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MathGroup Archive 1997

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Re: Re: Useful Dumb User Questions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg9114] Re: [mg9080] Re: [mg8988] Useful Dumb User Questions
  • From: Mark Evans <evans at gte.net>
  • Date: Mon, 13 Oct 1997 23:33:26 -0400
  • Organization: None
  • Sender: owner-wri-mathgroup at wolfram.com

I think the Q idea of yours is fabulous.  It might be a good way to
debug code.

I wonder if, as well, Mathematica should have an option on some of these
functions that causes it to double-check its own answer.  In school, you
solve a differential equation, then the assignment may ask you to verify
that your solution satisfies the equation.  That verification is what I
am talking about.  It would be like you telling your computer to write a
file to disk, then do a read-verify when it's finished, so that you are
sure the computer wrote what it was told.

It may be possible to use Trace[] to obtain a partial fulfillment of
your Q idea, but I never use Trace[], because it is awkward and there
are faster ways to debug code.

Mark





Olivier Gerard wrote:
[snip]
> First: formal or peer-reviewed certification of Mathematica algorithms
> would certainly be a very strong point for WRI both as a public mark of
> excellence and as a token of openness towards users and the research community.
> Just quoting (but without bibliography) bunches of algorithm names as
> it is done in the Book is not enough. There is certainly a middle
> point to find between protecting industrial secrets and giving a fair
> chance to researcher and users to give a valuable input to WRI in return.
> This would also certainly help researchers recognize WRI achievements
> and the help Mathematica has provided to so many people.
[snip]
> Third: It leads naturally to an interesting problem in Mathematica:
> accessing the mathematical knowledge it contains. Large Black Boxes
> like Integrate or Sum or DSolve are organized in a competitive spirit:
> "Do everything you can to get a definitive answer but if you do not
> succeed just leave it alone".
> A computer algebra system or a human being cannot solve every mathematical
> problem one can dream of. But a human learns a lot asking questions
> and partial answers are informative. If we want to make Mathematica
> a more pleasant system to use in many situations we must learn from
> its (sometimes unsuccessful) tentatives to solve our question and
> make it a way to share the scientific knowledge it contains which was
> accumulated by generations of people for several thousands of years.
> This is why I propose a new series of commands, something we could
> call QSolve, QDSolve, QIntegrate, etc... (to mimic the current N
> prefix of numerical versions) which would analyze the
> input and give as many conclusions on its nature and qualitative
> aspects as possible (Q is for Query or Question).
> 
> A trivial example:
> 
> QDSolve[ y''[x] + y'[x] + y[x] == f[x], y[x], x]
> 
> would give something like:
> 
> "This looks like a second-order linear differential equation.
> The unknown function is y and the variable is x.
> There is a 2-dimensional set of solutions. You can specify
> a precise solution by giving 2 initial conditions.
> I will not be able to integrate it completely for y[x] until I have
> more information on f[x]. f[x] should be continuous."
> 
> And much more...
> I am very interested by your opinion on this proposal.
[snip]



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