Re: [Axiom-mail] manipulating series not as streams but as sumations

2014-10-21 Thread Ralf Hemmecke 
On 10/21/2014 05:58 AM, Gustavo Goretkin wrote:
 Is it possible to get out of
 
 series(sin(x),x=0)
 
 an object that looks more like sum_n=0^n=\infty  (-1)ˆn * x^(2n+1) /
 (2n+1)! than
 
 x - (1/6)x^3 + (1/120) x^5 
 
 If this is documented somewhere, I'd appreciate a pointer!

I don't exactly understand what you mean. I get the following, and you
certainly get the same.

=
$ fricas -nosman
Checking for foreign routines
AXIOM=/home/hemmecke/g/fricas-bisect/install/lib/fricas/target/x86_64-unknown-linux
spad-lib=/home/hemmecke/g/fricas-bisect/install/lib/fricas/target/x86_64-unknown-linux/lib/libspad.so
foreign routines found
openServer result -2
   FriCAS Computer Algebra System
  Version: FriCAS d8caf7978e4e8a5775ed13bcc847c8d3a01b2c2e
  Timestamp: Sun Sep  7 12:43:55 CEST 2014
-
   Issue )copyright to view copyright notices.
   Issue )summary for a summary of useful system commands.
   Issue )quit to leave FriCAS and return to shell.
-

(1) - s := series(sin(x),x=0)

1  31   5 1   7  19   1 11  12
   (1)  x - - x  + --- x  -  x  + -- x  -  x   + O(x  )
6  120  5040  362880  39916800
   Type:
UnivariatePuiseuxSeries(Expression(Integer),x,0)
(2) - coefficient(s,42)

   (2)  0
Type:
Expression(Integer)
(3) - coefficient(s,43)

1
   (3)  - -
  604152630633738356373551320685139975072645120
Type:
Expression(Integer)

=

Yes, AXIOM treats a series (in contrast to Maple or Mathematica) as an
infinite object, i.e. the internal structure is such that any
coefficient of this series can be extracted from s.

See for example Chapter 1.11 in the Book.
http://hemmecke.de/fricas/book.pdf
Also Chapter 8.9 might help.

Ralf

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Re: [Axiom-mail] manipulating series not as streams but as sumations

2014-10-21 Thread Ralf Hemmecke 
On 10/21/2014 05:58 AM, Gustavo Goretkin wrote:
 Is it possible to get out of
 
 series(sin(x),x=0)
 
 an object that looks more like sum_n=0^n=\infty  (-1)ˆn * x^(2n+1) /
 (2n+1)! than
 
 x - (1/6)x^3 + (1/120) x^5 

Ooops, sorry, I haven't read carefully enough.

The answer is no. At least the series command isn't doing that.
Internally a series is stored (more or less) as the list of coefficients
plus a function to extract the next coefficient. Yes there is a
function object, but there is no explicit expression like

  (-1)ˆn * x^(2n+1) / (2n+1)!

stored internally.

Ralf

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