Thanks Jason, I have made some changes. Can you please review those? I have
also added some comments along with yours.

I didn't get you in this comment. Can you please elaborate it?
"*Comment from Jason: You will need to make sure everything is backwards
compatible. See the wiki for our policy.*"




Regards
Sampad Kumar Saha
Mathematics and Computing
I.I.T. Kharagpur

On Tue, Mar 22, 2016 at 8:53 PM, Jason Moore <[email protected]> wrote:

> The example you show doesn't seem to reflect what we may actually see when
> using this for beams. I'd suggest picking a simple beam problem and showing
> what all of your code will look like. You did that pretty well for the
> later examples, but this one with the random polynomials wasn't that clear.
>
>
> Jason
> moorepants.info
> +01 530-601-9791
>
> On Tue, Mar 22, 2016 at 7:43 AM, SAMPAD SAHA <[email protected]>
> wrote:
>
>> Thank You Jason. I will put it.
>>
>> I have a doubt about this comment in my proposal :
>>
>> *"Comment from Jason: It would be more informative to show what a beam
>> equation would look like in Piecewise form. This is a little abstract."  *
>>
>> Can you explain it a little more?
>>
>> I have also added some comment next to yours, I am still working on some
>> of your comments.
>>
>> Regards
>> Sampad Kumar Saha
>> Mathematics and Computing
>> I.I.T. Kharagpur
>>
>> On Tue, Mar 22, 2016 at 8:08 PM, Jason Moore <[email protected]>
>> wrote:
>>
>>> Sounds good, just put it in your proposal.
>>>
>>>
>>> Jason
>>> moorepants.info
>>> +01 530-601-9791
>>>
>>> On Tue, Mar 22, 2016 at 7:32 AM, SAMPAD SAHA <[email protected]>
>>> wrote:
>>>
>>>> I will start coding along with community bonding. I will spend 3-4
>>>> hours extra in the last week of the community bonding period in order to
>>>> achieve the proposed target in my proposal. I will have no problem managing
>>>> with those extra hours since I will be having Summer break at that time and
>>>> along with that I have no other commitments. And I will also have fun
>>>> working those extra hours.
>>>>
>>>>
>>>>
>>>>
>>>> Regards
>>>> Sampad Kumar Saha
>>>> Mathematics and Computing
>>>> I.I.T. Kharagpur
>>>>
>>>> On Tue, Mar 22, 2016 at 4:13 AM, Jason Moore <[email protected]>
>>>> wrote:
>>>>
>>>>> No need to cancel your vacation. Just give a plan for how you will
>>>>> make up the days.
>>>>>
>>>>>
>>>>> Jason
>>>>> moorepants.info
>>>>> +01 530-601-9791
>>>>>
>>>>> On Mon, Mar 21, 2016 at 2:52 PM, SAMPAD SAHA <[email protected]>
>>>>> wrote:
>>>>>
>>>>>> Thank You Jason for the suggestions in my proposal. I will work on
>>>>>> those and let you know as soon as possible.
>>>>>>
>>>>>> I have mentioned in my proposal about the days of the vacation and
>>>>>> how can I compensate the work. If this vacation raises any problem, I can
>>>>>> cancel it . That will not be a problem for me. I don't want to let 
>>>>>> anything
>>>>>> ruin the progess of the project as this Summer of Code will become an
>>>>>> integral part of all my learning throughout the summer.
>>>>>>
>>>>>> ----------------
>>>>>> Regards
>>>>>> Sampad
>>>>>>
>>>>>>
>>>>>> Regards
>>>>>> Sampad Kumar Saha
>>>>>> Mathematics and Computing
>>>>>> I.I.T. Kharagpur
>>>>>>
>>>>>> On Tue, Mar 22, 2016 at 2:33 AM, Jason Moore <[email protected]>
>>>>>> wrote:
>>>>>>
>>>>>>> I've put some comments in your proposal.
>>>>>>>
>>>>>>>
>>>>>>> Jason
>>>>>>> moorepants.info
>>>>>>> +01 530-601-9791
>>>>>>>
>>>>>>> On Sat, Mar 19, 2016 at 10:58 AM, SAMPAD SAHA <[email protected]
>>>>>>> > wrote:
>>>>>>>
>>>>>>>> Jason,
>>>>>>>>
>>>>>>>> Actually I have misunderstood earlier.
>>>>>>>>
>>>>>>>> I have updated my proposal here
>>>>>>>> <https://github.com/sympy/sympy/wiki/GSoC-2016-Application-Sampad-Kumar-Saha-:-Singularity-Functions>
>>>>>>>>  .
>>>>>>>> Can you please review it and suggest me to improve it.
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>> Regards
>>>>>>>> Sampad Kumar Saha
>>>>>>>> Mathematics and Computing
>>>>>>>> I.I.T. Kharagpur
>>>>>>>>
>>>>>>>> On Sat, Mar 19, 2016 at 9:14 PM, Jason Moore <[email protected]>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>> I don't think we should do "a hack". If we follow the patterns in
>>>>>>>>> the integration code, we should leave the constants of integration 
>>>>>>>>> off. But
>>>>>>>>> in the Beam classes you can have them manage the constants of 
>>>>>>>>> integration.
>>>>>>>>> What you show above looks fine.
>>>>>>>>>
>>>>>>>>> I didn't mean to use dsolve in any way. I just meant to have a
>>>>>>>>> look at that code because they include constants of integration when 
>>>>>>>>> you
>>>>>>>>> solve the ode. You can also set the boundary conditions in the 
>>>>>>>>> constructor.
>>>>>>>>> It can give you ideas of how to design your api.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Jason
>>>>>>>>> moorepants.info
>>>>>>>>> +01 530-601-9791
>>>>>>>>>
>>>>>>>>> On Sat, Mar 19, 2016 at 8:27 AM, SAMPAD SAHA <
>>>>>>>>> [email protected]> wrote:
>>>>>>>>>
>>>>>>>>>> Jason,
>>>>>>>>>>
>>>>>>>>>> I went through the ode package. I felt that it would be difficult
>>>>>>>>>> to use boundary condition to solve for the constants of integration 
>>>>>>>>>> using
>>>>>>>>>> the exisiting *dsolve() *method. It seems that it is still under
>>>>>>>>>> development.
>>>>>>>>>>
>>>>>>>>>> So I thought of implementing that functionality explicitly for
>>>>>>>>>> solving beam problems.
>>>>>>>>>>
>>>>>>>>>> I would be taking Boundary conditions as input as:
>>>>>>>>>>
>>>>>>>>>> *bcs = Beam.BoundaryCondition( {f(0) : 5, f.diff(0) : 4 } )* and
>>>>>>>>>> so on.
>>>>>>>>>>
>>>>>>>>>> If nothing is provided then  *f(0) !=  0 , f.diff(0) = 0 *or
>>>>>>>>>> something like this would be assumed.
>>>>>>>>>>
>>>>>>>>>> Depending on this boundary condition I would add the required
>>>>>>>>>> constants by myself while finding the slope and deflection function 
>>>>>>>>>> and
>>>>>>>>>> output the value by solving for those constants.
>>>>>>>>>>
>>>>>>>>>> By this way, the hack would be easier. What do you suggests?
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Regards
>>>>>>>>>> Sampad Kumar Saha
>>>>>>>>>> Mathematics and Computing
>>>>>>>>>> I.I.T. Kharagpur
>>>>>>>>>>
>>>>>>>>>> On Sat, Mar 19, 2016 at 7:17 AM, SAMPAD SAHA <
>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>
>>>>>>>>>>> Yah, you are right . We should not have the name simplify() as a
>>>>>>>>>>> method since it have already created some issues in  #7716
>>>>>>>>>>> <https://github.com/sympy/sympy/issues/7716> and #8798
>>>>>>>>>>> <https://github.com/sympy/sympy/issues/8798>. So i will keep it
>>>>>>>>>>> as  *to_piecewise()*  . it would be fine then.
>>>>>>>>>>>
>>>>>>>>>>> As you suggested I will be look at ode package for this constant
>>>>>>>>>>> of integration thing.
>>>>>>>>>>>
>>>>>>>>>>> Thank You...
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> Regards
>>>>>>>>>>> Sampad Kumar Saha
>>>>>>>>>>> Mathematics and Computing
>>>>>>>>>>> I.I.T. Kharagpur
>>>>>>>>>>>
>>>>>>>>>>> On Sat, Mar 19, 2016 at 7:07 AM, Jason Moore <
>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Simplification means something very specific in SymPy, see the
>>>>>>>>>>>> simplify() function. I think you need to choose a different method 
>>>>>>>>>>>> name for
>>>>>>>>>>>> converting to piecewise continuous. Maybe: .to_piecewise()?
>>>>>>>>>>>>
>>>>>>>>>>>> You will need to implement some method for dealing with the
>>>>>>>>>>>> constants of integration and boundary conditions. Maybe you should 
>>>>>>>>>>>> have a
>>>>>>>>>>>> look at the ordinary differential equations package in SymPy to 
>>>>>>>>>>>> get some
>>>>>>>>>>>> ideas about that.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Jason
>>>>>>>>>>>> moorepants.info
>>>>>>>>>>>> +01 530-601-9791
>>>>>>>>>>>>
>>>>>>>>>>>> On Fri, Mar 18, 2016 at 4:04 PM, SAMPAD SAHA <
>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> Thank You Jason for the appreciation.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Yah, that *Simplify  * method would convert  into continous
>>>>>>>>>>>>> piecewise. Like this :-
>>>>>>>>>>>>>
>>>>>>>>>>>>> In    [ ] : F = singularityFunc(x, 0, 1) +  singularityFunc(x,
>>>>>>>>>>>>> 3, 2)
>>>>>>>>>>>>>
>>>>>>>>>>>>> In    [ ] : F
>>>>>>>>>>>>> Out [ ] :
>>>>>>>>>>>>>                     2
>>>>>>>>>>>>> <x> + <x - 3>
>>>>>>>>>>>>>
>>>>>>>>>>>>> In [ ] : F.simplify()
>>>>>>>>>>>>> Out [ ] :
>>>>>>>>>>>>>
>>>>>>>>>>>>> 0                   for x < 0
>>>>>>>>>>>>> x                   for 0 <= x < 3
>>>>>>>>>>>>> x + (x-3)^2    for x  >= 3
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> As you have suggested earlier, I have solved some examples by
>>>>>>>>>>>>> hand and then tried to implement a desired api. From that I came 
>>>>>>>>>>>>> to this
>>>>>>>>>>>>> conclusion that if we implement Addition, Substraction,
>>>>>>>>>>>>> Integration, Differentiation, Simplify on Singularity Functions 
>>>>>>>>>>>>> then we can
>>>>>>>>>>>>> successfully solve out the beam problems.
>>>>>>>>>>>>>
>>>>>>>>>>>>> But i got doubt while implementing the boundary constants. I
>>>>>>>>>>>>> mean to say that sympy dont gives constant of integration while 
>>>>>>>>>>>>> doing
>>>>>>>>>>>>> indefinite integration. We can take boundary conditions as input 
>>>>>>>>>>>>> from users
>>>>>>>>>>>>> that is not a problem, but we cant use it since there will be no 
>>>>>>>>>>>>> constant
>>>>>>>>>>>>> of integration.
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Regards
>>>>>>>>>>>>> Sampad Kumar Saha
>>>>>>>>>>>>> Mathematics and Computing
>>>>>>>>>>>>> I.I.T. Kharagpur
>>>>>>>>>>>>>
>>>>>>>>>>>>> On Sat, Mar 19, 2016 at 4:07 AM, Jason Moore <
>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> Sounds like a good start. How about a method to convert to
>>>>>>>>>>>>>> continuous piecewise?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Like I said earlier, you should pick some examples that you
>>>>>>>>>>>>>> want the software to be able to solve and then implement methods 
>>>>>>>>>>>>>> and
>>>>>>>>>>>>>> functionality based on those examples. It's hard to think of all 
>>>>>>>>>>>>>> the needed
>>>>>>>>>>>>>> functionality and API without motivating examples first.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Jason
>>>>>>>>>>>>>> moorepants.info
>>>>>>>>>>>>>> +01 530-601-9791
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 10:27 AM, SAMPAD SAHA <
>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Jason,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I have thought of implementing Addition, Substraction,
>>>>>>>>>>>>>>> Integration, Differentiation, Simplify on Singularity Functions.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> What are the other functionalities we should implement?
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Regards
>>>>>>>>>>>>>>> Sampad Kumar Saha
>>>>>>>>>>>>>>> Mathematics and Computing
>>>>>>>>>>>>>>> I.I.T. Kharagpur
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 8:16 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Yah you are correct. Differentiation of heaviside and
>>>>>>>>>>>>>>>> diracdelta also exists.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> It was my mistake. Thanks for rectifying me.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Regards
>>>>>>>>>>>>>>>> Sampad Kumar Saha
>>>>>>>>>>>>>>>> Mathematics and Computing
>>>>>>>>>>>>>>>> I.I.T. Kharagpur
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On Fri, Mar 18, 2016 at 8:02 PM, Tim Lahey <
>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> For differentiation you’re missing a case,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> if n = 0 or n = -1
>>>>>>>>>>>>>>>>>    return Singularity(x, a, n-1)
>>>>>>>>>>>>>>>>> else if n < -1
>>>>>>>>>>>>>>>>>    return error
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> In other words, you can still differentiate for the n = 0
>>>>>>>>>>>>>>>>> and n = -1 cases.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Tim.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> > On Mar 18, 2016, at 10:22 AM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > And what about the pseudocode of integration and
>>>>>>>>>>>>>>>>> differentiation i have posted earlier , is it alright?
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > Regards
>>>>>>>>>>>>>>>>> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> > Mathematics and Computing
>>>>>>>>>>>>>>>>> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:51 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> > Thanks Tim,
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > It is really a nice and effective solution.
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > Regards
>>>>>>>>>>>>>>>>> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> > Mathematics and Computing
>>>>>>>>>>>>>>>>> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > On Fri, Mar 18, 2016 at 7:46 PM, Tim Lahey <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> > Add the constants when you integrate in your beam class.
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> > On 2016-03-18, at 10:12 AM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >> Thanks TIm,
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Integration and Differentiation are really very
>>>>>>>>>>>>>>>>> straight forward that is why i am thinking to add diff and 
>>>>>>>>>>>>>>>>> integrate method
>>>>>>>>>>>>>>>>> to the Singularity function class itself.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> For integrate the pseuesocode will be :-
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> if(n<0)
>>>>>>>>>>>>>>>>> >>     return SingularityFunction(x , a, n+1)
>>>>>>>>>>>>>>>>> >> else
>>>>>>>>>>>>>>>>> >>     return (1/n+1 * SingularityFunction(x , a, n+1))
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Similarly for differentiation:
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> if (n>0)
>>>>>>>>>>>>>>>>> >>    return n * SingularityFunction(x , a, n - 1)
>>>>>>>>>>>>>>>>> >> else
>>>>>>>>>>>>>>>>> >>    Error message
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> My doubt regarding Boundary condition was actually was
>>>>>>>>>>>>>>>>> that since sympy don't provide constant of integration while 
>>>>>>>>>>>>>>>>> performing
>>>>>>>>>>>>>>>>> indefinite integration on any expression, how to use the 
>>>>>>>>>>>>>>>>> boundary
>>>>>>>>>>>>>>>>> conditions to find the exact values of constant of 
>>>>>>>>>>>>>>>>> integration?
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Regards
>>>>>>>>>>>>>>>>> >> Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> Mathematics and Computing
>>>>>>>>>>>>>>>>> >> I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> On Fri, Mar 18, 2016 at 6:09 PM, Tim Lahey <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> Hi,
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Do you know the integration and differentiation rules
>>>>>>>>>>>>>>>>> for singularity functions? They’re pretty straightforward.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> As for boundary conditions, the beam will have supports
>>>>>>>>>>>>>>>>> (or a free end) at each end of the beam and as part of the 
>>>>>>>>>>>>>>>>> beam creation
>>>>>>>>>>>>>>>>> each end type is specified. Each type corresponds to a 
>>>>>>>>>>>>>>>>> specific set of
>>>>>>>>>>>>>>>>> conditions on that end (either at x=0 or x=L). You substitute 
>>>>>>>>>>>>>>>>> those
>>>>>>>>>>>>>>>>> conditions in the appropriate equation and solve for the 
>>>>>>>>>>>>>>>>> integration
>>>>>>>>>>>>>>>>> constant as necessary. All of the conditions should be in any 
>>>>>>>>>>>>>>>>> decent
>>>>>>>>>>>>>>>>> mechanics of deformable solids text book.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> You’ll want to do sums of forces and moments as well to
>>>>>>>>>>>>>>>>> solve for reaction forces as well.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> The only trick is making sure you don’t double count
>>>>>>>>>>>>>>>>> things. If you have a step function due to a reaction force 
>>>>>>>>>>>>>>>>> at the start of
>>>>>>>>>>>>>>>>> the beam and assume it’s zero at x=0 (effectively the limit 
>>>>>>>>>>>>>>>>> at x=0^-) you
>>>>>>>>>>>>>>>>> can get a non-zero integration constant that can be double 
>>>>>>>>>>>>>>>>> counting that
>>>>>>>>>>>>>>>>> reaction since at x=0^+ that reaction force is non-zero. Note 
>>>>>>>>>>>>>>>>> that you can
>>>>>>>>>>>>>>>>> get a non-zero integration constant (even when including 
>>>>>>>>>>>>>>>>> reaction forces in
>>>>>>>>>>>>>>>>> the loading function) for shear and moment equations if you 
>>>>>>>>>>>>>>>>> have
>>>>>>>>>>>>>>>>> non-polynomial loads (e.g., sine and cosine). You’ll also 
>>>>>>>>>>>>>>>>> have to think
>>>>>>>>>>>>>>>>> about the other end as well. I leave it up to you to reason 
>>>>>>>>>>>>>>>>> that out. Make
>>>>>>>>>>>>>>>>> sure you completely document how you’ve implemented it for 
>>>>>>>>>>>>>>>>> the user (and
>>>>>>>>>>>>>>>>> why).
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Beam coordinate systems must start at the left end and
>>>>>>>>>>>>>>>>> increase to the right. The definition of the singularity 
>>>>>>>>>>>>>>>>> functions require
>>>>>>>>>>>>>>>>> this.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> I hope this helps.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Cheers,
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> Tim.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >> > On Mar 18, 2016, at 8:17 AM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I am also confused about implementing the boundary
>>>>>>>>>>>>>>>>> conditions for getting the deflection curve.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Any suggestions on how to implement it.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 5:36 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Yah, you are right multiplication of singularity
>>>>>>>>>>>>>>>>> functions are not needed for solving beam problems. 
>>>>>>>>>>>>>>>>> Mathematically, it is
>>>>>>>>>>>>>>>>> also not used that much. So lets leave this multiplication 
>>>>>>>>>>>>>>>>> and powers part.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I was thinking about the integrate and diff methods.
>>>>>>>>>>>>>>>>> I feel that we should define instance methods diff and  
>>>>>>>>>>>>>>>>> integrate  in the
>>>>>>>>>>>>>>>>> singularity function module which would internally use the 
>>>>>>>>>>>>>>>>> existing diff
>>>>>>>>>>>>>>>>> and integrate function for Differentiation and Integration 
>>>>>>>>>>>>>>>>> respectively.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I need your suggestions.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 3:14 AM, Jason Moore <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > I think you need to override the operators. I'm not
>>>>>>>>>>>>>>>>> sure if multiplying singularity functions is needed (at least 
>>>>>>>>>>>>>>>>> for beam
>>>>>>>>>>>>>>>>> problems), even if it is mathematically correct, you don't 
>>>>>>>>>>>>>>>>> have to
>>>>>>>>>>>>>>>>> implement it. If it is easy to implement then, sure, do so.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Jason
>>>>>>>>>>>>>>>>> >> > moorepants.info
>>>>>>>>>>>>>>>>> >> > +01 530-601-9791
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Thu, Mar 17, 2016 at 1:34 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Jason,
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > For implementing Additon , Multiplication Do we need
>>>>>>>>>>>>>>>>> to over ride __mul__ , __add__  these methods inside the class
>>>>>>>>>>>>>>>>> SingularityFunction or we can just use simplify for getting 
>>>>>>>>>>>>>>>>> the results.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I am really confused.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Fri, Mar 18, 2016 at 1:59 AM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I was thinking about multiplication of two
>>>>>>>>>>>>>>>>> singularity functions. It is possible and it is 
>>>>>>>>>>>>>>>>> mathematically significant.
>>>>>>>>>>>>>>>>> We can implement this too in Sympy. Similarly with powers.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I need your suggestions.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 9:41 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Yah , You are right . A software having good
>>>>>>>>>>>>>>>>> documentations about all the functionality is preffered more 
>>>>>>>>>>>>>>>>> over the
>>>>>>>>>>>>>>>>> others by the users. I will be spending a good amount of time 
>>>>>>>>>>>>>>>>> in preparing
>>>>>>>>>>>>>>>>> the documentation citing plenty of examples and tutorials.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Here is link to my proposal. I have almost added all
>>>>>>>>>>>>>>>>> the things which we have disscussed. I still need to add the 
>>>>>>>>>>>>>>>>> example and
>>>>>>>>>>>>>>>>> many more "TODO"s are left. I am working on those.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Suggestions are welcomed.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 6:18 AM, Jason Moore <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Looks good. I think you should have plenty of
>>>>>>>>>>>>>>>>> examples in the docs. People tend to use software more if the 
>>>>>>>>>>>>>>>>> docs are top
>>>>>>>>>>>>>>>>> notch. So plenty of examples and tutorials will really help.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Jason
>>>>>>>>>>>>>>>>> >> > moorepants.info
>>>>>>>>>>>>>>>>> >> > +01 530-601-9791
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 5:25 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > You are right. delta_function.py needs to be
>>>>>>>>>>>>>>>>> improved. I will to be using only DiracDelta and Heaviside 
>>>>>>>>>>>>>>>>> for generating
>>>>>>>>>>>>>>>>> almost all the Singularity Functions.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I was also thinking to complete this project in four
>>>>>>>>>>>>>>>>> phases:
>>>>>>>>>>>>>>>>> >> >       • Improving existiing Functions.
>>>>>>>>>>>>>>>>> >> >       • Creating Singularity Functions module
>>>>>>>>>>>>>>>>> >> >       • Creating beam Module
>>>>>>>>>>>>>>>>> >> >       • Documentation
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:44 AM, Jason Moore <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > https://www.python.org/dev/peps/pep-0008/
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > I think you will need a pure singularity function
>>>>>>>>>>>>>>>>> module and then you will need a beam module that utlizes the 
>>>>>>>>>>>>>>>>> singularity
>>>>>>>>>>>>>>>>> function module. You will also likely need to improve the 
>>>>>>>>>>>>>>>>> discontinuous
>>>>>>>>>>>>>>>>> functions that are already in sympy. There are at least three 
>>>>>>>>>>>>>>>>> layers to
>>>>>>>>>>>>>>>>> this in my eyes.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Jason
>>>>>>>>>>>>>>>>> >> > moorepants.info
>>>>>>>>>>>>>>>>> >> > +01 530-601-9791
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 5:07 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Jason
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Pardon please. I couldn't get you by "You will need
>>>>>>>>>>>>>>>>> to follow PEP8 for the method and class names".
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > and yah, i also felt that it would be better if i use
>>>>>>>>>>>>>>>>> the input and output values of the example problem done by 
>>>>>>>>>>>>>>>>> hand.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > So , what do you suggest, Would it be better if we
>>>>>>>>>>>>>>>>> create a different module ,other than the singularity 
>>>>>>>>>>>>>>>>> function module, for
>>>>>>>>>>>>>>>>> solving beam problems?  That module would import the 
>>>>>>>>>>>>>>>>> singularity function
>>>>>>>>>>>>>>>>> module for using them.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:22 AM, Jason Moore <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > I think it is a good start. You will need to follow
>>>>>>>>>>>>>>>>> PEP8 for the method and class names. But I just want to see 
>>>>>>>>>>>>>>>>> desired
>>>>>>>>>>>>>>>>> functionality. The more you can think up, the better. I would 
>>>>>>>>>>>>>>>>> suggest doing
>>>>>>>>>>>>>>>>> a beam problem by hand and then translating that to a desired 
>>>>>>>>>>>>>>>>> API. You can
>>>>>>>>>>>>>>>>> mock up what you think the inputs and outputs should be for 
>>>>>>>>>>>>>>>>> that example
>>>>>>>>>>>>>>>>> problem.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Jason
>>>>>>>>>>>>>>>>> >> > moorepants.info
>>>>>>>>>>>>>>>>> >> > +01 530-601-9791
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 4:46 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Ok Jason,
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > And what about the API I have posted just before the
>>>>>>>>>>>>>>>>> earlier post?
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Any suggestions
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 5:10 AM, Jason Moore <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > The file locations and method class names are just
>>>>>>>>>>>>>>>>> fine details that can be worked out later. They are generally 
>>>>>>>>>>>>>>>>> not important
>>>>>>>>>>>>>>>>> for your proposal. Just focus on describing what the future 
>>>>>>>>>>>>>>>>> modules should
>>>>>>>>>>>>>>>>> do.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Jason
>>>>>>>>>>>>>>>>> >> > moorepants.info
>>>>>>>>>>>>>>>>> >> > +01 530-601-9791
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Tue, Mar 15, 2016 at 4:36 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Hi Jason,
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > As I am thinking to create a another module for
>>>>>>>>>>>>>>>>> solving especially beam problems (suppose beambending.py) , 
>>>>>>>>>>>>>>>>> what will be
>>>>>>>>>>>>>>>>> its file location?
>>>>>>>>>>>>>>>>> >> > Similarly for Singularity Functions (suppose
>>>>>>>>>>>>>>>>> singularity_function.py), What will be its location?
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > And what about the names of methods and classes, Can
>>>>>>>>>>>>>>>>> I give any name or we will be discussing it at the time of 
>>>>>>>>>>>>>>>>> developing them?
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > ---------------------
>>>>>>>>>>>>>>>>> >> > Regards,
>>>>>>>>>>>>>>>>> >> > Sampad
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 3:56 AM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > Thank You Tim and Jason for your suggestions and
>>>>>>>>>>>>>>>>> clearing my doubts.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > We can also have an another module for solving beam
>>>>>>>>>>>>>>>>> problems. As Jason Have suggested earlier.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Some of its classes would be Beam, DistributedLoad,
>>>>>>>>>>>>>>>>> PointLoad, Moment.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > We can have the API as:-
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > from sympy import
>>>>>>>>>>>>>>>>> SingularityFunction,Beam,DistributedLoad,PointLoad,Moment
>>>>>>>>>>>>>>>>> >> > b = Beam(length = 1, E = 1.87, I = 12)
>>>>>>>>>>>>>>>>> >> > Load1 = DistrubutedLoad(start=l/2, end=l, value= 50)
>>>>>>>>>>>>>>>>> >> > Load2 = PointLoad(location=l/3, value=60)
>>>>>>>>>>>>>>>>> >> > Load3 = Moment(locaton = 1, value = 40, anticlockwise
>>>>>>>>>>>>>>>>> = True)
>>>>>>>>>>>>>>>>> >> > b.apply(Load1,Load2,Load3)
>>>>>>>>>>>>>>>>> >> > b.loadDistribution    # Outputs the loading function
>>>>>>>>>>>>>>>>> in the form of singularity function
>>>>>>>>>>>>>>>>> >> > b.shearForce          # Outputs the Shear Force
>>>>>>>>>>>>>>>>> Function
>>>>>>>>>>>>>>>>> >> > b.bendingMoment       # Outputs the bending Moment
>>>>>>>>>>>>>>>>> Function
>>>>>>>>>>>>>>>>> >> > b.slope               # Outputs the Slope Function
>>>>>>>>>>>>>>>>> >> > b.deflection          # Outputs the deflection
>>>>>>>>>>>>>>>>> Function
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > b.plotLoadDistribution   # Outputs the plot of load
>>>>>>>>>>>>>>>>> Distribution Curve
>>>>>>>>>>>>>>>>> >> > b.plotBendingMoment      # Outputs the plot of
>>>>>>>>>>>>>>>>> Bending Moment Curve
>>>>>>>>>>>>>>>>> >> > b.plotDeflection         # Outputs the plot of
>>>>>>>>>>>>>>>>> Deflection Curve
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Regards
>>>>>>>>>>>>>>>>> >> > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > On Wed, Mar 16, 2016 at 2:45 AM, Tim Lahey <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > I agree. One should start directly from the loading
>>>>>>>>>>>>>>>>> function q(x). The general steps are:
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > 1. Start with the loading function q(x)
>>>>>>>>>>>>>>>>> >> > 2. Integrate to get the shear function V(x).
>>>>>>>>>>>>>>>>> >> > 3. Integrate again to get the bending moment function
>>>>>>>>>>>>>>>>> M(x).
>>>>>>>>>>>>>>>>> >> > 4. Integrate to get the slope function E*I*v’(x).
>>>>>>>>>>>>>>>>> >> > 5. Integrate to get the displacement function
>>>>>>>>>>>>>>>>> E*I*v(x).
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Note that the singularity functions can be multiplied
>>>>>>>>>>>>>>>>> by arbitrary functions of x as well. This allows for varied 
>>>>>>>>>>>>>>>>> loads and cases
>>>>>>>>>>>>>>>>> where E and I vary too. To be strictly correct one should 
>>>>>>>>>>>>>>>>> include the
>>>>>>>>>>>>>>>>> integration constants as well and then solve for the reaction 
>>>>>>>>>>>>>>>>> forces and
>>>>>>>>>>>>>>>>> the constants.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > You’ll need to carefully consider how you handle
>>>>>>>>>>>>>>>>> evaluating at transition points, especially the beam 
>>>>>>>>>>>>>>>>> boundaries.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Cheers,
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > Tim.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > > On Mar 15, 2016, at 4:53 PM, Jason Moore <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > I think you'd want the user to input the loads on
>>>>>>>>>>>>>>>>> the beam as singularity functions or some higher level 
>>>>>>>>>>>>>>>>> abstraction. If you
>>>>>>>>>>>>>>>>> require them to manually compute the bending moment then you 
>>>>>>>>>>>>>>>>> are defeating
>>>>>>>>>>>>>>>>> the purpose of having a CAS do it for you.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Jason
>>>>>>>>>>>>>>>>> >> > > moorepants.info
>>>>>>>>>>>>>>>>> >> > > +01 530-601-9791
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > On Sun, Mar 13, 2016 at 2:25 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > > Hi Jason,
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > I have a confusion regarding the user inputs for
>>>>>>>>>>>>>>>>> the beam problems.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > I think that we should take only the Bending Moment
>>>>>>>>>>>>>>>>> Function (in the form of singularity functions) and the 
>>>>>>>>>>>>>>>>> boundary conditions
>>>>>>>>>>>>>>>>> as inputs.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > I mean to say that generally in a given beam
>>>>>>>>>>>>>>>>> bending problem, a diagram of a beam and distributed loads 
>>>>>>>>>>>>>>>>> are provided. So
>>>>>>>>>>>>>>>>> it is not possible to get these data as an user input. Rather 
>>>>>>>>>>>>>>>>> we can expect
>>>>>>>>>>>>>>>>> that the user would formulate the bending moment function, in 
>>>>>>>>>>>>>>>>> the form of
>>>>>>>>>>>>>>>>> Singularity function, and then provide that function as an 
>>>>>>>>>>>>>>>>> input for
>>>>>>>>>>>>>>>>> getting the elastic curve equation.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Note:- Values of  E , I , Boundary Conditions are
>>>>>>>>>>>>>>>>> also expected as an input.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > I need your suggestions.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > -----------------
>>>>>>>>>>>>>>>>> >> > > Regards,
>>>>>>>>>>>>>>>>> >> > > Sampad
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Regards
>>>>>>>>>>>>>>>>> >> > > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > On Sat, Mar 12, 2016 at 11:50 AM, Aaron Meurer <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > > It should give (-1)**n*f^(n)(0) (that is,
>>>>>>>>>>>>>>>>> (-1)**n*diff(f(x), x, n).subs(x, 0)), if I remember the 
>>>>>>>>>>>>>>>>> formula correctly.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Aaron Meurer
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > On Fri, Mar 11, 2016 at 9:00 AM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > > Hi Aaron,
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > I have a doubt .
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Do we want:
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >  integrate(f(x)*DiracDelta(x, n), (x, -oo, oo))
>>>>>>>>>>>>>>>>> would output as
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > <image.png>
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Regards
>>>>>>>>>>>>>>>>> >> > > Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > > Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > > I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > On Wed, Mar 9, 2016 at 3:11 AM, Aaron Meurer <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > > DiracDelta(x, k) gives the k-th derivative of
>>>>>>>>>>>>>>>>> DiracDelta(x) (or you
>>>>>>>>>>>>>>>>> >> > > can write DiracDelta(x).diff(x, k)).
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > It does look like the delta integrate routines
>>>>>>>>>>>>>>>>> could be improved here, though:
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > In [2]: integrate(f(x)*DiracDelta(x), (x, -oo, oo))
>>>>>>>>>>>>>>>>> >> > > Out[2]: f(0)
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > In [3]: integrate(f(x)*DiracDelta(x, 1), (x, -oo,
>>>>>>>>>>>>>>>>> oo))
>>>>>>>>>>>>>>>>> >> > > Out[3]:
>>>>>>>>>>>>>>>>> >> > > ∞
>>>>>>>>>>>>>>>>> >> > > ⌠
>>>>>>>>>>>>>>>>> >> > > ⎮  f(x)⋅DiracDelta(x, 1) dx
>>>>>>>>>>>>>>>>> >> > > ⌡
>>>>>>>>>>>>>>>>> >> > > -∞
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Since the integration rules for derivatives of
>>>>>>>>>>>>>>>>> delta functions are
>>>>>>>>>>>>>>>>> >> > > simple extensions of the rules for the delta
>>>>>>>>>>>>>>>>> function itself, this is
>>>>>>>>>>>>>>>>> >> > > probably not difficult to fix.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > Aaron Meurer
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > On Mon, Feb 29, 2016 at 3:39 AM, Tim Lahey <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > > > Hi,
>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>> >> > > > Singularity functions are actually extremely easy
>>>>>>>>>>>>>>>>> to implement given that we have a Dirac delta and Heaviside 
>>>>>>>>>>>>>>>>> functions.
>>>>>>>>>>>>>>>>> Assuming that the Dirac delta and Heaviside functions 
>>>>>>>>>>>>>>>>> properly handle
>>>>>>>>>>>>>>>>> calculus, it’s trivial to wrap them for use as singularity 
>>>>>>>>>>>>>>>>> functions. The
>>>>>>>>>>>>>>>>> only thing that will need to be added is the derivative of 
>>>>>>>>>>>>>>>>> the Dirac delta
>>>>>>>>>>>>>>>>> (assuming it’s not already there). I implemented singularity 
>>>>>>>>>>>>>>>>> functions in
>>>>>>>>>>>>>>>>> Maple in less than an afternoon.
>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>> >> > > > I was a TA for a Mechanics of Deformable Solids
>>>>>>>>>>>>>>>>> course about 11 or 12 times and wrote it to help the students 
>>>>>>>>>>>>>>>>> (as we have a
>>>>>>>>>>>>>>>>> site license for Maple). I also wrote a set of lecture notes 
>>>>>>>>>>>>>>>>> on the topic.
>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>> >> > > > Cheers,
>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>> >> > > > Tim.
>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>> >> > > >> On Feb 26, 2016, at 4:29 PM, SAMPAD SAHA <
>>>>>>>>>>>>>>>>> [email protected]> wrote:
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> Hi Jason,
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> Thank you for the explanation. It really helped
>>>>>>>>>>>>>>>>> me.
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> So, basically we want to start it, firstly, by
>>>>>>>>>>>>>>>>> creating a module which would deal with the mathematical 
>>>>>>>>>>>>>>>>> operations
>>>>>>>>>>>>>>>>> performed on Singularity Functions. After this whole module 
>>>>>>>>>>>>>>>>> is prepared, we
>>>>>>>>>>>>>>>>> would focus on how to use this module for solving beam 
>>>>>>>>>>>>>>>>> problems. Am I
>>>>>>>>>>>>>>>>> correct?
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> Can you please explain me in brief that what are
>>>>>>>>>>>>>>>>> the mathematical operations we wanted to implement on that 
>>>>>>>>>>>>>>>>> module?
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> On Friday, February 26, 2016 at 4:54:59 PM
>>>>>>>>>>>>>>>>> UTC+5:30, SAMPAD SAHA wrote:
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> Hi,
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> I am Sampad Kumar Saha , an Undergraduate
>>>>>>>>>>>>>>>>> Mathematics and Computing Student at I.I.T. Kharagpur.
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> I have gone through the idea page and I am
>>>>>>>>>>>>>>>>> interested in working on the project named Singularity 
>>>>>>>>>>>>>>>>> Function.
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> By going through the Idea, I understood that we
>>>>>>>>>>>>>>>>> want to add a package to Sympy which can be used for for 
>>>>>>>>>>>>>>>>> solving beam
>>>>>>>>>>>>>>>>> bending stress and deflection problems using singularity 
>>>>>>>>>>>>>>>>> function. Am I
>>>>>>>>>>>>>>>>> correct?
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> We can by this way:-
>>>>>>>>>>>>>>>>> >> > > >> While solving we will be having the moment
>>>>>>>>>>>>>>>>> function as an input which we can arrange in the form of 
>>>>>>>>>>>>>>>>> singularity
>>>>>>>>>>>>>>>>> functions and then integrate it twice to get the deflection 
>>>>>>>>>>>>>>>>> curve and we
>>>>>>>>>>>>>>>>> can give the plot or the equation obtained of deflection 
>>>>>>>>>>>>>>>>> curve as an output.
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> I have gone through some documents available on
>>>>>>>>>>>>>>>>> internet which have brief studies on solving beam bending 
>>>>>>>>>>>>>>>>> stress and
>>>>>>>>>>>>>>>>> deflection problems using singularity functions.
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> References:-
>>>>>>>>>>>>>>>>> >> > > >>       • Beam Deflection By Discontinuity
>>>>>>>>>>>>>>>>> Functions.
>>>>>>>>>>>>>>>>> >> > > >>       • Beam Equation Using Singularity
>>>>>>>>>>>>>>>>> Functions.
>>>>>>>>>>>>>>>>> >> > > >>       • Enhanced Student Learning in Engineering
>>>>>>>>>>>>>>>>> Courses with CAS Technology.
>>>>>>>>>>>>>>>>> >> > > >> Since there is just a brief idea given in the
>>>>>>>>>>>>>>>>> idea page, I have a doubt that what are the things other than 
>>>>>>>>>>>>>>>>> solving beam
>>>>>>>>>>>>>>>>> bending stress and deflection problems to be implemented in 
>>>>>>>>>>>>>>>>> the project?
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> Any type of suggestions are welcome.
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> ==========================================================================================================================================
>>>>>>>>>>>>>>>>> >> > > >> Regards
>>>>>>>>>>>>>>>>> >> > > >> Sampad Kumar Saha
>>>>>>>>>>>>>>>>> >> > > >> Mathematics and Computing
>>>>>>>>>>>>>>>>> >> > > >> I.I.T. Kharagpur
>>>>>>>>>>>>>>>>> >> > > >>
>>>>>>>>>>>>>>>>> >> > > >> --
>>>>>>>>>>>>>>>>> >> > > >> You received this message because you are
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>>>>>>>>>>>>>>>>> >> > > >> Visit this group at
>>>>>>>>>>>>>>>>> https://groups.google.com/group/sympy.
>>>>>>>>>>>>>>>>> >> > > >> To view this discussion on the web visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/7cbe2101-fd59-484b-9e25-f563636d6366%40googlegroups.com
>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > > >> For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> > > >
>>>>>>>>>>>>>>>>> >> > > > --
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>>>>>>>>>>>>>>>>> >> > > > To view this discussion on the web visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/1795A385-4AEA-44FD-BEE8-8115D53DA14B%40gmail.com
>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > > > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > --
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>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > --
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>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > --
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>>>>>>>>>>>>>>>>> https://groups.google.com/d/msgid/sympy/CAKgW%3D6KrEOoZ-CvGJ_HTBVSpTLVkW6geUfvXdP8GAiBNO4y8qQ%40mail.gmail.com
>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > --
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>>>>>>>>>>>>>>>>> >> > > To view this discussion on the web visit
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>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > >
>>>>>>>>>>>>>>>>> >> > > --
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>>>>>>>>>>>>>>>>> >> > > To view this discussion on the web visit
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>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >> >
>>>>>>>>>>>>>>>>> >> > --
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>>>>>>>>>>>>>>>>> >> > To view this discussion on the web visit
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>>>>>>>>>>>>>>>>> .
>>>>>>>>>>>>>>>>> >> > For more options, visit
>>>>>>>>>>>>>>>>> https://groups.google.com/d/optout.
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >>
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>> >
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>
>>>
>>
>

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