Henry,
load(ineq) does some of the inequality manipulations you ask for, like
(-1)*(a<b)
=> -b < -a.
As for expressions of the form a<b<=c, if I were to be designing such a
feature (which I'm not), I'd treat that as a shorthand for (a<b) and (b<=c).
That fits into Maxima's general philosophy of representing things in
quasicanonical ways. But that presupposes that Maxima can do useful things
with Boolean compositions of predicates (inequalities or otherwise), which
it currently cannot, even in the simplest cases. For example, a and not a
and a<b and b<a currently don't simplify to false. I think that capability
is not only a prerequisite, but useful functionality in itself.
-s
On Fri, Jul 20, 2012 at 9:21 AM, Henry Baker <hbaker1 at pipeline.com> wrote:
> 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]
> >=====================
> >
> >[Link to mailing list thread if applicable]
> >
> >[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
>
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