Thank you Lee for your quick reply.
I will recheck it.
בתאריך יום ג׳, 16 בפבר׳ 2021, 19:36, מאת S.Y. Lee <[email protected]>:
> SciPy's implementation is to minimize c^{T} x while my implementation is
> to maximize c^{T} x
> I verified that it gives same result result with scipy when I changed the
> problem to minimize -c^{T} x
>
> I have given a brief documentation about how to use in the comment, but
> not in the docstring, because the project is totally skeletal.
> # Maximize Cx + D constrained with Ax <= B and x >= 0
> # Minimize y^{T}B constrained with y^{T}A >= C^{T} and y >= 0
> I haven't studied the simplex algorithm for a while, but at least I don't
> think that that there was a discovered flaw in the algorithm.
> On Wednesday, February 17, 2021 at 2:01:36 AM UTC+9 [email protected]
> wrote:
>
>> Hey Oscar,
>>
>> sorry for the late reply, I was overloaded with exams.
>>
>> For your first question, I intend to create a new function that when
>> given a set of linear inequalities and a target inequality it would output
>> True if the target is implied by this set, False if it is not, and Unknown
>> otherwise. I wrote doctests to make it all more clear.
>>
>> You can see it here –
>>
>> https://github.com/orielmalihi/Final-Project/blob/main/iset%20tests.py
>>
>> (the main function there is called 'is_implied_by')
>>
>> For your second question, I intended to use Scipy LP solver, but as far
>> as I can tell it only works with floats. I could convert every coefficient
>> to float using the 'evalf()' function but then we would get 99.9% accurate
>> results and not 100%.
>>
>> Other option is to use the LP solver suggested by Lee (above), but it is
>> unclear for me how it works, since it has no documentation of input/output.
>> Moreover, I ran the example mentioned there with Scipy LP solver and got
>> different results somehow. (if I understood right, Matric A is the lhs of
>> the constraints, matric B is the rhs, matric c is the objective, and D is
>> the lower bounds. if I am wrong I would be happy if you could tell me why)
>>
>> On Thu, 31 Dec 2020 at 23:38, S.Y. Lee <[email protected]> wrote:
>>
>>> I have a full implementation of linear programming in
>>> https://github.com/sympy/sympy/issues/20391
>>> Although if you may or may not want the code, I hope it can reduce any
>>> duplicate efforts if you were intending to implement the same method.
>>>
>>> On Thursday, December 31, 2020 at 5:58:55 AM UTC+9 Oscar wrote:
>>>
>>>> On Wed, 30 Dec 2020 at 19:47, אוריאל מליחי <[email protected]>
>>>> wrote:
>>>> >
>>>> > > Okay, well if you want this to be included in sympy I suggest to
>>>> begin.
>>>> > > by making some specific proposals either here or in github issues.
>>>> We
>>>> > > should agree the basic ideas before too much work is done. Of
>>>> course
>>>> > > you don't have to implement all the proposals but we should agree
>>>> what
>>>> > > makes sense as part of sympy even if your project is only a part of
>>>> > > what we would want.
>>>> >
>>>> > > Where possible it is best to improve the implementation of existing
>>>> > > API functions rather than introduce new ones but there certainly
>>>> are
>>>> > > reasons for wanting some new functions for working with
>>>> inequalities:
>>>> > > exactly what those new functions would be is the part that needs to
>>>> be
>>>> > > agreed if this is to be included in sympy.
>>>> >
>>>> > > I would say that eliminating one or more variables from a system of
>>>> > > inequalities is very useful and there is e.g. Fourier-Motzkin
>>>> > > elimination
>>>> > > https://en.wikipedia.org/wiki/Fourier%E2%80%93Motzkin_elimination
>>>> > > as well as linear programming:
>>>> > > https://en.wikipedia.org/wiki/Linear_programming
>>>> >
>>>> > > Actually one of the most useful things at least for internal use in
>>>> > > sympy would be being able to ask whether an inequality is implied
>>>> by a
>>>> > > collection of inequalities. A simple example is that x > 0 implies
>>>> > > that x > 1
>>>> >
>>>> > I think you meant that x > 1 implies that x > 0, but I get the point.
>>>> >
>>>> > > but we would like to pose more complicated questions like:
>>>> >
>>>> > > Given that x > y, y > 0, x + y > z is it the case that 2*x > 0
>>>> >
>>>> > > The possible answers to a problem like this are "yes", "no" or
>>>> "maybe".
>>>> >
>>>> > I see. Well I believe I can implement this function using the Linear
>>>> Programing technique.
>>>> >
>>>> > if that is okay with you, I would like to start working on it right
>>>> after my semester exams (in 3 weeks).
>>>> >
>>>> > Is there anything more I need to know/do before I start coding?
>>>>
>>>> I think the main thing is that if you are looking to contribute this
>>>> to sympy then you should specify whether you are hoping to change
>>>> existing public functions (which functions and how would they change?)
>>>> or whether you are introducing new public API and if so what that API
>>>> would be. It's not possible for me to say on behalf of sympy that any
>>>> work would likely be included in sympy without knowing what the
>>>> expected output is.
>>>>
>>>> The other thing I would say is that it's important to consider the
>>>> symbolic case in sympy. Algorithms in the symbolic case are different
>>>> from algorithms intended for an explicit numeric representation. As an
>>>> example of what I mean the wikipedia article describes Fourier-Motzkin
>>>> elimination as something that generates an exponentially growing
>>>> number of cases and therefore is computationally awkward. That isn't
>>>> true in sympy though because we can represent limits symbolically
>>>> using something like `Max(a, b)` where `a` and `b` are symbols and
>>>> that is a useful representation in situations where it isn't known
>>>> which symbol is greater. It isn't clear to me how easily the linear
>>>> programming techniques can apply in a situation where the coefficients
>>>> in the inequalities are symbolic.
>>>>
>>>> Oscar
>>>>
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