Running tests on HEAD I get the following error:
sympy/solvers/tests/test_ode.py:test_nth_linear_constant_coeff_variation_of_parameters
File "/Users/aterrel/workspace/sympy/sympy/solvers/tests/test_ode.py",
line 899, in test_nth_linear_constant_coeff_variation_of_parameters
assert dsolve(eq6, f(x), hint=hint) == sol6
AssertionError
tests finished: 1615 passed, 1 failed, 2 skipped, 44 xfailed, 1
xpassed in 333.83 seconds
-- Andy
On Thu, Aug 20, 2009 at 6:23 AM, Vinzent
Steinberg<vinzent.steinb...@googlemail.com> wrote:
> Thank you, this is an impressive result. :)
>
> 2009/8/20 Aaron S. Meurer <asmeu...@gmail.com>
>>
>> I have finished up my Google Summer of Code 2009 project, which was to
>> implement various ODE solvers in SymPy. Please pull
>> fromhttp://github.com/asmeurer/sympy/tree/odes-review
>> . Note that I have elected to do only moderate rebasing from my
>> original tree (branch odes), so you should really only be reviewing
>> the HEAD.
>>
>> This includes the following features:
>>
>> - All ODE solving now happens in ode.py, instead of solvers.py where
>> it was crowding stuff.
>> - dsolve() remains the function to use to solve an ODE. The syntax is
>> the same for default solving: dsolve(ode, func).
>> For example:
>> >>> dsolve(diff(f(x), x, 2) - 1, f(x))
>> f(x) == C1 + C2*x + x**2/2
>>
>> dsolve() always returns an Equality instance, because it very often
>> cannot solve for f(x) and must return an implicit solution.
>>
>> - The function classify_ode() was added. This function classifies
>> ODEs into the various methods (or "hints", as I also call them) that
>> dsolve() can use to solve them.
>> For example:
>> >>> classify_ode(f(x).diff(x) - 1, f(x))
>> ('separable', '1st_exact', '1st_linear', 'Bernoulli',
>> '1st_homogeneous_coeff_best',
>> '1st_homogeneous_coeff_subs_indep_div_dep',
>> '1st_homogeneous_coeff_subs_dep_div_indep',
>> 'nth_linear_constant_coeff_undetermined_coefficients',
>> 'nth_linear_constant_coeff_variation_of_parameters',
>> 'separable_Integral', '1st_exact_Integral', '1st_linear_Integral',
>> 'Bernoulli_Integral',
>> '1st_homogeneous_coeff_subs_indep_div_dep_Integral',
>> '1st_homogeneous_coeff_subs_dep_div_indep_Integral',
>> 'nth_linear_constant_coeff_variation_of_parameters_Integral')
>>
>> - The function deriv_degree() remains the function to use for
>> determining the degree, or order, of an ODE.
>> For example:
>> >>> deriv_degree(f(x).diff(x, 5) + sin(x) + f(x).diff(x, 2), f(x))
>> 5
>>
>> - The new function checkodesol() checks if a solution to an ODE is
>> valid by substituting it in and either returning True if it finds 0
>> equivalence or the expression that it could not reduce to 0.
>> For example:
>> >>> checkodesol(f(x).diff(x, 2) - 1, f(x), Eq(f(x), C1 + C2*x +
>> x**2/2))
>> True
>> >>> checkodesol(f(x).diff(x, 2) - 1, f(x), Eq(f(x), C1 + C2*x + x**2))
>> 1
>
> This is problematic, because this way
>
> if not checkodesol(...):
> print 'not a solution'
>
> does not work, because most expressions evaluate to True. I'd prefer
> returning just 0 instead of True, this is more consistent and useful.
>
>>
>> - The function separatevars(), which I wrote to help with the 1st
>> order separable method, attempts to intelligently separate variables
>> an expression multiplicatively.
>> For example:
>> >>> separatevars(x**2 + x**2*sin(y))
>> x**2*(1 + sin(y))
>> >>> separatevars(exp(x + y))
>> exp(x)*exp(y)
>>
>> This function resides in simplify.py.
>>
>> - The new function homogeneous_order(), which I wrote to help with the
>> 1st order ODE with homogeneous coefficients method, determines the
>> homogeneous order of an expression. An expression F(x, y, ...) is
>> homogeneous of order n if F(x*t, y*t, t*...) == t**n*F(x, y, ...).
>> For example:
>> >>> homogeneous_order(x**2*sqrt(x**2 + y**2) + x*y**2*sin(x/y), x, y)
>> 3
>>
>> - dsolve() will simplify arbitrary constants, and renumber them in
>> order in the expression. You should never see something like x + 2*C1
>> or 1 + C2*x + C1*x**2 returned from dsolve(). You can disable this by
>> using simplify=False in dsolve().
>>
>> - Internally, the solving engine has been completely refactored. The
>> old way was to match the ODE to various solvers in a predetermined
>> order, and as soon as it matched one, it would solve it using that
>> method and return a result. This had several problems with it.
>>
>> First, several ODEs can be solved with more than one method (c.f. the
>> simple ODE in the classify_ode() example above), and sometimes you
>> want to see the result from a different method.
>>
>> Second, sometimes the default solver would return a result that was
>> much more complex than another one would have returned if the ODE had
>> gotten to it. For example, it may return an implicit solution that is
>> difficult for solve() to solve, whereas the other method would return
>> the equation already solver.
>
>
> typo
>
>>
>> Another common case is that one method
>> would set up an integral that integrate() could not do, whereas
>> another method would set up a simpler integral. That leads to the
>> third point.
>>
>> Third, whenever a solver would set up a hard integral, integrate()
>> would either hand for a while then return an Integral, or it would
>> hang forever. Either way, you would get an unevaluatable (by SymPy)
>> integral, when sometimes another method might not give you that.
>>
>> Fourth, there was a lot of code duplicated this way. For example,
>> whenever a method had the potential to return an implicit solution, it
>> had to duplicate the same code chunk that tried to solve it and return
>> a solved solution if it could be solved or else an implicit solution.
>>
>> The new way is for dsolve to have an optional hint argument that you
>> can use to specify whatever method you want to use, if it fits.
>> dsolve() calls classify_ode() on the ODE and gets all of the possible
>> hints. By default, hint="default" is used, which uses a predetermined
>> order, much like the old way. But you can easily use something like
>> hint="1st_exact" to change the hint from the default method to the 1st
>> order exact ODE solver. Aside from "default", there are also some
>> other 'meta-hints' that you can use. "all" will return a dictionary
>> of hint: solution terms for all matching hints. "best" will use a
>> heuristic to return the simplest of all possible solutions. This
>> heuristic is based on whether the solution has unevaluated Integrals
>> in it, whether it can be solved explicitly, and finally, just which
>> one is the shortest. All hints that set up integrals also have a
>> coresponding "hint_Integral" hint, which will not attempt to evaluate
>> the integrals but instead return unevaluated Integrals in the
>> solution. "all_Integral" acts like "all", but it skips hints that
>> attempt to evaluate integrals. This is so you can quickly get an
>> unevaluated integral of something you know SymPy cannot do, instead of
>> letting integrate() hang. It also lets you discover how the solvers
>> work by showing you what integrals they do.
>>
>> - Along with extensive documentation on all of the functions, I have
>> included a guide in the module docstring on how to add more methods to
>> the module using the hints system. It can give you an idea of how the
>> system works internally.
>>
>>
>> The following ODE solving methods have been implemented. See the
>> internal docstrings for more information on each method:
>> - 1st order separable differential equations
>> - 1st order differential equations whose coefficients or dx and dy
>> are functions homogeneous of the same order.
>> - 1st order exact differential equations.
>> - 1st order linear differential equations. (this is already
>> implemented in the current SymPy)
>> - 1st order Bernoulli differential equations. (this is already
>> implemented in the current SymPy by a patch I sent in in the spring)
>> - 2nd order Liouville differential equations.
>> - nth order linear homogeneous differential equation with constant
>> coefficients.
>> - nth order linear inhomogeneous differential equation with constant
>> coefficients using the method of undetermined coefficients.
>> - nth order linear inhomogeneous differential equation with constant
>> coefficients using the method of variation of parameters.
>>
>> In addition to the ode module, this branch includes fixes to the
>> following issues, which were necessary for me throughout my work:
>> - Issues 1582, 1566, 1530, and 1429 (the first part only).
>> - Integral.__getnewargs__ now properly works. If r is an Integral
>> instance, then r == r.new(r.__getnewargs__(r.args)) should always be
>> True.
>> - Changed two assertions and one raise TypeError in solve() to raise
>> NotImplementedError. This way, you do not have to check for
>> AssertionError or TypeError to see if solve() has failed, only
>> NotImplementedError. See issues 1425 and 1338.
>
> I'll have to play around with this. :)
>
> Vinzent
>
> >
>
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