Hi,

> How to I define the natural logarithm in FriCAS?

It depends on what you mean. FriCAS deals with symbolics, so you can type.

(7) -> exp(log x)

   (7)  x
                           Type: Expression(Integer)

(9) -> log exp x

   (9)  x

So, obviously, log is the name of the natural logarith in FriCAS.

If you enter floating point numbers as argument, you get floating point
results.

(10) -> log(2.0)

   (10)  0.6931471805_5994530942

> How do I draw the graph N(x)=-x^2+20x?

draw(-x^2+20*x, x=0..20)

> Is it possible to do more advanced calculations with vectors etc.?

Yes. Vectors is easy. There's even more. Look at the examples at

http://fricas.github.io/

You find plenty of examples in the FriCAS book.
http://fricas.github.io/book.pdf

Ralf

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