# [Maxima] Solving an equation with integral

Henry Baker hbaker1 at pipeline.com
Fri Jul 20 08:21:11 CDT 2012

I've been using Maxima to "prove" a number of standard plane geometry
theorems, but using analytic geometry (real & complex algebra) instead
of Euclid.  It's actually surprisingly difficult to beat Maxima into
submission in order to do this.

I wish I could summarize my experience into some succinct recommendations,
but so far I can't.

There is one area that I recommended some improvement on a while back, but
so far no one has picked up the ball & run with it.

I was doing some Khan Academy high school algebra exercises with Maxima, and
it would be useful to add high-school-type inequalities to Maxima.

Briefly, in addition to having equality equations with a left-hand-side ("lhs")
and right-hand-side ("rhs"), it would be nice to allow

declare([x,y,z],real);

x < y+z;

%-z;

(outputs x-z < y)

%*(-1);

(outputs -x+z >= -y)

There are also extended inequalities:

x < y <= z, so it would be nice to have more than just lhs(), rhs(), etc.

You get the idea.

At 02:20 AM 7/20/2012, Rupert Swarbrick wrote:
>Raymond Toy <toy.raymond at gmail.com> writes:
>> I think having examples like this on the wiki would be very nice too.  I
>> always learn a lot from examples like this, and such examples are easier
>> for me to find on a wiki than on a mailing list with lots of other
>> discussions.
>>
>> Ray
>
>I suppose that the problem is how one might categorise them. Also, I'm
>pretty certain that there are exactly two things that allow me to come
>up with steps like this:
>
> (1) I've used Maxima for some time, so I am sort of fluent with the
>     different simplification functions and know what is likely to do
>     what.
>
> (2) I'm a maths PhD student and recently did an undergraduate maths
>     degree. Making sense of how to solve a problem like this does
>     require some knowledge of analysis. Being au fait with Taylor
>     expansions and when they do/do not work makes it easy to see what
>     "should happen".
>
>Maybe we could come up with some "ratsimp training" Wiki pages, which
>show how to use (say) expand, factor, gfactor, subst, ratsubst, ratsimp
>to wrangle expressions in a useful way. I can definitely see that this
>could make (1) easier to attain.
>
>For (2), well I realise that I've got much less training in numerical
>analysis and/or symbolic algebra than most of the people on this list
>that answer questions. Those who ask them tend to be maths, physics or
>engineering undergrads as far as I can tell. Some sort of "management of
>expectations" could maybe help people realise when they are expecting
>Maxima to do the impossible! (Or implausible, maybe).
>
>I should have some time this weekend and it would be fun to collect up a
>list as you suggest. I'll email Lyosha Beshenov for an account in a
>minute. Any suggestions on how to format the results?
>
>I was thinking something like:
>
>---------------
>How to [Do Something]
>=====================
>
>
>[Some background information along with a (possibly simplified)
> statement of the problem]
>
>[First thoughts: Is it reasonable to expect Maxima to solve this? How
> might I make it easier]
>
>[A solution]
>
>[Things that don't work and why]
>
>---------------
>
>But maybe others have better ideas?
>
>Rupert