JPI's profile - activity

Can one easily get the list of all defined functions in Sage to something like a directory including at least following information:

[

• function name
• allowed input argument numbers (possibly several)
• allowed input argument types for each allowed input argument
• function result values numbers (possibly several depending on input arguments)
• function result values types for each result value

,

• next similar etc.

]

so that for example one could easily construct an expression-set having all allowed functions in function argument places up to a given level?

For example:

Expression-set for 3 levels is something like:

[

sin(cos(x))

sin(sin(x))

sin(tan(x))

sin(x^a)

(x^a)^b

myfun(sin(k),cos(n))

etc.

];

(All combinations. Here only 3 levels given as an example. Here function myfun may have several return variables each can be a variable, vector, matrix, function name etc.)

In MATLAB one can write:

A = [1,2,3]; B = 2*A.^3;

where B gets element-wise result of the function 2*A.^3 given matrix (or vector) A.

In Sage the notation .^ does not function. How to do this in Sage?

Then how to calculate the element-wise sin(A) in Sage?

How to find polynomial p_N(n) coefficients a_i_N,

p_N(n) = sum_i ( a_i_N * n^i , i=0:N )

such that p_N(n) gives the decimals of pi (where n=0...N) up to N:th decimal place. I did not find this in Sage ready made.

Does Sage have a function or another way to do this (returning a_i_N for each p_N, N ={1,2,...})? It should be both a numerical value up to a certain precision and a symbolic accurate answer?