Re: [Maxima-discuss] Why does 'solve' not work here?

[Richard F. <fa...@be...>]

On 2/15/2014 11:00 AM, Mark wrote:
> On 02/15/2014 05:28 PM, Richard Fateman wrote:
>>> Given the two simultaneous equations:
>>> sin(y) = 0
>>> sin(x-y) = sin(y)
>>> will Maxima solve them using a single input command, calling just a
>>> single one of its built in functions?
>> So far as I can tell, there is no single current built-in function
>> that will solve this problem.
> Ok. Simple question. Simple answer. Thanks.
>
> The rest of you answer seems not completely Maxima related, but was kind
> of fun too.
>
>> Let me ask you an analogous question.  Can you make a sandwich with a
>> single piece of
>> bread using your standard method of making a sandwich with two pieces
>> of bread?
>>
>> (My) answer:  No.   But I can make a sandwich by folding a single
>> piece of bread or cutting it in half, etc.
> (My) answer: Yes.  With so many competing bakeries around, why starve
> from less lunch? Go and get yourself the second piece of bread everyone
> else is enjoying already.
>
>>> If so, which built in function?
>> Why must all tasks be solved by a single built-in function?  Why not a
>> combination?
> That's a simple one: because when humble-me turns to a CAS I expect the
> CAS to tell me the solution - not vice versa.
>
>>    For example, if
>> you took the inputs, converted them to exponentials you could make
>> some headway. e.g.
>> to_poly_solve(exponentialize([(sin(x-y)-sin(y)=0),sin(y)=0],[exp(-%i*x),exp(-%i*y)]);
>>
> That's the same point I already made in my question: there are many ways
> to solve such kind of equations with several in-between-steps. Your's is
> one. The one I gave is another one. As you know, I could 'map' the
> asin() function to the list of equations and then call 'solve' which can
> also be written in one line.
>
>>> But that's not what I'm looking for.
>> No, apparently what you want is to have a somewhat longer and in some
>> cases slower
>>   program that spends some  more time looking for trivial solutions.
> No. Totally misunderstood.
I think not.
> What I want from a CAS is a 'solve' command that I can rely on to do the
> simple things right, before I apply it to a case where neither I nor you
> can just guess the solution.
Such a program would necessarily be longer and in some cases slower.  
Sometimes it
would be MUCH slower because the search for a trivial solution that 
appears only after
a non-trivial simplification can require lots of time. How much time do 
you wish to spend
on (for example) radcan() or trigsimp() or ... as part of solve()?

>
> Actually there is an analogous question I have to you:
> There is a grad student wanting to joint a project of your's. So you
> tell the student that you have one piece of bread and that you take
> another piece of bread and that you place it on top of the first one.
> Now you ask the student: how many pieces of bread do I have on the
> stack? The student answers: I cannot solve this.
If I had a computer that was programmed to do X  and I asked it to do Y 
different from X, and it
said "I cannot solve this" I would probably not complain.  I might 
actually be happy that it
could provide that information, as opposed to crashing or not returning.

I expect human graduate students to have a more "flexible program" so to 
speak.  If you
want to write an artificial-intelligence style mathematician simulator, 
you could look at the
history of this kind of research, and perhaps look at the claims for 
Wolfram Alpha.
There are interesting efforts to have a computer solve "word problems".  
Maybe not
so much for "bread problems."

RJF