1 Nov 16:06 2011

### Treat inequalities like equations?

```(%i121) y=m*x+b;
(%o121)                           y = m x + b
(%i122) %-b;
(%o122)                           y - b = m x

but

(%i123) y<m*x+b;
(%o123)                           y < m x + b
(%i124) %-b;
(%o124)                        (y < m x + b) - b
(%i125) %,expand;
(%o125)                        (y < m x + b) - b

Can we handle inequalities like this any better?
```
1 Nov 19:38 2011

### strange question when using interface to integrate

```I am trying to start an isolation of integrate
behavior, error messages, etc.
from the nint.mac user, and have a short
function called nint_integrate. It only uses
the function complex_number_p defined
in nint.lisp.

I get the question: "is 1 zero or nonzero? ",
when the integrand is bessel_i(1,%i*x) and
integrating over (1,inf).

As an experiment, I also tried using
bessel_i(1.0,%i*x), which produced
a different error message:
"integrate: variable must not be a number; found: 1".

--------------------------
Maxima 5.25.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
2011-11-01

(%o1) "c:/work2/temp.mac"

(%i2) nint_integrate(bessel_i(1,%i*x),x,1,inf);
Is  1  zero or nonzero?

```

1 Nov 20:02 2011

### rectform strange question, was: strange question when using interface to integrate

```On Nov. 1, 2011, I wrote:
-----------------------
>I get the question: "is 1 zero or nonzero? ",
>when the integrand is bessel_i(1,%i*x) and
>integrating over (1,inf).
>
>(%i2) nint_integrate(bessel_i(1,%i*x),x,1,inf);
>Is  1  zero or nonzero?
>
>nonzero;
>defint: integral is divergent.
>#0: nint_integrate(ue=bessel_i(1,%i*x),uvar=x,ua=1,ub=inf)
> -- an error. To debug this try: debugmode(true);
-------------------------

debug printouts now show this question
comes from rectform:

----------------------------------------
Maxima 5.25.1 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
2011-11-01

(%i1) display2d:false\$
(%i2) rectform(%i*bessel_i(0,%i*inf));
Is  1  zero or nonzero?

```

1 Nov 21:19 2011

### Re: rectform strange question

```On Nov. 1, 2011, I wrote:
--------------------------
>debug printouts now show this question
>comes from rectform:
>
>(%i2) rectform(%i*bessel_i(0,%i*inf));
>Is  1  zero or nonzero?
>
>nonzero;
>(%o2) %i*bessel_i(0,%i*inf)
-------------------------------------
This doesn't happen if I use limit inside the
code, which replaces %i*inf by infinity.
-------------------------------------
(%o7) "c:/work2/temp.mac"
(%i8) nint_integrate(bessel_i(1,%i*x),x,1,inf);
vx = %i*bessel_i(0,%i*x)

vxop = "*"

vxa = %i*bessel_i(0,%i)

vxa = 0.76519768655797*%i

vxb = %i*bessel_i(0,infinity)

vxb = %i*'realpart(bessel_i(0.0,infinity))
-1.0*'imagpart(bessel_i(0.0,infinity))

```

2 Nov 05:32 2011

### Re: got error when try to run calculation

Dear Raymond Toy and Maxima users,

I already update my clisp to 2.49 but still can't run my code given before...
1 questions, what is maxima cvs?is it different with standard maxima for ubuntu?

On Tue, Oct 25, 2011 at 12:14 PM, Raymond Toy wrote:
On 10/24/11 8:43 PM, razif razali wrote:
> ok here i attach the file,
>
> braket.mac i put in /usr/local/share/maxima/5.24.0/share/ folder,
>
> then in maxima i give below command,
>

I didn't have any problems with this using maxima cvs and clisp 2.49.

Do you have any information on exactly where the problem is occurring?
I did notice that I can't load pnn_4 twice because tellsimp complains
about circular rules, which I guess is true.

Ray

--
Regards,

RAZIF RAZALI,
Tutor & Master Student,
Physics Department,
Faculty Of Science,
Universiti Teknologi Malaysia(UTM).
+60199393606

```_______________________________________________
Maxima mailing list
Maxima <at> math.utexas.edu
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```
2 Nov 05:56 2011

### Re: Treat inequalities like equations?

```There is a share package, ineq, which might be helpful.

ineq is not too complicated -- it defines simplifications rules
(via tellsimp and tellsimpafter) for some basic operations on
inequalities. Maybe it's enough, I don't know.

Hope this helps,

Robert Dodier
```
2 Nov 06:06 2011

### Re: Re-implementing R in Maxima

On 10/31/11 11:42 AM, Stavros Macrakis wrote:
On Mon, Oct 31, 2011 at 13:38, Raymond Toy wrote:
I also notice that ratepsilon is still 2e-8, even though maxima has been using double precision for years (decades?) now.

Argh!  I thought we'd agreed multiple times (starting at least as long ago as 2005) that ratepsilon should be much smaller, say 2.0e-15 (about 9 ulps).  This is plenty of slop for returning "nice" rationals in the face of rounding error.

It's been finally changed to 2d-15, after all these years.

No problems with the testsuite, FWIW.

Ray

```_______________________________________________
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```
2 Nov 06:08 2011

### Re: got error when try to run calculation

```On 11/1/11 9:32 PM, razif razali wrote:
> Dear Raymond Toy and Maxima users,
>
> I already update my clisp to 2.49 but still can't run my code given
> before...
> 1 questions, what is maxima cvs?is it different with standard maxima
> for ubuntu?
I guess it's not maxima cvs anymore.  I meant the current version of
maxima in the sourceforge git repository.  I'm pretty sure this is
different from what ubuntu has.

Sorry, I haven't done anything more with your code.

Ray
```
2 Nov 13:38 2011

### Re: Treat inequalities like equations?

```Cool! "ineq" seems to do nearly everything that I wanted.  Thank you!

This sort of behavior on inequalities seems pretty orthogonal to the rest of Maxima.  How come Maxima can't
just incorporate it into the standard mechanisms?  I would be surprised if it broke anything.

At 09:56 PM 11/1/2011, Robert Dodier wrote:
>There is a share package, ineq, which might be helpful.
>
>ineq is not too complicated -- it defines simplifications rules
>(via tellsimp and tellsimpafter) for some basic operations on
>inequalities. Maybe it's enough, I don't know.
>
>Hope this helps,
>
>Robert Dodier
```
2 Nov 14:42 2011

### Re: Treat inequalities like equations?

ineq is not particularly robust or general.

For example:

(a=b)*(c=d) => a*c = b*d (base Maxima, OK)
With ineq, (a=b)*(c<d) asks if a and b are PNZ (second question is redundant) and returns
a*c<a*d = (b*c<b*d)  (?!); I'd think this should be a*c < b*d (if a>=0)

(a<b)*(c<d) => is a<b PNZ (nonsense question) => (a<b)*c < (a<b)*d (nonsense value).  This should presumably either be returned unmodified or as a*c<b*d (if signs are appropriate).

0*(a<b) => 0  -- not clear what this should be, but probably not 0

but

assume(equal(q,0))\$
q*(a<b) => q*(a<b)    -- again, not clear what this should be

Of course, base Maxima doesn't do too well, either, for equation manipulation:

exp(a=b) => exp(a=b), not exp(a)=exp(b)

Ineq also slows down simplification:

(%i8) expand((a+b+a*b-2)^50)\$
Evaluation took 0.9830 seconds (1.0200 elapsed)
tellsimp: warning: putting rules on '+' or '*' is inefficient, and may not work.
...(%i10) expand((a+b+a*b-2)^50)\$
Evaluation took 2.0750 seconds (2.0940 elapsed)

-s

On Wed, Nov 2, 2011 at 08:38, Henry Baker wrote:
Cool! "ineq" seems to do nearly everything that I wanted.  Thank you!

This sort of behavior on inequalities seems pretty orthogonal to the rest of Maxima.  How come Maxima can't just incorporate it into the standard mechanisms?  I would be surprised if it broke anything.

At 09:56 PM 11/1/2011, Robert Dodier wrote:
>There is a share package, ineq, which might be helpful.
>
>ineq is not too complicated -- it defines simplifications rules
>(via tellsimp and tellsimpafter) for some basic operations on
>inequalities. Maybe it's enough, I don't know.
>
>Hope this helps,
>
>Robert Dodier

_______________________________________________
Maxima mailing list
Maxima <at> math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima

```_______________________________________________
Maxima mailing list
Maxima <at> math.utexas.edu
http://www.math.utexas.edu/mailman/listinfo/maxima
```

Gmane