clue needed on using results of previous computations

One way is to manipulate the expression is by using rhs, or lhs which take the
right hand side
or left hand side of a equation.  You then use funmake to create the lambda
expression.
For example:
r:funmake(lambda,[[g],rhs(eq2)]);
r(1);
-5/2

Rich Drewes wrote:

> Hello,
>
> I am making a dogged effort to use Maxima in a graduate math class,
> despite the bias toward Maple and Mathematica.  I have had some success
> but I am having great problems doing a couple of things that seem trivial
> in Maple.  I think this is because I just lack one crucial clue, and
> hopefully someone out there can help me out.
>
> Here is one problem I am having.  Take a function, e.g.:
>
> y=x*x + 5*g*x;
>
> Say I want to plot x and g that maximizes y.  So, differentiate the
> function with respect to y, set equal to 0, and plot the x and g that
> satisfy that equation.  Sounds simple, and in Maple it is, but in Maxima I
> can't get past some conceptual hurdle.  Let's try this in Maxima:
>
> eq1: y(x, g):=x*x + 5*g*x;
>
> and that works.  We can differentiate with respect to x just fine:
>
> diff(y(x, g), x);
>
> which gives 2 x + 5 g as we expect.  So set this =0 and solve for x:
>
> eq2:solve(diff(y(x, g), x) = 0, x);
>
> This gives us a result of x=-5*g/2 as it should.  However, and this is
> where my conceptual problem arises, Maxima seems to treat that result
> as (forgive my terminology) an 'equation' rather than a 'function',
> and further manipulation is therefore difficult.  We can examine eq2:
>
> eq2;
>
> and that does spit back x=-5*g/2.  But how can we plot this?  How can
> we differentiate it further, with respect to g say?  For example,
>
> plot2d(x, [g, 0, 10]);
>
> fails, saying that the 'function ~a is undefined', whatever that is.
> Nor does:
>
> plot2d(eq2, [g, 0, 10]);
>
> work.  I can use ev() to evaluate this equation at some g, for example:
>
> ev(eq2, g:5);
>
> does what you would expect.  I could do an explicit redifinition by typing
> this in:
>
> f(g):=-(5*g)/2;
>
> and then this plot works:
>
> plot2d(f(g), [g, 0, 10]);
>
> But that's a pain in general.  I also can't differentiate this again:
>
> diff(eq2, g);
>
> since that returns the nonsensical "0=-5/2" rather than something
> symbolically reasonable like dx/dg=-5/2, where dx/dg can be referenced
> symbolically in another computation.  (Interestingly, if I do a
> "depends(f, g)" and then do the "diff(eq2, g)", I do get the result
> dx/dg=-5/2, but I still cannot reference the dx/dg result in other
> computations as a symbol . . .)
>
> I guess the clearest statement of my conceptual problem is this:  whereas
> Maple's results seem to be treated in the same class as the stuff you type
> in directly, and these results are trivial to manipulate further and
> combine with other equations, in Maxima the results of operations seem to
> be treated as equations rather than functions, and they become difficult
> to manipulate further and I quickly get into the position of having to
> redefine functions explicitly by typing it back in as above, which is
> obviously a waste of time.
>
> Does this make sense to anyone?
>
> Thanks,
> Rich
>
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