Re: [Maxima-discuss] Stair function

[Jaime V. <vi...@fe...>]

On 06/04/24 19:30, Jaime Villate via Maxima-discuss wrote:
> stair(f,n,a,b):=block
>    ([r:[[a,f(a)]], s:(b-a)/n, y: f(a)],
>     for x:a+s thru b step s do
>       (r: append(r, [[x, y], [x, f(x)]]), y: f(x)),
>     r)$
> f(x):=1/(1+x)$
> plot2d([f,[discrete, f,10,0,1)]], [x,0,1], nolegend);

Please keep in mind that this is a hack for this case but should be used 
with caution.

If I now write:

g(x):=sin(x)$
plot2d([g,[discrete, stair(g,10,0,%pi)]], [x,0,%pi], nolegend);

the plot shows the function sin(x) but the stair for function 
f(x):=1/(1+x), because f is not really an input parameter for function 
stair, but it has been "hard-coded" into that function. It is usually 
easier to deal with expressions than with functions, which is the 
approach used in the command staircase in share/dynamics/dynamics.mac.

How about

f(x):=sin(x)$
plot2d([f,[discrete, stair(f,10,0,%pi)]], [x,0,%pi], nolegend);

it shows the correct stair corresponding to sin(x) but that stair is 
below the function, where the function is increasing, and above the 
function once it starts decreasing, which is probably not what we would 
want.

Regards,

Jaime