Subject:* Re: [sympy] My raw application layout
>>
>> Sorry but I am waiting for the reply please guide me through problem if
>> any mentor can help it would be great
>>
>> Get Outlook for Android 
>>
>> --
>> *From:* vinit wadgaonkar 
>> *Sent:* Tuesday, March 10, 2020 4:38:00 PM
>> *To:* sympy@googlegroups.com ; asmeu...@gmail.com
>> 
>> *Subject:* Re: [sympy] My raw application layout
>>
>> As I mentioned earlier this rough estimate implementation of Newton
>> eurler methods can take up to 4 weeks so this plan naturally gets extended
>> upto 11 weeks or more please guide more through this topic
>> but can i work on this topic
>>
>> On Tue, 10 Mar 2020, 16:02 vinit wadgaonkar,  wrote:
>>
>> As I mentioned earlier this rough estimate implementation of Newton
>> eurler methods can take up to 4 weeks so this plan naturally gets extended
>> upto 11 weeks or more please guide more through this topic
>> but can i work on this topic
>>
>> On Tue, 10 Mar 2020 at 16:01, vinit wadgaonkar 
>> wrote:
>>
>> but can i work on this topic
>>
>>
>> On Tue, 10 Mar 2020 at 09:18, vinit wadgaonkar 
>> wrote:
>>
>> As I mentioned earlier this rough estimate implementation of Newton
>> eurler methods can take up to 4 weeks so this plan naturally gets extended
>> upto 11 weeks or more please guide more through this topic
>>
>> On Tue, 10 Mar, 2020, 12:06 AM Aaron Meurer,  wrote:
>>
>> Hi.
>>
>> There are roughly 12 weeks of coding for GSoC. See
>> https://summerofcode.withgoogle.com/dashboard/timeline/.
>>
>> Aaron Meurer
>>
>> On Mon, Mar 9, 2020 at 10:59 AM vinit wadgaonkar 
>> wrote:
>> >
>> > Namaste sympy community,
>> > I am Vinit Wadgaonkar a first year computer science engineering,student
>> I want to spend my summer coding for sympy community through GSOC platform
>> , I want to improve a code base for classical equation generation with
>> python under physics module because it caught my attention among other
>> projects ideas i have experience of engineering level mathematics,
>> classical and modern mechanics, I have fair experience of coding in python
>> moreover it is interest driven , I want to improve code base for kane's
>> equation solving and newton eurler methods for me classical mechanics is of
>> great interest
>> > raw schedule planned is:
>> > First week:
>> > 1) Digging up reason responsible for slow ouput
>> > 2) Implementing newton eurler methods
>> > 3) Testing them under test cases
>> > Second week:
>> > 1)  Clearing any backlogs under first week
>> > 2)   Improving kanes method by adding functions of newton eurlers
>> methods
>> > 3)  Cleaning up the code base
>> >
>> > As mentioned in the description cleaning of the code base.
>> >
>> > Third week:
>> >
>> > 1)Backlogs of second week if any
>> > 2)Improvising code to make overall sympy code base faster
>> > 3)Checking out equations solving with kane's method
>> >
>> > Fourth week:
>> > Documentation because this section would require a crystal clear
>> explanations for furthers users to understand
>> >
>> > this is my rough estimate please suggest corrections as your guidance
>> is much sacrosanct for me, also if anybody guide me more through those
>> solver methods it would be highly appreciated
>> > I am currently reading articles:
>> > 1)
>> https://ocw.mit.edu/courses/mechanical-engineering/2-12-introduction-to-robotics-fall-2005/lecture-notes/chapter7.pdf
>> > 2)https://link.springer.com/chapter/10.1007/978-1-84800-391-0_5
>> >
>> >
>> > if approved it would be a great endeavour for me,
>> >
>> >
>> > Thanks and regards
>> >
>> > Vinit Wadgaonkar
>> > Pune,India
>> > +91 9067639592
>> >
>> >
>> >
>> >
>> >
>> >
>> > --
>> > You received this message because you are subscribed to the Google
>> Groups "sympy" group.
>> > To unsubscribe from this group and stop receiving emails from it, send
>> an email to sympy+unsubscr...@googlegroups.com.
>> > To view this discussion on the web visit
>> https://groups.goog

[sympy] Gsoc 2020 Introduction sympy

[muskan gupta]

Hello everyone,

I am Muskan Gupta,  a 2nd-year undergraduate pursuing computer science 
engineering from Guru Nanak Dev University.

I have worked with python,c++ and java coding languages but have a better 
experience and interest in python. Furthermore, I have great interest and 
understanding of mathematical equations solving. So, Sympy seems to be the 
perfect platform for me to work on.

I am interested in working on the "Solvers" project. I would be immensely 
grateful if I could get some guidance on this project.

I look forward to contributing to this wonderful community of GSoC.

Thank You.

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[sympy] GSOC 2020 Introduction

[muskan gupta]

Hello everyone,

I am Muskan Gupta,  a 2nd-year undergraduate pursuing computer science 
engineering from Guru Nanak Dev University.

I have worked with python,c++ and java coding languages but have a better 
experience and interest in python. Furthermore, I have great interest and 
understanding of mathematical equations solving. So, Sympy seems to be the 
perfect platform for me to work on.

I am interested in working on the "Solvers" project. I would be immensely 
grateful if I could get some guidance on this project.

I look forward to contributing to this wonderful community of GSoC.

Thank You.

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Re: [sympy] Re: [Discussion] GSoC 2020: Improving and extending ODE

[Milan Jolly]

So, I have made a rough layout of the main function that will be used to 
solve ODEs with the methods like 
neq_nth_order_linear_constant_coeff_homogeneous/nonhomogeneous, 
neq_nth_linear_symmetric_coeff_homogeneous/nonhomogeneous, special case 
non-linear solvers, etc.

Some notations used:
   eqs: Equations, funcs: dependent variables, t: independent variable, 
wcc: weakly connected component, scc: strongly connected component

Introduction to helper functions that will be used(these are temporary 
names, parameters and return elements and may be changed if required):

1. match_ode:- 
Parameters: eqs, funcs, t
Returns: dictionary which has important keys like: order(a dict 
that has func as a key and maximum order found as value), is_linear, 
is_constant, is_homogeneous, eqs, funcs.

2. component_division:-
Paramters: eqs, funcs
Returns: A 3D list where the eqs are first divided into its wccs 
and then into its sccs.
This function is suggested to be implemented later. So, until all 
the other solvers are not ready(tested and working), this function will 
just take eqs and return [[eqs]].

3. get_coeff_matrix:-
Parameters: eqs, funcs
Returns: coefficient matrix A(t) and f(t)
This function takes in a first order linear ODE and returns matrix 
A(t) and f(t) from X' = A(t) * X + f(t).

4. nth_order_to_first_order:-
Parameters: eqs, order
Returns: first order ODE with new introduced dependent variables.

And all the first order linear solvers mentioned above.

Now, besides the main function, there are two separate functions depending 
on whether the system of ODEs is linear or not, namely _linear_ode_sol and 
_non_linear_ode_sol.

1. _first_order_linear_ode_sol:-
Parameters: match dict(obtained earlier and maybe modified in 
ode_sol)
Returns: Dict with keys as func and value as its solution that 
solves the ODE.
Working: First, extracts A(t) and f(t) using get_coeff_matrix, then 
using match dict, identify which solver is required and solve the ODE if it 
is possible to do so. For example: Case where A(t) is not symmetric isn't 
solved.

2. _non_linear_ode_sol has similar Parameters and Returns but the function 
operates differently that's why it is essential to use a different 
function. But I don't have a clear understanding
   of how to design _non_linear_ode_sol yet but here is what I have came up 
with: First match the condition where it is possible seperate out the 
independent variable to get a relationship
   between the dependent variables and then finally, just use the special 
solver to solve the ODE.

Now, coming to the main function ode_sol(for now, I haven't considered 
initial values):-
  Parameters: eqs, funcs, t
  Returns: Solution in a dict form where func is the key and value is the 
solution for that corresponding func.

  Working: 
  The steps of its working-
  1. Preprocess the equations.
  2. Get the match dict using match_ode function.
  3. Convert nth order equations to first order equations using 
nth_order_to_first_order while storing the funcs seperately so that we can 
later filter out the dependent variables that were introduced in this step.
  4. Get the 3D list of equations using component_division function.
  5. Iterate through the wccs and solve and store solutions seperately 
but for sccs, first solve the first set of equations in a scc, then 
substitute the solutions found in the first set of the current scc to the 
second 
 set of current scc. Keep doing this until the all the sets for a 
particular scc is solved.
  6. For solving a component, choose either _linear_ode_sol or 
_non_linear_ode_sol depending upon the set of equations to be solved.
  7. Return a dict by taking out values from the solution obtained 
using all the dependent variables in funcs as there may be more variables 
introduced when we made the system into first order.

For now, this is what I have came up with. Obviously the order in which we 
will proceed is, build the basic layout of the main function and 
component_division will just increase the number of dimensions to 3 
rudimentarily as we
will have to first ensure that the general solvers work well since working 
on both of them simultaneously will make it tough to pinpoint the errors. 
Along with that, non-linear solvers can be implemented later, we can just 
raise a 
NotImplementedError for now till we have completed both the general linear 
solvers and the component_division and then add the special case solvers.

On Tuesday, March 17, 2020 at 3:02:29 AM UTC+5:30, Oscar wrote:
>
> There are possibilities to go from nonlinear to linear e.g.: 
>
> In [6]: x, y = symbols('x, y', cls=Function) 
>
> In [7]: eqs = [x(t).diff(t)**2 - y(t)**2, y(t).diff(t)**2 - x(t)**2] 
>
> In [8]: eqs 
> Out[8]: 
> ⎡2  2⎤ 
> ⎢   2  ⎛d   ⎞  2  ⎛d   ⎞ ⎥ 
> ⎢- y (t) + ⎜──(

Re: [sympy] GSoC 2020: Introduction

[Aaron Meurer]

If you are not aware, you should follow the group theory channel on
gitter https://gitter.im/sympy/GroupTheory

Aaron Meurer

On Tue, Mar 17, 2020 at 11:32 AM Sumit Bisht  wrote:
>
> Greetings everyone,
>
> I am a third-year student at Birla Institute of Technology and Science, 
> Pilani pursuing a dual major in M.Sc Mathematics and B.E. Computer Science. I 
> have done the course on Abstract Algebra and have thoroughly studied it from 
> Gallian's Contemporary Abstract Algebra. I have tried implementing a few 
> computational algebraic algorithms from the Handbook of Computational Group 
> Theory and found out about SymPy while working on them. I have also used the 
> GAP library while working on the same.
>
> I have been using python for the last 1.5 years implementing 
> graph-theoretical algorithms. I have been working on a python-based program 
> which helps in obtaining a rectangular dual from an input graph. I would like 
> to contribute in Computational Group Theory in Sympy. I aim to implement the 
> algorithms for quotient groups, automorphism groups and subgroup intersection 
> inspired by their implementation in the GAP library. Further, I would also 
> like to extend Divyanshu's work in polycyclic groups and implement those 
> functionalities as discussed in Handbook of Computational Group Theory.
>
> I look forward to contributing to this wonderful community this GSoC and 
> extend the group theory functionality of the combinatorics module.
>
> Thank you!
>
> --
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> "sympy" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to sympy+unsubscr...@googlegroups.com.
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Re: [sympy] GSoC 2020 introduction

[Aaron Meurer]

The best place to start is to look at this project from last year.
https://github.com/sympy/sympy/wiki/GSoC-2019-Proposal-Shubham-Kumar-Jha-:-Improving-Assumptions
and pick up where it left off (see
https://github.com/sympy/sympy/wiki/GSoC-2019-Report-Shubham-Kumar-Jha:-Improving-Assumptions
and https://github.com/sympy/sympy/pulls/ShubhamKJha).

I would focus on improving the sorts of things that the new
assumptions (ask() and so on) can work with.

Aaron Meurer

On Tue, Mar 17, 2020 at 11:32 AM David Santistevan
 wrote:
>
> Greetings everyone, my name is David Santistevan. I'm a second year Computer 
> Science student about to enter third year of college. I've worked with Python 
> for the last 3 years with some experience beyond regular class projects, such 
> as some hackathon participations and a collaboration project between my 
> college and me as a result for a 1st place in one of the before mentioned 
> hackathons.
>
> About my programming experience, I've tried to optimize the code I write with 
> memory and execution time, as well as trying to keep it clean. I've shown a 
> significant evolution with my code that progressed as I've learnt new topics 
> such as Data Structures or Algorithms for example, which you can verify in my 
> Github profile. As well as Python, I have experience with Java, and I've 
> theoretically studied C family languages, but haven't done a separate project 
> on them.
>
> Other than programming, I've always enjoyed exploring math topics. Right now 
> I'm familiar with:
>
> Linear Algebra
> Boolean Algebra
> Univariable and multivariable calculus
> Ordinary Differential Equations
> Numerical Analysis
> Combinatorics
> Mathematical Logic
>
> I would like to work in the Assumptions project, due to the math involved as 
> well with the coding challenges, which motivate me help the community while 
> having personal growth.
>
> I apologize if I made a grammatical mistake, English is my second language 
> and my native language is Spanish. I wish I could have some feedback about 
> where to start, as well as some recommendations.
>
> --
> You received this message because you are subscribed to the Google Groups 
> "sympy" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to sympy+unsubscr...@googlegroups.com.
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> https://groups.google.com/d/msgid/sympy/29af2d4b-4daa-4adf-b454-8791c7fe8721%40googlegroups.com.

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[sympy] GSoC 2020 introduction

[David Santistevan]

Greetings everyone, my name is David Santistevan. I'm a second year 
Computer Science student about to enter third year of college. I've worked 
with Python for the last 3 years with some experience beyond regular class 
projects, such as some hackathon participations and a collaboration project 
between my college and me as a result for a 1st place in one of the before 
mentioned hackathons.

About my programming experience, I've tried to optimize the code I write 
with memory and execution time, as well as trying to keep it clean. I've 
shown a significant evolution with my code that progressed as I've learnt 
new topics such as Data Structures or Algorithms for example, which you can 
verify in my Github  profile. As well as 
Python, I have experience with Java, and I've theoretically studied C 
family languages, but haven't done a separate project on them.

Other than programming, I've always enjoyed exploring math topics. Right 
now I'm familiar with:

   - Linear Algebra
   - Boolean Algebra
   - Univariable and multivariable calculus
   - Ordinary Differential Equations
   - Numerical Analysis
   - Combinatorics
   - Mathematical Logic

I would like to work in the Assumptions project, due to the math involved 
as well with the coding challenges, which motivate me help the community 
while having personal growth.

I apologize if I made a grammatical mistake, English is my second language 
and my native language is Spanish. I wish I could have some feedback about 
where to start, as well as some recommendations.

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[sympy] GSoC 2020: Introduction

[Sumit Bisht]

Greetings everyone,

I am a third-year student at Birla Institute of Technology and Science, 
Pilani pursuing a dual major in M.Sc Mathematics and B.E. Computer Science. 
I have done the course on Abstract Algebra and have thoroughly studied it 
from Gallian's Contemporary Abstract Algebra. I have tried implementing a 
few computational algebraic algorithms from the Handbook of Computational 
Group Theory and found out about SymPy while working on them. I have also 
used the GAP library while working on the same.

I have been using python for the last 1.5 years implementing 
graph-theoretical algorithms. I have been working on a python-based program 
which helps in obtaining a rectangular dual from an input graph. I would 
like to contribute in Computational Group Theory in Sympy. I aim to 
implement the algorithms for quotient groups, automorphism groups and 
subgroup intersection inspired by their implementation in the GAP library. 
Further, I would also like to extend Divyanshu's work in polycyclic groups 
and implement those functionalities as discussed in Handbook of 
Computational Group Theory.

I look forward to contributing to this wonderful community this GSoC and 
extend the group theory functionality of the combinatorics module.

Thank you!

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[sympy] Re: GSOC 2020 Introduction

[Psycho-Pirate]

After observing what has been already done, i would like to develop 2d 
beams more and then start working on 3d beam class. If time permits, i 
would also like to develop the truss class as well.

Here's my to do list:

   - Adding more functions to 2D beam class for various properties
   - Developing 3D beam class
   - Enhancing the plotting of 2D and 3D beams and introducing new plots
   - 
   
   Making a class for truss analysis and implemening method of joints and 
   sections
   - Improving documentation and adding more examples

I would also like to work on the column class(once it gets merged).
I would love to discuss these ideas in detail with mentors.
On Sunday, March 15, 2020 at 9:14:32 AM UTC+5:30, Psycho-Pirate wrote:
>
> Hello Sympy Developers,
> My name is Prakhar Saxena. I am a second year undergraduate pursuing civil 
> engineering at Indian Institute of Technology, Varanasi.
> I have a decent experience of coding in python and have been contributing 
> to sympy for quite a while now. While going through the ideas page, I found 
> "Continuum 
> Mechanics: Create a Rich 2D Beam Solving System" intriguing. I have studied 
> structural mechanics in college and would really love to discuss ideas with 
> Jason Moore and other potential mentors.
>

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[sympy] i want to contribute on classical physics module

[ritwik chakraborty]

there will be some classes which will help to solve classical physics 
problem with mathematical solutions and graphical representation of 
everything.
let me know how to start with?
how to contribute?
is any improvement needed then please suggest.

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[sympy] Re: GSOC Introduction

[Shubham thorat]

I have created the first draft of my proposal for "Optimising 
floating-point expressions", 
https://docs.google.com/document/d/12eBRsCbZkBfh4pj2MAaurdMWx6nd1MTYxXTmlRKriJ8/edit?usp=sharing

Mentors, please suggest changes.

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