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Posted to dev@commons.apache.org by Sharon Lourduraj <sh...@gmail.com> on 2006/03/11 03:09:39 UTC
[math] Prime Numbers Library.
Hello,
As you know every math library needs to have a relation to prime number
algorithms, so just wondering if drafting something for prime number
library would be a good idea. I am thinking of providing a patch with
very (very) basic prime number functions. What do you think?
Let me know :-)
-Sharon
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Re: [math] Prime Numbers Library.
Posted by Paul Libbrecht <pa...@activemath.org>.
Phil Steitz wrote:
> On 3/11/06, Paul Libbrecht <pa...@activemath.org> wrote:
>
>> I would fear of a library providing such functionality be enormous...
>> any modularity in commons-math planned ?
> Good question, which comes up over and over again in [math]. That's
> why I suggested that we focus on primality testing, which is something
> with practical applications and that could define a more narrow scope.
> I don't see any harm in experimenting a little in this area.
I think indeed this would be good as first stab.
> [...] When you say "modularity" do you mean splitting up the jar artifacts produced? I thnk we have talked about that before and could be it will make sense eventually to do this. Do you think the 1.1 jar is too big?
>
Right, it was about it...
It could also be about dependencies and/or scopes of each projects.
For example for Jelly it was *needed* because, for example, some taglibs
have picky dependencies. I don't think it's the case here.
The current commons-math is quite small thus far... indeed... So it'd be
just a long term suggestion.
paul
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Re: [math] Prime Numbers Library.
Posted by Phil Steitz <ph...@gmail.com>.
On 3/12/06, Bill Barker <wb...@wilshire.com> wrote:
>
> "Sharon Lourduraj" <sh...@gmail.com> wrote in message
> news:4414B5DA.5090101@gmail.com...
> > Hello,
> >
> > Thank you for the positive input on implementing Prime Number functions. I
> > have created a 'wish' on the Math Wish List page. I would like to lay out
> > an initial plan before everyone starts to jump into coding the algorithms.
> >
> > Here is the base "off-my-head" plan, in the order that might prove the
> > implementation to be of positive value, also the order of difficulty:
> >
> > 1. Implement naive primality (quick tests, but are slow for large numbers)
> > testing algorithms. These algorithms are not very fast and are mainly
> > intended for small numbers. Some involve trial and error methods. Some
> > involve generating a sieve, as aligned, to test the given number and
> > derive result from the contents of the sieve.
> >
>
> +1 IMHO, this really should be a part of [math].
+1 for API, +0 for naive implementation. I am OK with starting with
naive implementations to get the API right, which is a strategy that
we have used before, but need to make sure the design will support
robust impls.
>
> > 2. Implement probabilistic testing (classical tests) algorithms. These
> > algorithms include tests that identify a number as a probable-prime, of
> > course using logical deduction (Fermat, Miller-Rabin, etc.) theorized by
> > mathematicians. These algorithms are relatively fast for large numbers,
> > but are sophisticated. They do contain a calculated error margin.
> >
>
> Currently, [math] doesn't support integer calculations bigger than 'int'.
> It could do 'long', but it's really not much of an improvement in this area.
> It's really is going to need a BigInteger class simply to handle the 2048+
> bit integers that are of interest to crypto providers. Of course, the
> number theorests will want much larger :).
>
> And, yes, I'm volunteering.
What about the jdk-supplied class? I don't know anything about the
implementation, but this class also supports a probablePrime method
that takes a Random and bit length as arguments. We could provide one
of our own (Random's) there and leverage the primitives in this class.
Assm you mean using or extending this, or accomodating BigIntegers in
the API. Or is the jdk impl not usable?
>
> > 3. Implement General purpose testing algorithms. These algorithms are
> > extremely advanced. They are significantly faster than any other
> > algorithms. Some of these algorithms have been widely accepted to work,
> > but are based on conjectures that have still not been proved true (but
> > are widely assumed to be). These algorithms will significantly test our
> > brains and the scope of [math].
> >
>
> Bring it on ;-).
+1 and of course the Riemann hypothesis is true ;-P
>
> >
> > Alright, all that thoughts are off my head now. Feel free to make any
> > corrections, I do not have much knowledge of advanced algorithms just a
> > keen interest. Also, feel free to make suggestions.
> >
> > I have created a wiki entry :-)
> > http://wiki.apache.org/jakarta-commons/PrimeNumbers
Thanks!!
Phil
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Re: [math] Prime Numbers Library.
Posted by Bill Barker <wb...@wilshire.com>.
"Sharon Lourduraj" <sh...@gmail.com> wrote in message
news:4414B5DA.5090101@gmail.com...
> Hello,
>
> Thank you for the positive input on implementing Prime Number functions. I
> have created a 'wish' on the Math Wish List page. I would like to lay out
> an initial plan before everyone starts to jump into coding the algorithms.
>
> Here is the base "off-my-head" plan, in the order that might prove the
> implementation to be of positive value, also the order of difficulty:
>
> 1. Implement naive primality (quick tests, but are slow for large numbers)
> testing algorithms. These algorithms are not very fast and are mainly
> intended for small numbers. Some involve trial and error methods. Some
> involve generating a sieve, as aligned, to test the given number and
> derive result from the contents of the sieve.
>
+1 IMHO, this really should be a part of [math].
> 2. Implement probabilistic testing (classical tests) algorithms. These
> algorithms include tests that identify a number as a probable-prime, of
> course using logical deduction (Fermat, Miller-Rabin, etc.) theorized by
> mathematicians. These algorithms are relatively fast for large numbers,
> but are sophisticated. They do contain a calculated error margin.
>
Currently, [math] doesn't support integer calculations bigger than 'int'.
It could do 'long', but it's really not much of an improvement in this area.
It's really is going to need a BigInteger class simply to handle the 2048+
bit integers that are of interest to crypto providers. Of course, the
number theorests will want much larger :).
And, yes, I'm volunteering.
> 3. Implement General purpose testing algorithms. These algorithms are
> extremely advanced. They are significantly faster than any other
> algorithms. Some of these algorithms have been widely accepted to work,
> but are based on conjectures that have still not been proved true (but
> are widely assumed to be). These algorithms will significantly test our
> brains and the scope of [math].
>
Bring it on ;-).
>
> Alright, all that thoughts are off my head now. Feel free to make any
> corrections, I do not have much knowledge of advanced algorithms just a
> keen interest. Also, feel free to make suggestions.
>
> I have created a wiki entry :-)
> http://wiki.apache.org/jakarta-commons/PrimeNumbers
>
> I will updated a full-fledged plan as time allows.
>
> Thanks,
> -Sharon
>
> P.S:
> Source 1: http://en.wikipedia.org/wiki/Primality_test
> Source 2: http://primes.utm.edu/prove/index.html
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Re: [math] Prime Numbers Library.
Posted by Sharon Lourduraj <sh...@gmail.com>.
Hello,
Thank you for the positive input on implementing Prime Number functions.
I have created a 'wish' on the Math Wish List page. I would like to lay
out an initial plan before everyone starts to jump into coding the
algorithms.
Here is the base "off-my-head" plan, in the order that might prove the
implementation to be of positive value, also the order of difficulty:
1. Implement naive primality (quick tests, but are slow for large
numbers) testing algorithms. These algorithms are not very fast and are
mainly intended for small numbers. Some involve trial and error methods.
Some involve generating a sieve, as aligned, to test the given number
and derive result from the contents of the sieve.
2. Implement probabilistic testing (classical tests) algorithms. These
algorithms include tests that identify a number as a probable-prime, of
course using logical deduction (Fermat, Miller-Rabin, etc.) theorized by
mathematicians. These algorithms are relatively fast for large numbers,
but are sophisticated. They do contain a calculated error margin.
3. Implement General purpose testing algorithms. These algorithms are
extremely advanced. They are significantly faster than any other
algorithms. Some of these algorithms have been widely accepted to work,
but are based on conjectures that have still not been proved true (but
are widely assumed to be). These algorithms will significantly test our
brains and the scope of [math].
Alright, all that thoughts are off my head now. Feel free to make any
corrections, I do not have much knowledge of advanced algorithms just a
keen interest. Also, feel free to make suggestions.
I have created a wiki entry :-)
http://wiki.apache.org/jakarta-commons/PrimeNumbers
I will updated a full-fledged plan as time allows.
Thanks,
-Sharon
P.S:
Source 1: http://en.wikipedia.org/wiki/Primality_test
Source 2: http://primes.utm.edu/prove/index.html
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Re: [math] Prime Numbers Library.
Posted by Phil Steitz <ph...@gmail.com>.
On 3/11/06, Bill Barker <wb...@wilshire.com> wrote:
>
> "Phil Steitz" <ph...@gmail.com> wrote in message
> news:8a81b4af0603111508o32d77fdfg5fa5a86cb31b5136@mail.gmail.com...
> On 3/11/06, Paul Libbrecht <pa...@activemath.org> wrote:
> >> I would fear of a library providing such functionality be enormous...
> >> any modularity in commons-math planned ?
> >>
> >
> >Good question, which comes up over and over again in [math]. That's
> >why I suggested that we focus on primality testing, which is something
> >with practical applications and that could define a more narrow scope.
> > I don't see any harm in experimenting a little in this area. Could
> >be I am wrong though and this will lead us off into a large amount of
> >code. I am not a number theorist and have only passing familiarity
> >with the algorithms for primality testing. WDYT?
> >
>
> Actually, I am a number theorist (by training, not my day-job :). I'm
> interested enough that I could review submissions in this area. Of course,
> I have karma to commit them as well, but I don't like to step on toes for
> projects that I haven't really been active in ;-).
+1 - consider youself drafted ;-) Please feel free to jump in any
time. I am sure the all of the eccentricly orbiting [math] ppl will
be happy to have a number theorist in our midst.
Thanks!
Phil
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Re: [math] Prime Numbers Library.
Posted by Bill Barker <wb...@wilshire.com>.
"Phil Steitz" <ph...@gmail.com> wrote in message
news:8a81b4af0603111508o32d77fdfg5fa5a86cb31b5136@mail.gmail.com...
On 3/11/06, Paul Libbrecht <pa...@activemath.org> wrote:
>> I would fear of a library providing such functionality be enormous...
>> any modularity in commons-math planned ?
>>
>
>Good question, which comes up over and over again in [math]. That's
>why I suggested that we focus on primality testing, which is something
>with practical applications and that could define a more narrow scope.
> I don't see any harm in experimenting a little in this area. Could
>be I am wrong though and this will lead us off into a large amount of
>code. I am not a number theorist and have only passing familiarity
>with the algorithms for primality testing. WDYT?
>
Actually, I am a number theorist (by training, not my day-job :). I'm
interested enough that I could review submissions in this area. Of course,
I have karma to commit them as well, but I don't like to step on toes for
projects that I haven't really been active in ;-).
>When you say "modularity" do you mean splitting up the jar artifacts
>produced? I thnk we have talked about that before and could be it
>will make sense eventually to do this. Do you think the 1.1 jar is
>too big?
>
>Phil
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Re: [math] Prime Numbers Library.
Posted by Phil Steitz <ph...@gmail.com>.
On 3/11/06, Paul Libbrecht <pa...@activemath.org> wrote:
> I would fear of a library providing such functionality be enormous...
> any modularity in commons-math planned ?
>
Good question, which comes up over and over again in [math]. That's
why I suggested that we focus on primality testing, which is something
with practical applications and that could define a more narrow scope.
I don't see any harm in experimenting a little in this area. Could
be I am wrong though and this will lead us off into a large amount of
code. I am not a number theorist and have only passing familiarity
with the algorithms for primality testing. WDYT?
When you say "modularity" do you mean splitting up the jar artifacts
produced? I thnk we have talked about that before and could be it
will make sense eventually to do this. Do you think the 1.1 jar is
too big?
Phil
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Re: [math] Prime Numbers Library.
Posted by Paul Libbrecht <pa...@activemath.org>.
I would fear of a library providing such functionality be enormous...
any modularity in commons-math planned ?
paul
Sharon Lourduraj wrote:
> Prime Number Theory is a huge subject. To start of with we can focus
> on implementing prime finding methods, such as divide by odd numbers
> up to the square root of a number, divide by primes up to the square
> root of a number and Sieve of Eratosthenes. As we move along, we can
> implement prime finding of specific types, Mersenne Prime, Twin
> Primes, Palindromic Primes etc. And as we move along with those
> implementations, we can introduce Primality Proving algorithms.
>
> Some sites:
> Basic Prime Number finding -
> http://www.troubleshooters.com/codecorn/primenumbers/primenumbers.htm
> Prime Numbers - http://mathworld.wolfram.com/PrimeNumber.html (good
> site to learn the ins/outs of prime numbers)
> Primality Proving - http://primes.utm.edu/
>
> Also, we can work on implementing optimized algorithms...I think that
> would be fun. The practical purpose of Prime Numbers can be extended
> into encryption/decryption algorithms, but implementing those
> algorithms might be beyond the scope of this project.
>
> Thanks,
> -Sharon
>
> Phil Steitz wrote:
>> This sounds interesting. Can you describe a little more what
>> algorithms you are thinking about implementing? Online references to
>> point us to a common set of definitions for discussion purposes would
>> be great.
>>
>> Also, if you have not aldeady read this, have a look at
>> http://jakarta.apache.org/commons/math/developers.html for info on how
>> to get set up, etc.
>>
>> Thanks!
>>
>> Phil
>>
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Re: [math] Prime Numbers Library.
Posted by Sharon Lourduraj <sh...@gmail.com>.
All right then, I will start by creating a Wiki entry in the Math Wish
list. And proceed form there on.
Thanks,
Sharon
Phil Steitz wrote:
> On 3/11/06, Sharon Lourduraj <sh...@gmail.com> wrote:
>
>> Hello Phil,
>>
>> Prime Number Theory is a huge subject. To start of with we can focus on
>> implementing prime finding methods, such as divide by odd numbers up to
>> the square root of a number, divide by primes up to the square root of a
>> number and Sieve of Eratosthenes. As we move along, we can implement
>> prime finding of specific types, Mersenne Prime, Twin Primes,
>> Palindromic Primes etc. And as we move along with those implementations,
>>
>
>
>> we can introduce Primality Proving algorithms.
>>
>> Some sites:
>> Basic Prime Number finding -
>> http://www.troubleshooters.com/codecorn/primenumbers/primenumbers.htm
>> Prime Numbers - http://mathworld.wolfram.com/PrimeNumber.html (good site
>> to learn the ins/outs of prime numbers)
>> Primality Proving - http://primes.utm.edu/
>>
>> Also, we can work on implementing optimized algorithms...I think that
>> would be fun. The practical purpose of Prime Numbers can be extended
>> into encryption/decryption algorithms, but implementing those algorithms
>> might be beyond the scope of this project.
>>
>
> Actually, this (optimized algorithms for primality testing /
> generating large primes) is what would fit into the scope and mandate
> of [math] and could also be eventually useful to [OpenPGP]
> (contributing to direct pgp impl or key generation either there or in
> [math]). We have tried up to now to stick with applied math topics in
> [math], so what we should be focussed on in number-theoretic topics is
> things with applications to areas like crypto, using standard
> algorithms with good performance and accuracy. Starting by doing
> some research on primality testing algorithms that perform well for
> large numbers would be good. The references here provide a good
> starting point:
> http://en.wikipedia.org/wiki/Primality_test
> http://en.wikipedia.org/wiki/Miller-Rabin_primality_test
>
> I think an API for primality testing (designed consistently with the
> rest of [math] - look at the distributions, analysis, stat packages
> for examples) with implementations of some standard algorithms would
> make a great addition to [math]. The probablilistic algorithms could
> leverage the stuff in the random package and also give us some
> motivation to extend the capabilities there to include faster random
> integer generation methods.
>
> Thanks again for your interest in [math].
>
> Phil
>
> Phil
>
>
>
> Phil
>
>
>> Thanks,
>> -Sharon
>>
>> Phil Steitz wrote:
>>
>>> Hi Sharon,
>>>
>>> This sounds interesting. Can you describe a little more what
>>> algorithms you are thinking about implementing? Online references to
>>> point us to a common set of definitions for discussion purposes would
>>> be great.
>>>
>>> Also, if you have not aldeady read this, have a look at
>>> http://jakarta.apache.org/commons/math/developers.html for info on how
>>> to get set up, etc.
>>>
>>> Thanks!
>>>
>>> Phil
>>>
>>> On 3/10/06, Sharon Lourduraj <sh...@gmail.com> wrote:
>>>
>>>
>>>> Hello,
>>>>
>>>> As you know every math library needs to have a relation to prime number
>>>> algorithms, so just wondering if drafting something for prime number
>>>> library would be a good idea. I am thinking of providing a patch with
>>>> very (very) basic prime number functions. What do you think?
>>>>
>>>> Let me know :-)
>>>> -Sharon
>>>>
>>>> ---------------------------------------------------------------------
>>>> To unsubscribe, e-mail: commons-dev-unsubscribe@jakarta.apache.org
>>>> For additional commands, e-mail: commons-dev-help@jakarta.apache.org
>>>>
>>>>
>>>>
>>>>
>>> ---------------------------------------------------------------------
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>>>
>>>
>>>
>>>
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>>
>>
>>
>
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>
>
>
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Re: [math] Prime Numbers Library.
Posted by Phil Steitz <ph...@gmail.com>.
On 3/11/06, Sharon Lourduraj <sh...@gmail.com> wrote:
> Hello Phil,
>
> Prime Number Theory is a huge subject. To start of with we can focus on
> implementing prime finding methods, such as divide by odd numbers up to
> the square root of a number, divide by primes up to the square root of a
> number and Sieve of Eratosthenes. As we move along, we can implement
> prime finding of specific types, Mersenne Prime, Twin Primes,
> Palindromic Primes etc. And as we move along with those implementations,
> we can introduce Primality Proving algorithms.
>
> Some sites:
> Basic Prime Number finding -
> http://www.troubleshooters.com/codecorn/primenumbers/primenumbers.htm
> Prime Numbers - http://mathworld.wolfram.com/PrimeNumber.html (good site
> to learn the ins/outs of prime numbers)
> Primality Proving - http://primes.utm.edu/
>
> Also, we can work on implementing optimized algorithms...I think that
> would be fun. The practical purpose of Prime Numbers can be extended
> into encryption/decryption algorithms, but implementing those algorithms
> might be beyond the scope of this project.
Actually, this (optimized algorithms for primality testing /
generating large primes) is what would fit into the scope and mandate
of [math] and could also be eventually useful to [OpenPGP]
(contributing to direct pgp impl or key generation either there or in
[math]). We have tried up to now to stick with applied math topics in
[math], so what we should be focussed on in number-theoretic topics is
things with applications to areas like crypto, using standard
algorithms with good performance and accuracy. Starting by doing
some research on primality testing algorithms that perform well for
large numbers would be good. The references here provide a good
starting point:
http://en.wikipedia.org/wiki/Primality_test
http://en.wikipedia.org/wiki/Miller-Rabin_primality_test
I think an API for primality testing (designed consistently with the
rest of [math] - look at the distributions, analysis, stat packages
for examples) with implementations of some standard algorithms would
make a great addition to [math]. The probablilistic algorithms could
leverage the stuff in the random package and also give us some
motivation to extend the capabilities there to include faster random
integer generation methods.
Thanks again for your interest in [math].
Phil
Phil
Phil
>
> Thanks,
> -Sharon
>
> Phil Steitz wrote:
> > Hi Sharon,
> >
> > This sounds interesting. Can you describe a little more what
> > algorithms you are thinking about implementing? Online references to
> > point us to a common set of definitions for discussion purposes would
> > be great.
> >
> > Also, if you have not aldeady read this, have a look at
> > http://jakarta.apache.org/commons/math/developers.html for info on how
> > to get set up, etc.
> >
> > Thanks!
> >
> > Phil
> >
> > On 3/10/06, Sharon Lourduraj <sh...@gmail.com> wrote:
> >
> >> Hello,
> >>
> >> As you know every math library needs to have a relation to prime number
> >> algorithms, so just wondering if drafting something for prime number
> >> library would be a good idea. I am thinking of providing a patch with
> >> very (very) basic prime number functions. What do you think?
> >>
> >> Let me know :-)
> >> -Sharon
> >>
> >> ---------------------------------------------------------------------
> >> To unsubscribe, e-mail: commons-dev-unsubscribe@jakarta.apache.org
> >> For additional commands, e-mail: commons-dev-help@jakarta.apache.org
> >>
> >>
> >>
> >
> > ---------------------------------------------------------------------
> > To unsubscribe, e-mail: commons-dev-unsubscribe@jakarta.apache.org
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> >
> >
> >
>
>
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Re: [math] Prime Numbers Library.
Posted by Sharon Lourduraj <sh...@gmail.com>.
Hello Phil,
Prime Number Theory is a huge subject. To start of with we can focus on
implementing prime finding methods, such as divide by odd numbers up to
the square root of a number, divide by primes up to the square root of a
number and Sieve of Eratosthenes. As we move along, we can implement
prime finding of specific types, Mersenne Prime, Twin Primes,
Palindromic Primes etc. And as we move along with those implementations,
we can introduce Primality Proving algorithms.
Some sites:
Basic Prime Number finding -
http://www.troubleshooters.com/codecorn/primenumbers/primenumbers.htm
Prime Numbers - http://mathworld.wolfram.com/PrimeNumber.html (good site
to learn the ins/outs of prime numbers)
Primality Proving - http://primes.utm.edu/
Also, we can work on implementing optimized algorithms...I think that
would be fun. The practical purpose of Prime Numbers can be extended
into encryption/decryption algorithms, but implementing those algorithms
might be beyond the scope of this project.
Thanks,
-Sharon
Phil Steitz wrote:
> Hi Sharon,
>
> This sounds interesting. Can you describe a little more what
> algorithms you are thinking about implementing? Online references to
> point us to a common set of definitions for discussion purposes would
> be great.
>
> Also, if you have not aldeady read this, have a look at
> http://jakarta.apache.org/commons/math/developers.html for info on how
> to get set up, etc.
>
> Thanks!
>
> Phil
>
> On 3/10/06, Sharon Lourduraj <sh...@gmail.com> wrote:
>
>> Hello,
>>
>> As you know every math library needs to have a relation to prime number
>> algorithms, so just wondering if drafting something for prime number
>> library would be a good idea. I am thinking of providing a patch with
>> very (very) basic prime number functions. What do you think?
>>
>> Let me know :-)
>> -Sharon
>>
>> ---------------------------------------------------------------------
>> To unsubscribe, e-mail: commons-dev-unsubscribe@jakarta.apache.org
>> For additional commands, e-mail: commons-dev-help@jakarta.apache.org
>>
>>
>>
>
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>
>
>
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Re: [math] Prime Numbers Library.
Posted by Phil Steitz <ph...@gmail.com>.
Hi Sharon,
This sounds interesting. Can you describe a little more what
algorithms you are thinking about implementing? Online references to
point us to a common set of definitions for discussion purposes would
be great.
Also, if you have not aldeady read this, have a look at
http://jakarta.apache.org/commons/math/developers.html for info on how
to get set up, etc.
Thanks!
Phil
On 3/10/06, Sharon Lourduraj <sh...@gmail.com> wrote:
> Hello,
>
> As you know every math library needs to have a relation to prime number
> algorithms, so just wondering if drafting something for prime number
> library would be a good idea. I am thinking of providing a patch with
> very (very) basic prime number functions. What do you think?
>
> Let me know :-)
> -Sharon
>
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