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## Re: [Axiom-developer] [Axiom-mail] manipulating series not as streams bu

 From: Raymond Rogers Subject: Re: [Axiom-developer] [Axiom-mail] manipulating series not as streams but as sumations Date: Tue, 21 Oct 2014 14:50:00 -0400 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.2.0

```
On 10/21/2014 04:39 PM, Raymond Rogers wrote:
```
```Let's think about this.
I think the question can be interpreted as a formating/display problem
for the underlying code.
```
```
If you believe so... Let me state it a bit differently what
datastructure comes out of the series command. Or rather what is stored
inside the data structure.

Here an example:

(1) -> Z==>Integer; Q==>Fraction Z;
Type:
Void
(2) -> f(q:Q):Q == truncate(abs(q*cos(q::Float))+1)*(q/2+1)

Function declaration f : Fraction(Integer) -> Fraction(Integer) has
Type:
Void
(3) -> s: Stream Q := stream(f, 0)
Compiling function f with type Fraction(Integer) -> Fraction(Integer
)

3 7 15 31 63 127 255 511
(3)  [0,1,-,-,--,--,--,---,---,---,...]
2 4  8 16 32  64 128 256
Type:
Stream(Fraction(Integer))
(4) -> p:=series(s)\$UnivariateFormalPowerSeries(Q)

(4)
3  2   7  3   15  4   31  5   63  6   127  7   255  8   511  9
x + - x  + - x  + -- x  + -- x  + -- x  + --- x  + --- x  + --- x
2      4       8      16      32       64      128      256
+
1023  10      11
---- x   + O(x  )
512
Type:
UnivariateFormalPowerSeries(Fraction(Integer))

The only thing that s (the Stream) knows is a function object f (if you
like you can use f=random). It cannot look inside f except to ask for
more values. Remember AXIOM code is compiled.

If from that you would somehow be able to extract a pattern, great, but
I doubt.

```
```Of course I am not that familiar with the Axiom internals.
```
```
Well, you might come from another CAS. AXIOM *is* different. It is in
general *not* dealing with expression trees. So what you have in mind
(adding presentation) does not work for Stream of Series.

That is not saying that it is impossible, but rather that the Stream and
PowerSeries domains are not appropriate for what you have in mind. (And
at the moment I don't think there is anything like what you want in Axiom.)

Ralf

```