## #2652 integrate(sin(nx)sin(p*x),x,0,%pi) fail to consider n=p case

None
open
nobody
None
5
2014-07-30
2013-10-31
SouForje
No

As it can be seen in the attached image (maxima session within TeXmacs), maxima gives the generic result 0 when asked to compute

```integrate(sin(n*x)*sin(p*x),x,0,%pi)
```

for integers n,p>0, which is correct, EXCEPT that in the case n=p the correct result is %pi/2.

1 Attachments

## Discussion

1 2 > >> (Page 1 of 2)

• Raymond Toy
2013-10-31

The current git version returns your result in %o47 in all cases.

• SouForje
2013-10-31

Hello, Raymond. Thak you for reacting so rapidly.

On 31/10/2013 15:53, Raymond Toy wrote:

The current git version returns your result in %o47 in all cases.

Do you mean even after indicating that n and p are positive integers?

Sorry, I didn't give that basic information:

Maxima version: 5.20.1
Maxima build date: 8:48 2/16/2010
Host type: i686-pc-linux-gnu
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.7

I usually kept my Ubuntu 10 updated...

Thank you again for the attention. Of course, I would like to know if
you consider it a bug, and if/when it's repaired.

Best regards,

• José Fortes

[bugs:#2652] integrate(sin(nx)sin(p*x),x,0,%pi) fail to consider n=p case

Status: open
Created: Thu Oct 31, 2013 01:13 AM UTC by SouForje
Last Updated: Thu Oct 31, 2013 01:13 AM UTC
Owner: nobody

As it can be seen in the attached image (maxima session within TeXmacs), maxima gives the generic result 0 when asked to compute

integrate(sin(nx)sin(p*x),x,0,%pi)

for integers n,p>0, which is correct, EXCEPT that in the case n=p the correct result is %pi/2.

Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/maxima/bugs/2652/

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#### Related

• Raymond Toy
2013-10-31

Sorry, it looks like I made some kind of mistake. I get 0 now. I don't know what I did.

My guess is that because maxima knows that n and p are integers, maxima immediately simplifies sin(n%pi) and sin(m%pi) immediately to 0.

• SouForje
2013-10-31

To be precise, my installed package is

maxima-src 5.20.1-5ubuntu1

A computer algebra system -- source code

Maxima is a fully symbolic computation program. It is full featured
doing symbolic manipulation of polynomials, matrices, rational
functions, integration, Todd-coxeter methods for finite group
analysis, graphing, multiple precision floating point computation.
It has a symbolic source level debugger for maxima code. Maxima is
based on the original Macsyma developed at MIT in the 1970s. It is
quite reliable, and has good garbage collection, and no memory leaks.
It comes with hundreds of self tests.

This package contains the lisp source code.

provided by the Ubuntu community.

On 31/10/2013 23:09, jfortes wrote:

Hello, Raymond. Thak you for reacting so rapidly.

On 31/10/2013 15:53, Raymond Toy wrote:

The current git version returns your result in %o47 in all cases.

Do you mean even after indicating that n and p are positive integers?

Sorry, I didn't give that basic information:

Maxima version: 5.20.1
Maxima build date: 8:48 2/16/2010
Host type: i686-pc-linux-gnu
Lisp implementation type: GNU Common Lisp (GCL)
Lisp implementation version: GCL 2.6.7

I usually kept my Ubuntu 10 updated...

Thank you again for the attention. Of course, I would like to know if
you consider it a bug, and if/when it's repaired.

Best regards,

• José Fortes

[bugs:#2652] integrate(sin(nx)sin(p*x),x,0,%pi) fail to consider
n=p case

Status: open
Created: Thu Oct 31, 2013 01:13 AM UTC by SouForje
Last Updated: Thu Oct 31, 2013 01:13 AM UTC
Owner: nobody

As it can be seen in the attached image (maxima session within
TeXmacs), maxima gives the generic result 0 when asked to compute

integrate(sin(nx)sin(p*x),x,0,%pi)

for integers n,p>0, which is correct, EXCEPT that in the case n=p the
correct result is %pi/2.

Sent from sourceforge.net because you indicated interest in
https://sourceforge.net/p/maxima/bugs/2652/

To unsubscribe from further messages, please visit
https://sourceforge.net/auth/subscriptions/

#### Related

• I tried replying to this bug by email and nothing seems to have happened, so maybe that doesn't work. So I'm pasting in the text again. If there's some massive time delay, and we end up with two copies then I'll delete one (and sorry for spamming subscribers to the bug!) The "email" follows:

This looked interesting, so I had a quick look at my end. It looks like
the definite integral is done by taking limits of an indefinite one:

```Maxima 5.31.3 http://maxima.sourceforge.net
using Lisp GNU Common Lisp (GCL) GCL 2.6.9 (a.k.a. GCL)
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) declare (n, integer);
(%o1)                                done
(%i2) declare (p, integer);
(%o2)                                done
(%i3) integrate (sin(n*x), x, 0, %pi);
n
1   (- 1)
(%o3)                             - - ------
n     n
(%i4) integrate (sin(n*x)*sin(p*x), x, 0, %pi);
(%o4)                                  0
(%i5) ?trace(?sinint);
(%o5)                              (sinint)
(%i6) integrate (sin(n*x)*sin(p*x), x, 0, %pi);

1> (SININT ((MTIMES SIMP) ((%SIN SIMP) ((MTIMES SIMP) \$N \$X))
((%SIN SIMP) ((MTIMES SIMP) \$P \$X)))
\$X)
<1 (SININT ((MPLUS SIMP)
((MTIMES SIMP) ((RAT SIMP) 1 2)
((MEXPT SIMP) ((MPLUS SIMP) \$N ((MTIMES SIMP) -1 \$P))
-1)
((%SIN SIMP)
((MTIMES SIMP) ((MPLUS SIMP) \$N ((MTIMES SIMP) -1 \$P))
\$X)))
((MTIMES SIMP) ((RAT SIMP) -1 2)
((MEXPT SIMP) ((MPLUS SIMP) \$N \$P) -1)
((%SIN SIMP) ((MTIMES SIMP) ((MPLUS SIMP) \$N \$P) \$X)))))
(%o6)                                  0
(%i7) ?trace(?defint);
(%o7)                              (defint)
(%i8) integrate (sin(n*x)*sin(p*x), x, 0, %pi);

1> (DEFINT ((MTIMES SIMP) ((%SIN SIMP) ((MTIMES SIMP) \$N \$X))
((%SIN SIMP) ((MTIMES SIMP) \$P \$X)))
\$X 0 \$%PI)
2> (SININT ((MTIMES SIMP) ((%SIN SIMP) ((MTIMES SIMP) \$N \$X))
((%SIN SIMP) ((MTIMES SIMP) \$P \$X)))
\$X)
<2 (SININT ((MPLUS SIMP)
((MTIMES SIMP) ((RAT SIMP) 1 2)
((MEXPT SIMP) ((MPLUS SIMP) \$N ((MTIMES SIMP) -1 \$P))
-1)
((%SIN SIMP)
((MTIMES SIMP)
((MPLUS SIMP) \$N ((MTIMES SIMP) -1 \$P)) \$X)))
((MTIMES SIMP) ((RAT SIMP) -1 2)
((MEXPT SIMP) ((MPLUS SIMP) \$N \$P) -1)
((%SIN SIMP) ((MTIMES SIMP) ((MPLUS SIMP) \$N \$P) \$X)))))
<1 (DEFINT 0)
(%o8)                                  0
(%i9) integrate (sin(n*x)*sin(p*x), x);

1> (SININT ((MTIMES SIMP) ((%SIN SIMP) ((MTIMES SIMP) \$N \$X))
((%SIN SIMP) ((MTIMES SIMP) \$P \$X)))
\$X)
<1 (SININT ((MPLUS SIMP)
((MTIMES SIMP) ((RAT SIMP) 1 2)
((MEXPT SIMP) ((MPLUS SIMP) \$N ((MTIMES SIMP) -1 \$P))
-1)
((%SIN SIMP)
((MTIMES SIMP) ((MPLUS SIMP) \$N ((MTIMES SIMP) -1 \$P))
\$X)))
((MTIMES SIMP) ((RAT SIMP) -1 2)
((MEXPT SIMP) ((MPLUS SIMP) \$N \$P) -1)
((%SIN SIMP) ((MTIMES SIMP) ((MPLUS SIMP) \$N \$P) \$X)))))
sin((n - p) x)   sin((p + n) x)
(%o9)                   -------------- - --------------
2 (n - p)        2 (p + n)
(%i10)
```

I think the problem is that substitituting x=%pi or x=0 in the above
gives zero. Which is fine, except when n-p = 0.

Rupert

• SouForje
2013-11-01

On 31/10/2013 23:46, Raymond Toy wrote:

Sorry, it looks like I made some kind of mistake. I get 0 now. I don't know what I did.

Thank you for recognizing this immediately, I was going right now trying
to manually install the latest version (which of course is always a good
idea), but now I see that it's low priority, and I'll go instead to my
online course on quantum mechanics!

My guess is that because maxima knows that n and p are integers, maxima immediately simplifies sin(n%pi) and sin(m%pi) immediately to 0.

I see. But the fact that the denominator may be 0 when n=m should
trigger, I think, to consider separetely that particular case /in the
original integral/. Of course, I don't know if that's easy or feasible.

Thank you again!

• José

[bugs:#2652] integrate(sin(nx)sin(p*x),x,0,%pi) fail to consider n=p case

Status: open
Created: Thu Oct 31, 2013 01:13 AM UTC by SouForje
Last Updated: Thu Oct 31, 2013 03:53 PM UTC
Owner: nobody

As it can be seen in the attached image (maxima session within TeXmacs), maxima gives the generic result 0 when asked to compute

integrate(sin(nx)sin(p*x),x,0,%pi)

for integers n,p>0, which is correct, EXCEPT that in the case n=p the correct result is %pi/2.

Sent from sourceforge.net because you indicated interest in https://sourceforge.net/p/maxima/bugs/2652/

To unsubscribe from further messages, please visit https://sourceforge.net/auth/subscriptions/

#### Related

• José,
thanks for reporting this bug with integrate. As it might take some time to be fixed, in the meantime that kind of problem can be avoided as follows:

```(%i2) r: integrate(sin(n*x)*sin(p*x),x,0,%pi);
(%o2) -((p-n)*sin(%pi*p+%pi*n)+(-p-n)*sin(%pi*p-%pi*n))/(2*p^2-2*n^2)

(%i3) s: limit (r,n,p);
(%o3) %pi/2-sin(2*%pi*p)/(4*p)

(%i4) declare(p,integer)\$
(%i5) ev(s);
(%o5) %pi/2
```

Cheers,
Jaime

Last edit: Jaime E. Villate 2013-11-01
• Description has changed:

Diff:

```--- old
+++ new
@@ -1,5 +1,5 @@
As it can be seen in the attached image (maxima session within TeXmacs), maxima gives the generic result 0 when asked to compute

-integrate(sin(n*x)*sin(p*x),x,0,%pi)
+    integrate(sin(n*x)*sin(p*x),x,0,%pi)

for integers n,p>0, which is correct, EXCEPT that in the case n=p the correct result is %pi/2.
```

• SouForje
2013-11-01

OK! Thanks, Jaime. Saludos -José

• SouForje
2013-11-06

If anyone was curious, Maple 16 and Mathematica 8 have the same bug!
This is not to say that it shouldn't be repaired in Maxima!

Last edit: SouForje 2013-11-06
1 2 > >> (Page 1 of 2)