Thank you Ondrej for the reply.
I think that's the way we should go at it. I can implement the
moduels to find the solution and return those naturally as a list.
Later we consider about the high level API's.
On Wed, Jun 19, 2013 at 1:28 AM, Ondřej Čertík <ondrej.cer...@gmail.com>wrote:
> Hi Thilina,
>
> On Tue, Jun 18, 2013 at 12:39 PM, Thilina Rathnayake
> <thilina.r...@gmail.com> wrote:
> > Hi everyone,
> >
> > Before continuing further with the Diophantine module development (PR
> #2168)
> > I thought it would be better for me to get other people's views on the
> > representation
> > of solutions returned by diop_solve().
>
> Thanks for discussing it.
>
> >
> > The main routine of the module is diop_solve(), which takes a Diophantine
> > equation
> > as an argument and returns the solution of the equation. Currently the
> > solution is
> > returned as a dictionary. Ex:
> >
> >> >>>diop_solve(4*x + 6*y - 4)
> >> {x: 6*t - 2, y: -4*t + 2}
> >> >>>diop_solve(3*x - 5*y + 7*z -5)
> >> {x: -25*t - 14*z + 10, y: -15*t - 7*z + 5, z: z}
> >
> >
> > Everything works fine here because the solutions are parametric.
>
> Right. For these equations I think a dictionary is the best solution,
> as it is simple and clear. You should allow the user to specify the
> "t" symbol, e.g. something like:
>
> var("x y z t")
> diop_solve(3*x - 5*y + 7*z -5, param=t)
>
> so that the user can specify other variables names besides "t" as well.
>
> >
> > But when I was trying to solve quadratic Diophantine equation ( this has
> the
> > form
> > Ax**2 + Bxy + Cy**2 + Dx + Ey + F), they involve solutions which are not
> > parametric.
> > For example, the equation 2*x*y + 5*x + 56*y + 7 = 0 (which is a special
> > case of the
> > quadratic equation) has 8 solution pairs (x, y). (-27, 64), (-29, -69),
> > (-21, 7) and five more.
> >
> > To represent these in a dictionary which has the above form, we have to
> > split the solution
> > pair and put it in to two lists which are keyed under x and y in the
> dict.
> > if the user want
> > to retrieve a solution pair he would have to find the x value and the y
> > value of the solution
> > separately. Returned value would look like,
> >
> >> {x: [-27, -29, -21, ...], y: [64, -69, 7, ...]}
> >
> >
> > Is this a good way to cope with this situation? I personally feel that
> it is
> > not natural to
> > split a solution pair and enable the access of it's elements separately.
> >
> > I would like to know what the others have to say on this.
>
>
> So for this I agree with Aaron:
>
> > You may want to look at
> > https://code.google.com/p/sympy/issues/detail?id=3560 and some of the
> > ideas for a unified solve object.
>
> We definitely need a consistent interface to the solve() command.
>
> > Already you have the issue that you
> > are returning a parameter, but there is no easy way to access that
> > parameter (and what happens if t is one of the variables?).
>
> The user can specify his own symbols as "params", as I suggested above.
>
> I would also look how Mathematica does it:
>
> http://reference.wolfram.com/mathematica/guide/DiophantineEquations.html
>
> e.g.:
>
> http://reference.wolfram.com/mathematica/ref/Reduce.html
>
>
>
> In general, I would suggest you simply write the low level modules for
> actually solving the equation.
> Those can return pretty much any representation that you think is the
> best for that particular type of the equation.
>
> Then we need a consistent high level API, and that will take some time
> to get right. But no matter what API we settle on in the end, it
> should be quite simple to call the low level solver and convert the
> result if needed. What do you think Aaron?
>
> Ondrej
>
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