Hi All,
I want to change the basic organization of Diophantine equation module so
that it can be extended and used more conveniently. Since I wish to develop
the module for CSymPy also, I thought this would be a good time to talk
about this.
Currently, the Diophantine module is invoked through the higher level API
function `diophantine()`. For example,
>>> from sympy.solvers.diophantine import diophantine
>>> x, y, z = symbols("x, y, z", Integer=True)
>>> diophantine(2*x + 3*y - 4*z - 7)
set([(3⋅t - 4⋅z - 7, -2⋅t + 4⋅z + 7, z)])
>>> diophantine(3*x**2 - 5*y**2 - 1)
set([])
I think that it will be better for us to go for an object oriented
representation of
Diophantine equations as SAGE does. Then we can simply supply member
functions that will do required operations. It will also be more reusable
and
extensible than now.
I propose a scheme like below.
>>> x, y, z = symbols("x, y, z", Integer=True)
>>> s = LinearDiophantineEqn(2*x + 3*y - 4*z - 7)
>>> t = LinearDiophantineEqn([2, 3, -4, -7])
>>> u = QuadraticDiophntineEqn(2*x**2 - 3*y**2 - 1)
>>> u.solve()
We can supply different constructors for a given kind of equation and we
can derive
all the equation schemas from a base schema.
Also, For the issue regarding the user specifying parameters, I vote
against it
since it can not be justified for the user requiring to know in advance the
number of
parameters we will be needing for a solution. We can keep the parameters in
the
equation object it self after calling the solve() method and provide other
methods
for the user to iterate over them. But one thing we can do is to let user
specify one
parameter and build other required parameters from it. i.e, if user input
`t` to be used
as a parameter, we use sub-scripted versions of t, ex. `t_{1}, t{2}, ...,
t_{n}`. Here also
we need to let user know of the `n`.
This is just a vague expression on some of the ideas I have and nothing is
finalized.
I would like to know what you guys think.
Regards,
Thilina.
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