[Maxima-discuss] Feature request: step by step, an error & not simplified...

[Jérémy B. <jer...@gm...>]

Stavros Macrakis do you mean
https://maxima.sourceforge.io/docs/manual/maxima_singlepage.html#Item_003a-Debugging_002fdeffn_002ftrace
?

E.g. inverse a function:

(%i1) assume(0<a,0<b,b<1,0<c,0<=x,x<=%pi);
y(x):=(a^(1/2)*(1-b*cos(x))^2)/c^(3/2);
trace(all);
solve(y=y(x),x);
(%o1)           [a > 0, b > 0, b < 1, c > 0, x >= 0, x <= %pi]
(%i2)
                                  1/2               2
                                 a    (1 - b cos(x))
(%o2)                    y(x) := ────────────────────
                                          3/2
                                         c
(%i3)
(%o3)                                 [y]
(%i4)
1 Call   y [x]
                                 2
           sqrt(a) (1 - b cos(x))
1 Return y ───────────────────────
                     3/2
                    c

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
                         3/4                         3/4
                        c    sqrt(y)   1            c    sqrt(y)   1
(%o4)   [x = %pi - acos(──────────── - ─), x = acos(──────────── + ─)]
                            1/4        b                1/4        b
                           a    b                      a    b

The 2nd result x is an error: it assumes the step
1-b*cos(x)=±y^(1/2)*c^(3/4)/a^(1/4)
but it is only
1-b*cos(x)=y^(1/2)*c^(3/4)/a^(1/4)

The 1st result x is true but not simplified: 2 instances of b & that
complication with pi, the simplified result:
x=acos((1-y^(1/2)*c^(3/4)/a^(1/4))/b)

Although trace(all); no step (with 1 wrong)...

I dream of e.g.:

step(all);
assume(0<a,0<b,b<1,0<c,0<=x,x<=%pi);
solve((a^(1/2)*(1-b*cos(x))^2)/c^(3/2)=y,x);

(1-b*cos(x))^2=y*c^(3/2)/a^(1/2)
1-b*cos(x)=y^(1/2)*c^(3/4)/a^(1/4)
b*cos(x=1-y^(1/2)*c^(3/4)/a^(1/4)
cos(x)=(1-y^(1/2)*c^(3/4)/a^(1/4))/b
x=acos((1-y^(1/2)*c^(3/4)/a^(1/4))/b)

Dear developers, you have work...

So now, step by step would be nice for verification... & also what I mean
in my 1st email are:
I like not to get a result without knowing where it comes from, without
step by step,
& you can still learn from a complicated software, e.g. a tip we would not
have thought of.