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Re: [cellml-discussion] Representing derivatives in plain-text content MathML input languages

From: Matt <matt.halstead@auckland.ac.nz>
Date: Mon, 20 Nov 2006 15:31:47 +1300
Message-ID: <60d4509f0611191831gec43bd6l531c6df0abc589a9@mail.gmail.com>
To: "For those interested in contributing to the development of CellML." <cellml-discussion@cellml.org>
Cc: www-math@w3.org

As a side note, here are the links to the matlab symbolic toolbox -

http://www.mathworks.com/access/helpdesk/help/toolbox/symbolic/

http://www.mathworks.com/products/symbolic/demos.html

look at the documentation on differential equations, Creating Symbolic
Variables and Expressions , and Several Differential Equations

On 11/20/06, Andrew Miller <ak.miller@auckland.ac.nz> wrote:
> Hi all,
>
> I have been developing a plain-text input language for the content
> MathML in CellML documents (so that it can be efficiently edited by users).
>
> I am seeking opinions on the best way to represent derivatives
> (including partials) in the input language.
>
> I have discussed this with the CellML team at the meeting today, and
> several options were suggested. I would welcome opinions on which of
> these options is the best, and I would also be keen to hear if you can
> think of another different but better representation in input languages.
>
> All examples refer to the representation of the following content MathML:
> <apply><eq/>
>   <apply><diff/>
>     <bvar><ci>t</ci></bvar>
>     <ci>x</ci>
>   </apply>
>   <ci>y</ci>
> </apply>
>
> Option one:
>   Representation: diff(x, t) = y.
>   Advantages:
>    * Succinct.
>    * Follows the same syntax as functions in the rest of the language,
> so makes it less complex and easier to understand.
>    * Easily generalises to partial differentials by replacing diff with
> partialdiff or pdiff.
>   Disadvantages:
>    * Non-obvious to new users: does diff mean differential, difference, ...?
>    * It is unclear to the user what the ordering of x after t means,
> i.e. which is the bound variable, so you just have to remember that the
> second 'argument' is the bound variable.
>
>
> Option two:
>   Representation: deriv(x, t) = y
>   Similar advantages as option one, but also:
>   Advantages:
>   * Slightly less potential for confusion.
>   Disadvantages:
>   * Slightly longer.
>
> Option three:
>   Representation: differential(x, t) or derivative(x, y)
>   Similar advantages as option one, but also:
>   Advantages:
>   * Clearer meaning.
>   Disadvantages:
>   * Longer. UIs could simplify input of this by tab-expansion or
> type-ahead features.
>
> Option four:
>   Representation: d(x)/d(t)
>   Advantages:
>   * Similarity to Leibniz notation (arguably more clear meaning)
>   * Clear distinction between the bound variable and the expression that
> the differential is being applied to.
>   Disadvantages:
>   * Syntax is inconsistent with the rest of the grammar.
>   * It incorrectly suggests that differentials could be moved around,
> while in reality it is a limited syntax for derivatives.
>   * Extending it to partial differentials could look messy and
> confusing, e.g. del(x)/del(t) .
>
> Any opinions are welcome.
>
> Best regards,
> Andrew Miller
>
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Received on Monday, 20 November 2006 02:31:51 GMT

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