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
>>>>>>>>> >> > > >>
>>>>>>>>> >> > > >> --
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>>>>>>>>> .
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>>>>>>>>> .
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>>>>>>>>> .
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>>>>>>>>> .
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>>>>>>>>> >>
>>>>>>>>> >>
>>>>>>>>> >
>>>>>>>>> >
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>>
>>>>>
>>>>
>>>
>>
>

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