#143 asymptotic expansion, formating output, genmatrix help, variables change in diff

[Mikhail Veysman]

I propose some improvement of Maxima:

1) the command genmatrix() creates matrix, which will not change if you change the parameters, which this matrix depends on. For example, if you input

beta:5
maa[i,j]:= f(i,j,beta)$
Ma:genmatrix(maa,6,6)$

and change beta from 5 to 7, this will not influence on the matrix Ma. To turn on the possibility of changes, you should write:

beta:5
maa[i,j]:= f(i,j,beta)$
Ma:genmatrix(maa,6,6)$
kill(maa)

I propose to describe this situation in Maxima help !

2) Again, speaking about the help system: from it's present version it is impossible to understand, how to use format output using the command printf, as long as there is nor clear and full description of the respective rules of formatting with respective examples. For users, not familiar with lisp language it's impossible to understand. I propose to add the respective information

3) Againe question about formatting: currently Maxima uses some intrinsic default representation of the floating point numbers. For example, any numbers greater than 99 are represented in exponential format in the maxima output. I propose to make the possibility to change the default representation! (say, using g-like format).

4) In the present version of Maxima it's impossible to make asymptotic analyses: taylor series doesn't work at infinity point (use taylor(bessel_j(0,x),x,inf,4); for example, doesn't work, while in CAS system Maple the command like asympt(BesselJ(0, x), x, 4) gives the answer).

The package "asympa" for asymptotic analyses is declared, but it's impossible to find the description of this package in the internet!

5) very often one have to change variables in differential equations. Presently, it's impossible to do in Maxima! For example,

eq1:diff(F(x),x,2);
eq2:subst(t^2,x,eq1);

or

depends(x,t);
diff(F(x(t)),t,2);

or something like

diff(F(t^3),t,2);

(if we want to substitute x by t^3, for example) dont' give rise to desired result!

Is it possible to introduce change of variables in differential equations into Maxima ?