One can always eliminate the fourth order by a translation, in this case by
one; one obtains then
``x**5 + 20*x**3 + 20*x**2 + 30*x + 10``, which is solved by SymPy; it
would be useful to automatize this step.
However the real solution is not simplified, it has ``count_ops = 267``, vs
``count_ops=11`` for the simplified
real solution ``S('2^(1/5) - 4^(1/5) + 8^(1/5) - 16^(1/5)')``
On Monday, January 27, 2014 11:42:03 AM UTC+1, Harsh Gupta wrote:
>
> > Apparently only for some of them: it does not solve
> > ``x**5 - 5*x**4 + 30*x**3 - 50*x**2 + 55*x - 21 = 0``
>
> Thanks. Yes, not all of them, Only equations of form x**5 + p*x**3 +
> q*x**2 + r*x + s, no fourth order terms are solvable.
>
> The implementation was added in
> https://github.com/sympy/sympy/pull/1746. So, there is scope of
> improvement. I wonder
> how many of other methods of solving solvable quintics can be
> implemented without a knowledge of abstract algebra.
> Aaron Meurer can you guide me on this?
>
> On 27 January 2014 13:28, mario <[email protected] <javascript:>>
> wrote:
> > You wrote "Methods to solve solvable quintics are implemented in sympy."
> >
> > Apparently only for some of them: it does not solve
> > ``x**5 - 5*x**4 + 30*x**3 - 50*x**2 + 55*x - 21 = 0``
> >
> > taken from http://en.wikipedia.org/wiki/Quintic_function
> >
> >
> >
> >
> > On Monday, January 27, 2014 3:11:37 AM UTC+1, Harsh Gupta wrote:
> >>
> >> I'm reading and understanding the solvers code. I have started
> >> documenting it here https://github.com/sympy/sympy/wiki/solvers.
> >>
> >> @Matthew
> >> For implementing and dealing with infinite sets I've found a draft by
> >> Richard Fateman
> >> http://www.cs.berkeley.edu/~fateman/papers/sets.pdf
> >>
> >> I have skimmed through it and it appears all of the techniques
> >> described there are implementable in sympy.
> >>
> >> On 25 January 2014 06:28, Aaron Meurer <[email protected]> wrote:
> >> > On Fri, Jan 24, 2014 at 2:02 PM, Harsh Gupta <[email protected]>
> >> > wrote:
> >> >>>> Great to hear it. As noted on the ideas page, this one will
> require a
> >> >>>> good deal of thought to be done in the application, so let's start
> >> >>>> discussing.
> >> >>
> >> >> Thanks a lot, and sorry for the late reply
> >> >>
> >> >>>> Another thing I'd like to know is if there's literature on solving
> >> >>>> algorithms, particularly solving transcendental equations, and
> very
> >> >>>> particularly on if there are any complete algorithms out there for
> >> >>>> some class of equations.
> >> >>
> >> >> I found a old paper called "SOLVING SYMBOLIC EQUATIONS WITH PRESS"
> >> >>
> >> >>
> http://www.research.ed.ac.uk/portal/files/413486/Solving_Symbolic_Equations_%20with_PRESS.pdf
>
> >> >>
> >> >>>> Do we know how other computer algebra systems solve this problem?
> >> >>>> How robust are the algorithms behind wolframalpha.com ?
> >> >>
> >> >> I have found another paper "A Review of Symbolic Solvers"
> >> >>
> >> >>
> http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.44.9444&rep=rep1&type=pdf
>
> >> >> and according to it Mathematica performs performs pretty bad.
> >> >
> >> > That was in 1996.
> >> >
> >> > Nonetheless this, along with the Wester paper, should provide some
> >> > good test cases so we can see what can be done that we can't do.
> >> >
> >> > Aaron Meurer
> >> >
> >> >>
> >> >>>> An audit of the current solve code might be in order. In
> particular,
> >> >>>> I'd like to know:
> >> >>>>
> >> >>>> 1. what are the different "solvers"? (if we split solve into
> "hints"
> >> >>>> like with dsolve, these would be the different hints), and
> >> >>>> 2. which are algorithmically complete (i.e., we know they will
> give
> >> >>>> all solutions, or they can detect somehow if they may have missed
> >> >>>> one)?
> >> >>>>
> >> >>>> And this may raise auxiliary questions, like:
> >> >>>>
> >> >>>> - to what degree can the different solvers be separated? For
> >> >>>> instance,
> >> >>>> one solver (I'm not sure if it's actually implemented) would use
> >> >>>> decompose() to solve recursively. How would such "recursive
> solvers"
> >> >>>> look in a hints system?
> >> >>>>
> >> >>>> - of those that are heuristic (not algorithmically complete), can
> >> >>>> they
> >> >>>> be improved?
> >> >>
> >> >> I'm going through the solvers code and will answer these questions
> >> >> soon.
> >> >>
> >> >> --
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> >>
> >> --
> >> Harsh
> >
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>
> --
> Harsh
>
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