1 Apr 06:34 2008

### Maxima 5.15 release branch scheduled for April 5

```Hello,

I am planning to make the 5.15 release branch on April 5
(probably circa 12h--18h UTC).

Keeping the world informed

Robert Dodier
```
1 Apr 09:03 2008

### Re: is it a bug in sum?

```On Mon, Mar 31, 2008 at 10:01 PM, laurent couraud <l.couraud <at> free.fr> wrote:
>  simpsum:true\$
>  sum((x[i]-sum(x[i],i,1,n)/n)^2,i,1,n)
>
>  The result is 0.

I don't have Maxima where I am (travelling), but I imagine that using
the same index names for the inner and outer sums will cause problems
(and is not standard mathematical usage either).

Try using j as the inner index, for example.

-s
```
1 Apr 12:40 2008

### Re: is it a bug in sum?

```Stavros is correct; with distinct sum indices, it works:

(%i6) sum((x[j]-sum(x[i],i,1,n)/n)^2,j,1,n);
(%o6) sum((x[j]-sum(x[i],i,1,n)/n)^2,j,1,n)

(%i7) ev(%,n=2,'sum);
(%o7) (x[2]-(x[2]+x[1])/2)^2+(x[1]-(x[2]+x[1])/2)^2

Barton

-----maxima-bounces <at> math.utexas.edu wrote: -----

>Try using j as the inner index, for example.
>
>        -s
```
1 Apr 15:21 2008

### FW: benchmarking CAS

```
> -----Original Message-----
> From: Roman Pearce [mailto:rpearcea <at> gmail.com]
> Sent: Monday, March 31, 2008 8:43 PM
> To: rjf
> Subject: Re: benchmarking CAS
>
> > Are you saying that if the polynomials were small, Maple
> would not use
> > the same routines and would not run with garbage collection?
>
> That's correct.  For small polynomials Maple expands and divides
> products in the kernel, using compiled C code that runs without
> garbage collection.  For large problems the kernel calls back into the
> Maple library, to the routines  `expand/bigprod` and `expand/bigdiv`
> and `expand/bigpow`.  These routines are recursive, interpreted Maple
> code that run with garbage collection.  That's why in your paper on
> sparse multiplication Maple 7 was found to be much slower than
> MapleVR4, etc.  They had to change it because for their algorithms,
> doing a big problem without garbage collection will crash the system.
>
> On 3/30/08, rjf <fateman <at> gmail.com> wrote:
> > On Mar 29, 6:28 pm, Roman Pearce <rpear... <at> gmail.com> wrote:
> >
> > >
> > > Because the polynomials are large, Maple uses interpreted routines
> > > that run with garbage collection.
> >
> > Are you saying that if the polynomials were small, Maple
> would not use
```

1 Apr 17:13 2008

### Re: is it a bug in sum?

```On 4/1/08, Stavros Macrakis <macrakis <at> alum.mit.edu> wrote:

> I don't have Maxima where I am (travelling), but I imagine that using
>  the same index names for the inner and outer sums will cause problems
>  (and is not standard mathematical usage either).

Well, as it stands, the sum-simplfication code attempts to treat
the summation index as a local variable, although it messes up
this problem.

(%i1) trace (?simpsum2, ?simpsum1, ?simpsum1\-save);
(%o1)          [simpsum2, simpsum1, simpsum1-save]
(%i2) display2d : false;
(%o2) false
(%i3) sum ((x[j] - sum (x[j], j, 1, n)/n)^2, j, 1, n);
1 Enter ?simpsum1 [x[?g15869],?g15869,1,n]
1 Exit  ?simpsum1 'sum(x[?g15869],?g15869,1,n)
1 Enter ?simpsum1 [x[?g15869],?g15869,1,n]
1 Exit  ?simpsum1 'sum(x[?g15869],?g15869,1,n)
1 Enter ?simpsum1 [x[j],j,1,n]
1 Exit  ?simpsum1 'sum(x[j],j,1,n)
1 Enter ?simpsum1 [(x[j]-('sum(x[j],j,1,n))/n)^2,j,1,n]
1 Exit  ?simpsum1 'sum((x[j]-('sum(x[j],j,1,n))/n)^2,j,1,n)
(%o3) 'sum((x[j]-('sum(x[j],j,1,n))/n)^2,j,1,n)
(%i4) %, simpsum;
1 Enter ?simpsum1 [x[?g15929],?g15929,1,n]
1 Enter ?simpsum1\-save [x[?g15929],?g15929,1,n]
1 Enter ?simpsum2 [x[?g15929],?g15929,1,n]
2 Enter ?simpsum1 [x[?g15929],?g15929,1,n]
2 Exit  ?simpsum1 'sum(x[?g15929],?g15929,1,n)
```

1 Apr 17:14 2008

### Re: vector geometrie

```On Monday 31 March 2008 17:25, Hans W. Hofmann wrote:

> I am searching for some macros to handle vector geometrie inclusive
> plotting. Is there a pending project or exist here some people zu start a
> project? As rookie in programming macros I want to discuss the basics and
> structur of a vector geometrie macros preferably in german-english .
>
> Some thoughts:
> Points should described as a list [y,x,z] and vectors as matrix
> matrix([x],[y],[z]).
> I tend to have e.g. a line object, pardon, will say a line list, which
> covers all/some details of describing/plotting a line. Input wellcome...

As far as I know, there are no special packages for analytic geometry, but
basic functions and linear algebra stuff are enough, I think. Introducing new
objects may produce more mess than advantages.

In vector calculus code, Maxima represents vectors as lists; "listarith" works
with lists in appropriate way. Vector plotting is already implemented in
draw2d / draw3d.

--

--
Alexey Beshenov <al <at> beshenov.ru>
http://beshenov.ru/
```
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```

1 Apr 18:55 2008

### besselarray?

```
Maxima has the variable besselarray.  It's no longer documented, but I
think it used to contain the values of the bessel functions since the
computation of a bessel function oftentimes computes the value of the
bessel function for all lower orders.

Bug 1920177
<https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1920177&group_id=4933>
has several fixes, and the besselarray, besides being currently
broken, also complicates the implementation a bit.

I guess it's important if you're using Fourier-Bessel expansions or
something like that, but perhaps we should provide a different
interface if you want the sequence of values.

Should we keep besselarray around?

Ray
```
1 Apr 19:09 2008

### Re: cardioid

```Hi

1. I think that in polar form cardioid:
e1:exp(t*%i)/2-exp(2*t*%i)/4;

can't be drawn since polar plots have "center " in point 0 (
This cardioid really has radius equation:
r:  (1-cos(theta))/2;

but it has to be moved to the right 1/4 unit.
It can't be done in polar form

2. You say: "You're converting expression to polar form incorrectly."
Can you show me how to do it correctly ?

Regards

```
1 Apr 20:15 2008

### Re: A partfrac limitation

Dear All, I have the same problem with partfrac like Albert Reiner had:

kovzol <at> pascal:~\$ maxima
Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp CLISP 2.38 (2006-01-24)
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(%i2) my_partfrac(e, x) := partfrac(num(e)/factor_with_solve(e, x), x)\$
(%i3) my_partfrac(1/(x^4+20*x^2+120), x);
Division by 0
#0: my_partfrac(e=1/(x^4+20*x^2+120),x=x)(simplify_sum.mac line 511)
-- an error.  To debug this try debugmode(true);

Am I using a too old version of Maxima?

Best regards, Zoltan

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Maxima <at> math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima
```
1 Apr 20:58 2008

### Re: A partfrac limitation

Hi Zoltan, I think that there should be denom(e)

my_partfrac(e, x) := partfrac(num(e)/factor_with_solve(denom(e), x), x)\$

Another problem is that factor_with_solve factors over complex numbers. I used the following:
(factor_with_solve_real is very close to factor_with_solve but gives factorization over reals)

factor_with_solve_real(expr, n) := block(
[sol, fac, expr1],
sol : solve(expr, n),
expr : ratexpand(expr),
fac : ratcoef(expr, n, hipow(expr, n)),
for i:1 thru length(sol) do (
if not(freeof(n, rhs(sol[i]))) then error(),
if imagpart(rectform(rhs(sol[i])))=0 then
fac : fac * (n - rhs(sol[i]))^multiplicities[i]
else
(if imagpart(rectform(rhs(sol[i])))>0 then
fac: fac*(ratsimp(expand((n-rhs(sol[i]))*(n-conjugate(rhs(sol[i]))))))^multiplicities[i])

),
if expand(expr)#expand(fac) then error(),
fac
)\$

my_partfrac(e, x) := partfrac(num(e)/factor_with_solve_real(denom(e), x), x);

Robert M.

On Tue, Apr 1, 2008 at 8:15 PM, Kovács Zoltán <kovzol <at> matek.hu> wrote:
Dear All, I have the same problem with partfrac like Albert Reiner had:

kovzol <at> pascal:~\$ maxima
Maxima 5.13.0 http://maxima.sourceforge.net
Using Lisp CLISP 2.38 (2006-01-24)
Dedicated to the memory of William Schelter.
This is a development version of Maxima. The function bug_report()
provides bug reporting information.
(%i2) my_partfrac(e, x) := partfrac(num(e)/factor_with_solve(e, x), x)\$
(%i3) my_partfrac(1/(x^4+20*x^2+120), x);
Division by 0
#0: my_partfrac(e=1/(x^4+20*x^2+120),x=x)(simplify_sum.mac line 511)
-- an error.  To debug this try debugmode(true);

Am I using a too old version of Maxima?

Best regards, Zoltan

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```_______________________________________________
Maxima mailing list
Maxima <at> math.utexas.edu
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```

Gmane