On Tue, Feb 17, 2015 at 10:41 PM, Petr Baudis <[email protected]> wrote:
> On Tue, Feb 17, 2015 at 02:58:35AM -0800, Petr Baudis wrote:
>>
>> On Tuesday, February 17, 2015 at 3:54:32 AM UTC+9, Jason Moore wrote:
>> >
>> > Here is one way to do it:
>> >
>> > https://gist.github.com/moorepants/858503aa180df60a7829
>>
>> Oh, thanks a lot! I didn't think about approaching it this way, and it
>> makes a lot of sense.
>> I'll play with this more, but it's a big step forward for me!
>
> I have rewrote your solution a bit to lend better to autogeneration from
> predicate form that I use as an intermediate form:
>
> import sympy as sym
> from sympy import init_printing
> t = sym.symbols('t', real=True)
> eqs = []
>
> g = sym.symbols('g', real=True, positive=True)
>
> x_r, v_r = sym.symbols('x_r, v_r', cls=sym.Function) # functions of
> time
> x0_r, v0_r = sym.symbols('x0_r, v0_r', real=True)
> accel_r = sym.Eq(x_r(t).diff(t, 2), -g)
> position_r = sym.dsolve(accel_r, x_r(t)).subs({'C1': x0_r, 'C2':
> v0_r})
> eqs.append(position_r)
> velocity_r = sym.dsolve(accel_r.subs({x_r(t).diff(t): v_r(t)}),
> v_r(t)).subs({'C1': v0_r})
> eqs.append(velocity_r)
>
> h = sym.symbols('h', real=True)
> eqs.append(position_r.subs({x_r(t): h, t: 0}))
> eqs.append(velocity_r.subs({v_r(t): 0, t: 0}))
>
> t_e2 = sym.symbols('t_e2', real=True)
> eqs.append(position_r.subs({x_r(t): 0, t: t_e2}))
>
> print(eqs)
> print(sym.solve(eqs, v_r(t)))
>
> So one curious observation I have is that even if sym.solve() is given
> multiple equations and only a single variable, it does yield a solution
> in this case. I'm still confused about what the exact API contract of
> sym.solve() is. Working "sometimes" leaves me unsure about what I can
> or cannot rely on...
Sadly, there is none. Part of this is due to algorithmic limitations
(solve() is basically a bunch of heuristics, there are few guarantees
that it will find a solution if it exists). But a lot of it is just
poor design. We are trying to make the design better with the new
solveset module.
Aaron Meurer
>
> Of course, the much more important problem for me is that this will
> again generate just a formula of v_r(t) depending on t, instead of the
> other parameters, and I see no easy way to ask SymPy for a solution
> without t in it. Jason's solution is to first compute the time:
>
> # Remove position_r, velocity_r from eqs
> sol = sym.solve(eqs, t_e2, x0_r, v0_r, dict=True)
> final_velocity = velocity.subs({t: tf}).subs(sol[0])
>
> but that's the problem - I need to know I need to compute the time
> first, and it's not clear what kind of rules to figure out what to
> compute I will need with different combinations of equations. (In other
> words, I would have hoped a CAS would have this figured out already. :-)
>
> (The other thing of also including x0_r, v0_r in solve set is not so
> bad, that might be fixed by a simple semi-automated substitution step.)
>
> Right now I'm inclined to conclude that what I want to do *is* rather
> hard and I'd have to come up with some new algorithms to deal with this.
> (Or likely take a look at some other CASes first if any handle this case
> for me already.)
>
> --
> Petr Baudis
> If you do not work on an important problem, it's unlikely
> you'll do important work. -- R. Hamming
> http://www.cs.virginia.edu/~robins/YouAndYourResearch.html
>
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