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are you interested in number theory AND programming

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  are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-12 02:25 -0700
    Re: are you interested in number theory AND programming root <NoEMail@home.org> - 2020-06-12 14:26 +0000
      Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-12 19:34 -0700
        Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-13 11:16 +0100
          Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-13 04:07 -0700
            Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-13 07:20 -0700
              Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-13 07:47 -0700
              Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-13 08:29 -0700
            Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-13 17:02 +0100
              Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-13 23:11 -0700
                Re: are you interested in number theory AND programming syedanwarowais5@gmail.com - 2020-06-13 23:23 -0700
                  Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-17 00:55 -0700
                    Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-17 09:30 +0100
                      Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-17 02:32 -0700
                        Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-20 08:26 +0100
                          Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-20 03:58 -0700
                            Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-20 14:55 +0100
                    Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-17 23:11 +0100
                    Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-20 04:44 -0700
                      Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-20 06:27 -0700
                        Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-21 17:31 -0700
                          Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-22 02:00 -0700
                            Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-22 05:34 -0700
                              Re: are you interested in number theory AND programming root <NoEMail@home.org> - 2020-06-22 14:05 +0000
                                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-23 04:50 -0700
                                  Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-23 15:50 +0200
                                    Re: are you interested in number theory AND programming Chad <cdalten@gmail.com> - 2020-06-23 14:34 -0700
                                    Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-24 01:39 -0700
                                      Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-24 15:48 +0200
                                    Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-24 13:52 +0100
                                      Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-24 16:00 +0200
                                        Re: are you interested in number theory AND programming Ben Bacarisse <ben.usenet@bsb.me.uk> - 2020-06-24 17:03 +0100
                                          Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-24 20:32 +0200
                                            Re: are you interested in number theory AND programming Chad <cdalten@gmail.com> - 2020-06-24 14:19 -0700
                                        Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:24 -0700
                                          Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 16:28 +0200
                                      Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:11 -0700
                              Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-22 09:39 -0700
                                Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-23 00:50 -0700
                                  Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-23 05:14 -0700
                                    Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-24 02:39 -0700
                                    Re: are you interested in number theory AND programming Richard Heathfield <rjh@cpax.org.uk> - 2020-06-25 20:48 +0100
                                      Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 08:48 +0200
                                        Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-06-26 01:25 -0700
                                          Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 11:10 +0200
                                            Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-26 03:56 -0700
                                              Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 13:34 +0200
                                                Re: are you interested in number theory AND programming Boris Dorestand <bdorestand@example.com> - 2020-06-27 11:22 -0300
                                                  Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-27 17:50 +0200
                                                    Re: are you interested in number theory AND programming Boris Dorestand <bdorestand@example.com> - 2020-06-27 13:42 -0300
                                                      Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-07-04 18:44 -0700
                                                        Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-07-09 19:51 -0700
                                                          Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-07-10 05:32 -0700
                                                            Re: are you interested in number theory AND programming syed owais <syedanwarowais5@gmail.com> - 2020-07-10 09:03 -0700
                                              Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:02 -0700
                                        Re: are you interested in number theory AND programming James Dow Allen <jdallen2000@yahoo.com> - 2020-06-26 01:58 -0700
                                          Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-26 11:14 +0200
                                          Re: are you interested in number theory AND programming Richard Damon <Richard@Damon-Family.org> - 2020-06-26 13:10 -0400
                          Re: are you interested in number theory AND programming Julio Di Egidio <julio@diegidio.name> - 2020-06-26 06:12 -0700
            Re: are you interested in number theory AND programming David Brown <david.brown@hesbynett.no> - 2020-06-13 23:28 +0200

Page 3 of 3 — ← Prev page 1 2 [3]

#10980

with regard to extending our explorations to sixth powers, do you regard the following as a hint?

(a+b)^6-a^6-b^6
Can be written as ab*(an expression in"a" and "b" in which the exponent in not greater than 4)

Would you like to do the interesting algebra here yourself? 

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#10992

On 23/06/2020 13:14, James Dow Allen wrote:

<snip>

> I am a C fan myself, which makes me rather obsolescent compared
> with the cool guys. :-)

Not so. There is no language cooler than C. The C in C actually stands 
for Cool.

> But I think almost any language would be
> more FUN than Fortran.

Unless you're writing a quine.

"FORTRAN was the language of choice, for the same reason that 
three-legged races are popular."

-- 
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
Sig line 4 vacant - apply within

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#10993

On 25/06/2020 21:48, Richard Heathfield wrote:
> On 23/06/2020 13:14, James Dow Allen wrote:
> 
> <snip>
> 
>> I am a C fan myself, which makes me rather obsolescent compared
>> with the cool guys. :-)
> 
> Not so. There is no language cooler than C. The C in C actually stands
> for Cool.
> 
>> But I think almost any language would be
>> more FUN than Fortran.
> 
> Unless you're writing a quine.
> 
> "FORTRAN was the language of choice, for the same reason that
> three-legged races are popular."
> 

Didn't some FORTRAN systems let you change the value of 3 if you don't
like the usual one?

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#10994

i have changed course in the pursuit of programming skills--i will first learn c and the python.

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#10996

On 26/06/2020 10:25, syed owais wrote:
> i have changed course in the pursuit of programming skills--i will first learn c and the python.
> 

Trust this from someone who works primarily with C and Python for a
living - that is a truly stupid idea.  It is perhaps not quite as bad as
picking FORTRAN, but it is /bad/.

There is little point in asking questions and having a discussion in a
Usenet group or other forum, if you are going to completely ignore the
advice you are given.

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#10998

On Friday, June 26, 2020 at 4:10:17 PM UTC+7, David Brown wrote:
> On 26/06/2020 10:25, syed owais wrote:
> > i have changed course in the pursuit of programming skills--i will first learn c and the python.
> > 
> 
> Trust this from someone who works primarily with C and Python for a
> living - that is a truly stupid idea.  It is perhaps not quite as bad as
> picking FORTRAN, but it is /bad/.

Why?  I think there's a case for first learning a language
"close to the hardware."  Is there some reason that C is a bad first
language?

In any event, different people will have preferences for different
types of language.  Dennis Ritchie, for example, was a fan of
procedural languages, not functional.  Individual tastes may be
especially important for our syed owais -- he seems as interested
in programming as an avocation more than as vocation.

My personal advice is that he spend an hour on each of a
few different languages, just to get an idea which has a flavor
that might appeal to him.

James

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#10999

On 26/06/2020 12:56, James Dow Allen wrote:
> On Friday, June 26, 2020 at 4:10:17 PM UTC+7, David Brown wrote:
>> On 26/06/2020 10:25, syed owais wrote:
>>> i have changed course in the pursuit of programming skills--i will first learn c and the python.
>>>
>>
>> Trust this from someone who works primarily with C and Python for a
>> living - that is a truly stupid idea.  It is perhaps not quite as bad as
>> picking FORTRAN, but it is /bad/.
> 
> Why?  I think there's a case for first learning a language
> "close to the hardware."  Is there some reason that C is a bad first
> language?

Yes, many reasons.

I can agree that learning a language "close to the hardware" is a good
idea if you want to understand about computer hardware.  The OP here
wants a tool to help automate his mathematics work - he does not (or
should not) care anything about the hardware.

But even if you want to learn about the hardware, /starting/ with such a
language can make it a lot harder.  You have to learn a lot before you
can do anything - that makes for a frustrating learning process.  And C,
certainly on a PC, is not a great choice anyway - step one is a
printf("Hello, world!\n") program that is totally disconnected from the
hardware.  For PC programming, the only thing "close to the hardware"
about C is that you have to use extra effort to get numbers bigger than
2G and you waste all your time and effort on memory management.

Anyone wanting to learn about hardware should look at embedded
programming - get an Arduino and work from that.

People wanting to learn /programming/, rather than wanting to learn C
(and there are good reasons to want to learn C), should pick a language
that is much higher up.

Python stands out as a language that is relatively easy to learn, can be
learned in stages, takes care of many details for you, supports high
performance for things that really need it, and will work well for the
needs of a mathematician.  It really is the only general-purpose choice
for the OP - the alternative would be a tool-specific language built
into a mathematics software package of his choice.  And for many
mathematics software packages, the built-in language is Python.
(Coincidence?  I don't think so.)


> 
> In any event, different people will have preferences for different
> types of language.

Of course.  I am by no means saying C is a bad language.  I am saying it
is a bad choice for the OP.

>  Dennis Ritchie, for example, was a fan of
> procedural languages, not functional.  Individual tastes may be
> especially important for our syed owais -- he seems as interested
> in programming as an avocation more than as vocation.
> 
> My personal advice is that he spend an hour on each of a
> few different languages, just to get an idea which has a flavor
> that might appeal to him.
> 

My personal advice is that he engages sensibly in the discussion rather
than jumping to conclusions that make no sense based on the advice given
and any reasonable research.  I assume that English is not his first
language, though I have seen much worse English from native speakers.
It may be that other discussion forums could help him.  (But it is
/really/ nice to see some life here.)

It might be that the best choice for him is Haskell or Lisp, rather than
Python, or that he has other requirements that haven't been discussed.
And it is entirely plausible that the best choice in the end will not be
the same as the /first/ choice - you can pick a different balance when
learning about programming, and later once you have a better
understanding and want something more advanced.  But I am very confident
that neither C nor FORTRAN are appropriate choices.

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#11006

David Brown <david.brown@hesbynett.no> writes:

> On 26/06/2020 12:56, James Dow Allen wrote:
>> On Friday, June 26, 2020 at 4:10:17 PM UTC+7, David Brown wrote:
>>> On 26/06/2020 10:25, syed owais wrote:
>>>> i have changed course in the pursuit of programming skills--i will
>>>> first learn c and the python.
>>>>
>>>
>>> Trust this from someone who works primarily with C and Python for a
>>> living - that is a truly stupid idea.  It is perhaps not quite as bad as
>>> picking FORTRAN, but it is /bad/.
>> 
>> Why?  I think there's a case for first learning a language
>> "close to the hardware."  Is there some reason that C is a bad first
>> language?
>
> Yes, many reasons.
>
> I can agree that learning a language "close to the hardware" is a good
> idea if you want to understand about computer hardware.  The OP here
> wants a tool to help automate his mathematics work - he does not (or
> should not) care anything about the hardware.

[...]

> It might be that the best choice for him is Haskell or Lisp, rather than
> Python, or that he has other requirements that haven't been discussed.
> And it is entirely plausible that the best choice in the end will not be
> the same as the /first/ choice - you can pick a different balance when
> learning about programming, and later once you have a better
> understanding and want something more advanced.  But I am very confident
> that neither C nor FORTRAN are appropriate choices.

Your entire post makes a lot of sense.  I'd like to contribute with an
addition here that might sound very controversial at the end, but here
it goes.

I think the OP should also consider not just the language but the book
too.  Because of the availability of ``the book'', I think a Lisp turns
out to the best thing for the OP.  Here's why.

The book 

  How to Design Programs
  http://htdp.org

is AFAIK the unique book in the entire world that seems to actually
teach programming without the usual strategy of presenting various
sample problems and solving them the programming language of choice.  It
seems HtDP is the only book that found a way to talk about programming
in a more general sense of the word.  Of course they solve lots of
sample simple problems, but only to illustrate the more general
strategy.

The books sends you towards functional programming --- which I guess
will suit the OP's mathematics work --- and Lisp seems to be the
language with least syntax, which seems like a good educational start.

But the choice for Lisp is due to HtDP.  This book is *the educational
first book* on programming.  Even experienced programmers should read
it, I think: if not for anything else, then at least so one would get
close to an educational approach one hasn't closely seen yet.

I have no association with the authors.  I speak for myself, of course.

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#11007

On 27/06/2020 16:22, Boris Dorestand wrote:
> David Brown <david.brown@hesbynett.no> writes:
> 
>> On 26/06/2020 12:56, James Dow Allen wrote:
>>> On Friday, June 26, 2020 at 4:10:17 PM UTC+7, David Brown wrote:
>>>> On 26/06/2020 10:25, syed owais wrote:
>>>>> i have changed course in the pursuit of programming skills--i will
>>>>> first learn c and the python.
>>>>>
>>>>
>>>> Trust this from someone who works primarily with C and Python for a
>>>> living - that is a truly stupid idea.  It is perhaps not quite as bad as
>>>> picking FORTRAN, but it is /bad/.
>>>
>>> Why?  I think there's a case for first learning a language
>>> "close to the hardware."  Is there some reason that C is a bad first
>>> language?
>>
>> Yes, many reasons.
>>
>> I can agree that learning a language "close to the hardware" is a good
>> idea if you want to understand about computer hardware.  The OP here
>> wants a tool to help automate his mathematics work - he does not (or
>> should not) care anything about the hardware.
> 
> [...]
> 
>> It might be that the best choice for him is Haskell or Lisp, rather than
>> Python, or that he has other requirements that haven't been discussed.
>> And it is entirely plausible that the best choice in the end will not be
>> the same as the /first/ choice - you can pick a different balance when
>> learning about programming, and later once you have a better
>> understanding and want something more advanced.  But I am very confident
>> that neither C nor FORTRAN are appropriate choices.
> 
> Your entire post makes a lot of sense.  I'd like to contribute with an
> addition here that might sound very controversial at the end, but here
> it goes.
> 
> I think the OP should also consider not just the language but the book
> too.  Because of the availability of ``the book'', I think a Lisp turns
> out to the best thing for the OP.  Here's why.
> 
> The book 
> 
>   How to Design Programs
>   http://htdp.org
> 
> is AFAIK the unique book in the entire world that seems to actually
> teach programming without the usual strategy of presenting various
> sample problems and solving them the programming language of choice.  It
> seems HtDP is the only book that found a way to talk about programming
> in a more general sense of the word.  Of course they solve lots of
> sample simple problems, but only to illustrate the more general
> strategy.
> 

I fully endorse the idea of learning to program rather than learning to
code.  Once you have learned to program, the particular language used
for coding the programs is a much smaller concern.  It's inevitable that
"learning to program" requires some sort of language or formal syntax,
and I think a functional style has a lot of advantages.  (When I learned
programming at university, the first two languages we used was a
functional programming language and a symbolic one that existed only on
paper and the blackboard.  By the time the courses required "real"
languages, we learned the languages as homework.)

There is, however, no "ideal" way to do this - different people have
different outsets, different aims, different abilities, different interests.

> The books sends you towards functional programming --- which I guess
> will suit the OP's mathematics work --- and Lisp seems to be the
> language with least syntax, which seems like a good educational start.
> 

Lack of syntax is not a benefit for learning a language.  With Lisp, a
beginner is going to feel they aren't actually doing very much except
writing far too many close-parenthesis symbols.  Begin able to write
"print('Hello, world!')" might not be as theoretically pure, but it
gives a lot more feedback to the learner.

> But the choice for Lisp is due to HtDP.  This book is *the educational
> first book* on programming.  Even experienced programmers should read
> it, I think: if not for anything else, then at least so one would get
> close to an educational approach one hasn't closely seen yet.
> 
> I have no association with the authors.  I speak for myself, of course.
> 

I can certainly agree on the idea that a good book (or course or
tutorial) can outweigh many other aspects of the choice of language.

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#11009

David Brown <david.brown@hesbynett.no> writes:

> On 27/06/2020 16:22, Boris Dorestand wrote:
>> David Brown <david.brown@hesbynett.no> writes:
>> 
>>> On 26/06/2020 12:56, James Dow Allen wrote:
>>>> On Friday, June 26, 2020 at 4:10:17 PM UTC+7, David Brown wrote:
>>>>> On 26/06/2020 10:25, syed owais wrote:
>>>>>> i have changed course in the pursuit of programming skills--i will
>>>>>> first learn c and the python.
>>>>>>
>>>>>
>>>>> Trust this from someone who works primarily with C and Python for a
>>>>> living - that is a truly stupid idea.  It is perhaps not quite as bad as
>>>>> picking FORTRAN, but it is /bad/.
>>>>
>>>> Why?  I think there's a case for first learning a language
>>>> "close to the hardware."  Is there some reason that C is a bad first
>>>> language?
>>>
>>> Yes, many reasons.
>>>
>>> I can agree that learning a language "close to the hardware" is a good
>>> idea if you want to understand about computer hardware.  The OP here
>>> wants a tool to help automate his mathematics work - he does not (or
>>> should not) care anything about the hardware.
>> 
>> [...]
>> 
>>> It might be that the best choice for him is Haskell or Lisp, rather than
>>> Python, or that he has other requirements that haven't been discussed.
>>> And it is entirely plausible that the best choice in the end will not be
>>> the same as the /first/ choice - you can pick a different balance when
>>> learning about programming, and later once you have a better
>>> understanding and want something more advanced.  But I am very confident
>>> that neither C nor FORTRAN are appropriate choices.
>> 
>> Your entire post makes a lot of sense.  I'd like to contribute with an
>> addition here that might sound very controversial at the end, but here
>> it goes.
>> 
>> I think the OP should also consider not just the language but the book
>> too.  Because of the availability of ``the book'', I think a Lisp turns
>> out to the best thing for the OP.  Here's why.
>> 
>> The book 
>> 
>>   How to Design Programs
>>   http://htdp.org
>> 
>> is AFAIK the unique book in the entire world that seems to actually
>> teach programming without the usual strategy of presenting various
>> sample problems and solving them the programming language of choice.  It
>> seems HtDP is the only book that found a way to talk about programming
>> in a more general sense of the word.  Of course they solve lots of
>> sample simple problems, but only to illustrate the more general
>> strategy.
>
> I fully endorse the idea of learning to program rather than learning to
> code.  Once you have learned to program, the particular language used
> for coding the programs is a much smaller concern.  It's inevitable that
> "learning to program" requires some sort of language or formal syntax,
> and I think a functional style has a lot of advantages.  (When I learned
> programming at university, the first two languages we used was a
> functional programming language and a symbolic one that existed only on
> paper and the blackboard.  By the time the courses required "real"
> languages, we learned the languages as homework.)
>
> There is, however, no "ideal" way to do this - different people have
> different outsets, different aims, different abilities, different interests.

That's an important point.  I did not study programming with a language
that only existed on paper the blackboard, but I did eventually practice
with one because I saw the value of such thing.  (Had someone introduced
that to me early on, *maybe* I would've thought it was a boring
subject.)

Learning is very much psychology-involved.  The taste and the fun of the
learner has to be taken into account, lest he distances himself from the
subject out of unpleasure and discomfort.

The young learner might be attracted to programming because of
computers.  If you remove the computer, he might lose the interest.
Maybe in the future he'll himself come up with the idea that having a
computer only in the mind is a good idea and has its uses.

[...]

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#11034

I uploaded the following today on the whatsapp discussion group which consists mainly of kashmiri diaspora skilled workers (I am based in Srinagar myself) :

I was working on positive integers that are sums of three cubes in two different ways; I had not seen discussions of this problem in number theory textbooks. 
I wrote a post at the google groups for programmers website... Take a look there and see how much progress was made!

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#11043

Here is a new area of exploration :
The diophantine equation a^2+b^2=c^2 is well-known. 
Conventionally,the (parameteric) solutions are studied in the set of natural numbers. 
I am exploring this diophantine equation in the set of complex (Gaussian) integers. 
What about a computer program that would list (all?) the solution sets of this diophantine equation IN THE SET OF GAUSSIAN INTEGERS? This is the first aspect of my undertaking in this problem  that I want to discuss at this forum!!!

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#11044

On Friday, July 10, 2020 at 9:51:48 AM UTC+7, syed owais wrote:
> I am exploring this diophantine equation in the set of complex (Gaussian) integers. 
> What about a computer program that would list (all?) the solution sets ...

PLEASE!  You may as well get the terminology right.
A SOLUTION is a triplet of Gaussian integers (a, b, c).
A SOLUTION SET would be a set like
  { (a1,b1,c1), (a2,b2,c2), ... }
which contains all such solution triplets.
YOU may prefer your terminology.  But it will make you look the fool.

As to your question, I've worked almost zero with complex numbers
and don't intend to start now.  But I'll offer three comments.
Only the first is relevant to programming, but I hope the others
-- related to the history of proving a^3 + b^3 = c^3 and
a^4 + b^4 = c^4 impossible in rational integers -- may be of interest also.

(1) Doing complex arithmetic in a programming language that
doesn't support them is a nuisance.  The ability to add such
abstractions as needed is an argument for languages like C++.
HOWEVER, [here comes a plug for my favorite language!]
Gnu's C language has supported complex numbers for DECADES.
You can solve an instance of your equation in C with simply
   _Complex double a, b, c;
   ...
   c = csqrt(a*a + b*b);

(2) Carl Gauss (the 3rd greatest mathematician ever according
to a popular webpage :-) ) is on record as implying that Fermat's
Last Theorem was a frivolous time-waster.  HOWEVER, by investigating
Gaussian integers rather than ordinary integers, he found a simpler
proof for the n=3 impossibility.  This proof of the complex case
was simpler than that of the real case, IIUC!  This discovery
advanced the use of complex numbers.

(3) The n=4 case of Fermat's Last Theorem is *much* easier to prove
than the n=3 case.  In fact it was proved way back in the 13th century
by the great mathematician Leonardo of Pisa.  It is a shame that
that great mathematician is linked to one minor discovery via his
nickname 'Fibonacci' -- he did much much more than that.

The fact that Leonardo 'Fibonacci' proved the impossibility
of a^4 + b^4 = c^4 is widely ignored or disputed.
(And I had my Edit reverted
when I noted this fact at Wikipedia.)  Leonardo didn't quite
connect all the dots as would be needed for publication today.
(And he actually proved the slightly stronger result that
a^4 + b^4 = c^2 is impossible in positive integers.)

Best ever,
James Dow Allen


    

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#11046

After giving the matter some thought, I think I want to take forward the discussion here with the following fact:
Number Theory textbooks give lists of Pythagorean Triplets, but conventionally they are natural numbers. 
For example,( 3,4,5) is the first Pythagorean Triplet.
A list of Gaussian (complex) Pythagorean Triplets would be a new addition to Number Theory. 

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#11000

On Friday, 26 June 2020 12:56:50 UTC+2, James Dow Allen  wrote:

> My personal advice is that he spend an hour on each of a
> few different languages, just to get an idea which has a flavor
> that might appeal to him.

One hour??  This discussion is getting fucking hilarious by the minute.

When Dunning-Kruger is a compliment...

*Plonk*

Julio

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#10995

On the topic of computer languages whose names rhyme
with 'Fortran' why has nobody mentioned Conway's Fractran?
    https://en.wikipedia.org/wiki/FRACTRAN
The example program:
     17/91; 78/85; 19/51; 23/38; 29/33; 77/29; 95/23;
     77/19; 1/17; 11/13; 13/11; 15/14; 15/2; 55/1;
produces all the prime numbers!  (It's a good thing nobody
added comments to this program -- though Turing-complete,
Fractran is breathtakingly inefficient.)

 

On Friday, June 26, 2020 at 1:48:29 PM UTC+7, David Brown wrote:
> On 25/06/2020 21:48, Richard Heathfield wrote:
> > On 23/06/2020 13:14, James Dow Allen wrote:
> >> I am a C fan myself, which makes me rather obsolescent compared
> >> with the cool guys. :-)
> > 
> > Not so. There is no language cooler than C. The C in C actually stands
> > for Cool.
> > 
> >> But I think almost any language would be
> >> more FUN than Fortran.
> > Unless you're writing a quine.
> > 
> > "FORTRAN was the language of choice, for the same reason that
> > three-legged races are popular."
> > 
> 
> Didn't some FORTRAN systems let you change the value of 3 if you don't
> like the usual one?

Some languages allowed that, IIRC.  I didn't know Fortran was one of them.
My first programs ran on an IBM 1620, where addition and multiplication
were performed by reading addition and multiplication tables from
low core!  (As a defense against saboteurs, those tables were
replenished before each job.)

I used to tag along when the object was to repair broken million-dollar
mainframes.  Once or twice, for comic relief, I'd patch the bitmaps
for the console printer, swapping '0' and 'F.'  Clear memory and
see 'ffffffff ...' instead of '00000000 ...'

"Now you've done it!  The whole D-Bus is upside down!"  Exciting days.
Now the most excitement I get is taking my temperature at 7-Eleven.

James Dow Allen

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#10997

On 26/06/2020 10:58, James Dow Allen wrote:
> On the topic of computer languages whose names rhyme
> with 'Fortran' why has nobody mentioned Conway's Fractran?
>     https://en.wikipedia.org/wiki/FRACTRAN
> The example program:
>      17/91; 78/85; 19/51; 23/38; 29/33; 77/29; 95/23;
>      77/19; 1/17; 11/13; 13/11; 15/14; 15/2; 55/1;
> produces all the prime numbers!  (It's a good thing nobody
> added comments to this program -- though Turing-complete,
> Fractran is breathtakingly inefficient.)
> 
>  
> 
> On Friday, June 26, 2020 at 1:48:29 PM UTC+7, David Brown wrote:
>> On 25/06/2020 21:48, Richard Heathfield wrote:
>>> On 23/06/2020 13:14, James Dow Allen wrote:
>>>> I am a C fan myself, which makes me rather obsolescent compared
>>>> with the cool guys. :-)
>>>
>>> Not so. There is no language cooler than C. The C in C actually stands
>>> for Cool.
>>>
>>>> But I think almost any language would be
>>>> more FUN than Fortran.
>>> Unless you're writing a quine.
>>>
>>> "FORTRAN was the language of choice, for the same reason that
>>> three-legged races are popular."
>>>
>>
>> Didn't some FORTRAN systems let you change the value of 3 if you don't
>> like the usual one?
> 
> Some languages allowed that, IIRC.  I didn't know Fortran was one of them.

The easiest for this is, I think, Forth:

: 3 2 ;

There.  Now "3" is defined as word that pushes the value "2" on the stack.

I wonder why there is no obfuscated Forth competition?

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#11005

On 6/26/20 4:58 AM, James Dow Allen wrote:
> On Friday, June 26, 2020 at 1:48:29 PM UTC+7, David Brown wrote:
>>
>> Didn't some FORTRAN systems let you change the value of 3 if you don't
>> like the usual one?
> 
> Some languages allowed that, IIRC.  I didn't know Fortran was one of them.
> My first programs ran on an IBM 1620, where addition and multiplication
> were performed by reading addition and multiplication tables from
> low core!  (As a defense against saboteurs, those tables were
> replenished before each job.)
> 
> I used to tag along when the object was to repair broken million-dollar
> mainframes.  Once or twice, for comic relief, I'd patch the bitmaps
> for the console printer, swapping '0' and 'F.'  Clear memory and
> see 'ffffffff ...' instead of '00000000 ...'
> 
> "Now you've done it!  The whole D-Bus is upside down!"  Exciting days.
> Now the most excitement I get is taking my temperature at 7-Eleven.
> 
> James Dow Allen
> 

FORTRAN did calls with pass by reference, by you could also call the
functions with constants. If the function changed the value of the
parameter that was assigned with a constant, it would change the
location that constant was stored in, which might affect other usages of
that same constant.

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#11002

On Monday, 22 June 2020 02:31:54 UTC+2, syed owais  wrote:

> Do you regard the following question as an interesting one in number thoery:

NO, not even near!  Now get the fuck out of here.

*Plonk*

Julio

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#10926

On 13/06/2020 13:07, syedanwarowais5@gmail.com wrote:
> As part of a (hopefully growing) exploration in number theory, I need to find solutions to the following diophantine equation :
> ab(a+b)=cd(c+d) (in positive integers)
> The first solution set is a=1,b=5 and c=2,d=3.
> I know there are several more solution sets, though I don't know if there are an infinite number of solutions sets to this diophantine equation. 
> Would you like to write a program to solve this puzzle?  
> Once you respond, I will go deeper into the mathematics this connects to. 
> 

If a₁, b₁, c₁, d₁ is one set, and a₁, b₁, c₂, d₂ is another set (same a,
b), then c₁, d₁, c₂, d₂ is another set.

And for each set a, b, c, d, you have the sets:

	a, b, c, d
	b, a, c, d
	a, b, d, c
	b, a, d, c

	c, d, a, b
	d, c, a, b
	c, d, b, a
	d, c, b, a

and for any n, you get n.a, n.b, n.c, n.d.

I assume that you want a, b to be different from c, d, though you didn't
state it.  So I'd say you are looking for numbers that can be written as
ab(a + b) in at least two different ways.


Here's a simple Python function for it:

def solutions(max_a = 200, min_len = 2) :
	d = {}
	for a in range(1, max_a) :
		for b in range(a + 1, max_a + 1) :
			s = a * b * (a + b)
			if s in d :
				d[s].append((a, b))
			else :
				d[s] = [(a, b)]
	return sorted([vs for vs in d.values() if len(vs) >= min_len])

(My results match Ben's, which is a good sign.)

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