Our constant simplifier work for only one variable. Someone might go try to implementing it for multiple variables. Our PDE module needs that.
There a paper on this by Neil Soiffer called "Collapsing Constants" that deals with such stuff. http://www.cs.berkeley.edu/~fateman/papers/CollapsingConstants-Soiffer.pdf On 9 March 2014 06:22, Aaron Meurer <[email protected]> wrote: > This is in some sense a bug. The solution is correct mathematically. > The biggest issue with it is actually that there are four constants, > not two. This is because the solver currently outputs four terms and > relies on the constant simplification to reduce them to two. But the > terms don't simplify in this case because they are so complicated. > > If you want something simpler, you should assume that f is real, like > > f = symbols('f', real=True) > > If you do that, you will get > > In [8]: print(dsolve(d2udt2, u(t))) > u(t) == C1*sin(t*Abs(f)) + C2*cos(t*Abs(f)) > > if you don't like the Abs you can assume f is positive instead. > > Ideally, dsolve would return a solution in terms of complex > exponentials in these sorts of cases, which would be a lot less > complicated. Any potential GSoC students out there, especially those > interested in the ODE module, this is a nice little project for your > patch requirement. > > Aaron Meurer > > On Sat, Mar 8, 2014 at 2:24 PM, Filipe Pires Alvarenga Fernandes > <[email protected]> wrote: >> Hi, >> I'm new to sympy and I'm trying to understand how to use dsolve. (I'm >> creating an ipython notebook for a class.) >> >> I'm creating my DE like this: >> de = Eq(u(t).diff(t, t) + 4*u(t), 0) >> print(de) >> >> 4*u(t) + Derivative(u(t), t, t) == 0 >> >> >> soln = dsolve(de, u(t)) >> print(soln) >> >> u(t) == C1*sin(2*t) + C2*cos(2*t) >> >> >> So far now everything is perfect. But if I try to change the number 4 for a >> "generic" symbol (f**2) I do not get >> >> u(t) == C1*sin(f*t) + C2*cos(f*t) as I expected, insted I get a more >> "comprehensive" solution below. >> >> >> What am I doing wrong? >> >> >>>>> d2udt2 = Eq(u(t).diff(t, t) - f*(-f*u(t)), 0) >>>>> print(d2udt2) >> f**2*u(t) + Derivative(u(t), t, t) == 0 >> >> u(t) == (C1*sin(t*((-re(f)**2 + im(f)**2)**2 + >> 4*re(f)**2*im(f)**2)**(1/4)*Abs(sin(atan2(-2*re(f)*im(f), -re(f)**2 + >> im(f)**2)/2))) + C2*cos(t*((-re(f)**2 + im(f)**2)**2 + >> 4*re(f)**2*im(f)**2)**(1/4)*sin(atan2(-2*re(f)*im(f), -re(f)**2 + >> im(f)**2)/2)))*exp(-t*((-re(f)**2 + im(f)**2)**2 + >> 4*re(f)**2*im(f)**2)**(1/4)*cos(atan2(-2*re(f)*im(f), -re(f)**2 + >> im(f)**2)/2)) + (C3*sin(t*((-re(f)**2 + im(f)**2)**2 + >> 4*re(f)**2*im(f)**2)**(1/4)*Abs(sin(atan2(-2*re(f)*im(f), -re(f)**2 + >> im(f)**2)/2))) + C4*cos(t*((-re(f)**2 + im(f)**2)**2 + >> 4*re(f)**2*im(f)**2)**(1/4)*sin(atan2(-2*re(f)*im(f), -re(f)**2 + >> im(f)**2)/2)))*exp(t*((-re(f)**2 + im(f)**2)**2 + >> 4*re(f)**2*im(f)**2)**(1/4)*cos(atan2(-2*re(f)*im(f), -re(f)**2 + >> im(f)**2)/2)) >> >> >> Thanks, >> >> -Filipe >> >> -- >> You received this message because you are subscribed to the Google Groups >> "sympy" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at http://groups.google.com/group/sympy. >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sympy/1395f3d9-f6ea-4167-bc0c-3a9b7e1e1e5d%40googlegroups.com. >> For more options, visit https://groups.google.com/d/optout. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6%2BKeqD5E8oghS0fw%2BxSzpG%3D94PSOv0LN%2BAfNYcSqZR9Xg%40mail.gmail.com. > For more options, visit https://groups.google.com/d/optout. -- Harsh -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CADN8iurs%3DCUsfRG-F%3Dw%2BBa0UGvFiWtK8vRAsohMxR%3DxSBYow4Q%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
