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Jul 1, 2010, 5:45:34 PM7/1/10

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Hi!

I'm working on modeling drums with bessel functions. However, I need

to calculate the zeroes of the bessel functions. Is there any way to

do that?

Thank you very much.

I'm working on modeling drums with bessel functions. However, I need

to calculate the zeroes of the bessel functions. Is there any way to

do that?

Thank you very much.

Jul 1, 2010, 7:02:28 PM7/1/10

to sage-s...@googlegroups.com

On 7/1/2010 4:45 PM, Jaasiel Ornelas wrote:

> I'm working on modeling drums with bessel functions. However, I need

> to calculate the zeroes of the bessel functions. Is there any way to

> do that?

> I'm working on modeling drums with bessel functions. However, I need

> to calculate the zeroes of the bessel functions. Is there any way to

> do that?

I'm not sure if this is the best way, but you could try, e.g.,

sage: import scipy.special

sage: [x for x in dir(scipy.special) if 'zero' in x]

['ai_zeros', 'bei_zeros', 'beip_zeros', 'ber_zeros', 'berp_zeros',

'bi_zeros', 'erf_zeros', 'flatnonzero', 'fresnel_zeros',

'fresnelc_zeros', 'fresnels_zeros', 'jn_zeros', 'jnjnp_zeros',

'jnp_zeros', 'jnyn_zeros', 'kei_zeros', 'keip_zeros', 'kelvin_zeros',

'ker_zeros', 'kerp_zeros', 'nonzero', 'trim_zeros', 'y0_zeros',

'y1_zeros', 'y1p_zeros', 'yn_zeros', 'ynp_zeros', 'zeros', 'zeros_like']

sage: scipy.special.jn_zeros?

sage: scipy.special.jn_zeros(int(0), int(3)).tolist()

[2.4048255576957724, 5.5200781102863106, 8.6537279129110125]

List of scipy.special functions:

http://www.scipy.org/SciPyPackages/Special

Possibly naive questions:

* Are there analogous arbitrary-precision routines in or wrapped by Sage?

* Is it possible to call these GSL functions easily from Sage:

http://www.gnu.org/software/gsl/manual/html_node/Zeros-of-Regular-Bessel-Functions.html

?

Jul 4, 2010, 2:25:02 AM7/4/10

to sage-s...@googlegroups.com

On 7/1/10 4:02 PM, Pat LeSmithe wrote:

> On 7/1/2010 4:45 PM, Jaasiel Ornelas wrote:

>> I'm working on modeling drums with bessel functions. However, I need

>> to calculate the zeroes of the bessel functions. Is there any way to

>> do that?

>

> I'm not sure if this is the best way, but you could try, e.g.,

>

> sage: import scipy.special

> sage: [x for x in dir(scipy.special) if 'zero' in x]

> ['ai_zeros', 'bei_zeros', 'beip_zeros', 'ber_zeros', 'berp_zeros',

> 'bi_zeros', 'erf_zeros', 'flatnonzero', 'fresnel_zeros',

> 'fresnelc_zeros', 'fresnels_zeros', 'jn_zeros', 'jnjnp_zeros',

> 'jnp_zeros', 'jnyn_zeros', 'kei_zeros', 'keip_zeros', 'kelvin_zeros',

> 'ker_zeros', 'kerp_zeros', 'nonzero', 'trim_zeros', 'y0_zeros',

> 'y1_zeros', 'y1p_zeros', 'yn_zeros', 'ynp_zeros', 'zeros', 'zeros_like']

> sage: scipy.special.jn_zeros?

> sage: scipy.special.jn_zeros(int(0), int(3)).tolist()

> [2.4048255576957724, 5.5200781102863106, 8.6537279129110125]

>

> List of scipy.special functions:

>

> http://www.scipy.org/SciPyPackages/Special

>

> Possibly naive questions:

>

> * Are there analogous arbitrary-precision routines in or wrapped by Sage?

> On 7/1/2010 4:45 PM, Jaasiel Ornelas wrote:

>> I'm working on modeling drums with bessel functions. However, I need

>> to calculate the zeroes of the bessel functions. Is there any way to

>> do that?

>

> I'm not sure if this is the best way, but you could try, e.g.,

>

> sage: import scipy.special

> sage: [x for x in dir(scipy.special) if 'zero' in x]

> ['ai_zeros', 'bei_zeros', 'beip_zeros', 'ber_zeros', 'berp_zeros',

> 'bi_zeros', 'erf_zeros', 'flatnonzero', 'fresnel_zeros',

> 'fresnelc_zeros', 'fresnels_zeros', 'jn_zeros', 'jnjnp_zeros',

> 'jnp_zeros', 'jnyn_zeros', 'kei_zeros', 'keip_zeros', 'kelvin_zeros',

> 'ker_zeros', 'kerp_zeros', 'nonzero', 'trim_zeros', 'y0_zeros',

> 'y1_zeros', 'y1p_zeros', 'yn_zeros', 'ynp_zeros', 'zeros', 'zeros_like']

> sage: scipy.special.jn_zeros?

> sage: scipy.special.jn_zeros(int(0), int(3)).tolist()

> [2.4048255576957724, 5.5200781102863106, 8.6537279129110125]

>

> List of scipy.special functions:

>

> http://www.scipy.org/SciPyPackages/Special

>

> Possibly naive questions:

>

> * Are there analogous arbitrary-precision routines in or wrapped by Sage?

You could also use mpmath to calculate the roots:

http://mpmath.googlecode.com/svn/tags/0.15/doc/build/functions/bessel.html?highlight=bessel

(specifically, see the example "Roots of Bessel functions are often used:")

Jason

Jul 4, 2010, 4:40:52 AM7/4/10

to sage-s...@googlegroups.com

On 07/ 4/10 07:25 AM, Jason Grout wrote:

> You could also use mpmath to calculate the roots:

>

> http://mpmath.googlecode.com/svn/tags/0.15/doc/build/functions/bessel.html?highlight=bessel

>

>

> (specifically, see the example "Roots of Bessel functions are often used:")

>

> Jason

> You could also use mpmath to calculate the roots:

>

> http://mpmath.googlecode.com/svn/tags/0.15/doc/build/functions/bessel.html?highlight=bessel

>

>

> (specifically, see the example "Roots of Bessel functions are often used:")

>

> Jason

It would be good if how to find these was more obvious. Roots of Bessel

functions are pretty common to want to find (at least in fields of engineering

I've worked in). It's not obvious that one would use the Sage interface to

mpmath to compute these.

MMA has these as BesselJZero[] and BesselYZero[]

http://reference.wolfram.com/mathematica/ref/BesselJZero.html

http://reference.wolfram.com/mathematica/ref/BesselYZero.html

If nobody beats me to it, when the OpenSolaris and 64-bit SPARC ports are

finished and I can concentrate on other aspects of Sage, I'll look into making

these more easily available.

Dave

Jul 10, 2010, 7:23:20 PM7/10/10

to sage-support

On Jul 2, 1:02 am, Pat LeSmithe <qed...@gmail.com> wrote:

> Possibly naive questions:

>

> * Are there analogous arbitrary-precision routines in or wrapped by Sage?

Arbitrary-precision computation of Bessel function zeros will be
> Possibly naive questions:

>

> * Are there analogous arbitrary-precision routines in or wrapped by Sage?

provided in the next version of mpmath. See

http://fredrik-j.blogspot.com/2010/07/sage-days-23-and-bessel-function-zeros.html

I'll make sure Sage gets an interface for Bessel function zeros. If it

doesn't happen during Sage Days 24 (which will focus on special

functions in Sage), I'll write one soon after SD24.

Fredrik

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