If you are used to a traditional programming language, then you have
variables that can be set to values.
You don't have indeterminates.
In a symbolic mathematics system, you have indeterminates or names that
can be manipulated.
When you assign a value to an indeterminate, the symbolic math system
must determine somehow
whether your utterance is to be treated as the indeterminate or its value.
One way of avoiding confusion is to have 2 sets of names. Names that
are used as containers to hold values, as
is traditional in programming languages, and another set of names that
are used literally.
Mathematicians are surprisingly sloppy notationally. That is, contrary
to the usual expectation of mathematicians,
they are usually not precise, formal, exacting, etc. in their
specification of everything...
Unfortunate for people trying to automate mathematics.
RJF
On 6/11/2011 7:14 PM, Robert Dodier wrote:
> On 6/8/11, Neilen Marais<nmarais at gmail.com> wrote:
>> Robert Dodier<robert.dodier<at> gmail.com> writes:
>>> On 7/2/10, Alexander Shulgin<alex.shulgin<at> gmail.com> wrote:
>>>
>>>> Is it possible to get a reference to a hash table in maxima?
>>> Yes: try use_fast_arrays:true $
>>> Instead of attaching the hash table to a symbol property,
>>> the hash table is put in the value slot of the symbol.
>>>
>>> The hash table is created the first time an attempt is
>>> made to store something in it.
>> Interesting, that also fixes the use of hash tables for my applicaion. Am I
>> alone in wondering why that isn't the default behaviour? The whole hash
>> table/symbol property seems like a black magic approach to me while the
>> latter approach seems to be how it works in most modern languages.
>> Simply a case of historic precedent?
> Well, I think there is a certain tension between name and value
> in mathematics. Sometimes it's more convenient to work with
> one or the other. For example, let X be an orthogonal matrix with
> some specific elements. Let's say sooner or later the product
> transpose(X) . X appears. If the value of X is substituted for the
> name, then we explicitly carry out the multiplication and get an
> identity matrix. But it's more mathematical to remember the
> properties of X and say, oh, we can skip a step here, we know the
> result is an identity matrix.
>
> Unfortunately Maxima's ability to separate name and value is kind
> of confused. But that's the motivation (I'm pretty sure, anyway;
> I wasn't around for the first several iterations of Maxima development)
> for the distinction between objects which are values and objects
> which are properties of symbols.
>
> Hope this clarifies the situation. Best,
>
> Robert Dodier
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