Maxima: what does Maxima call an "array"?

Question

I am a bit confused ; I noticed that if I do :

a[sqrt(2)] : 1;
arrays;

I would get :

[a]

So a is an array for Maxima… yet sqrt(2) is an irrational number.

I use to think of an array as a collection of items sorted by indices, where those indices are integer numbers… I acknowledge that my definition for "array" has been strongly influenced by other, "non-symbolic" programming languages. In those languages, arrays "map" to a certain contiguous region of a computer's memory. It is therefore natural to use integer number as indices since integer number are countable. However, real numbers are not countable.

Obviously, maxima seems to have a different definition for the term "array" : what is it exactly ? (the documentation does not define it, at least there is no introductory paragraph in the documentation section dedicated to arrays)

Answer 1

Maxima's concept of arrays, lists, and matrices is pretty confused, since various ideas have accreted in the many years of the project.

Maxima's "subscripted variable" = symbol with subscript (with arbitrary index) and no assigned value. E.g. a[sqrt(2)] with no value assigned.

Maxima's "undeclared array" = hash table with arbitrary keys, associated with array symbol as a symbol property, not a value. Your a[sqrt(2)] : 1 is an example of an undeclared array. Maxima creates the array a the first time a value is assigned.

Maxima's "declared array" = contiguous storage, associated with array symbol as a symbol property, not a value.

Maxima's "Lisp array" = contiguous storage, associated with array symbol as symbol value.

Maxima's "fast array" = hash table, associated with array symbol as a symbol value.

Yes, this is a mess. Sorry about that. These are all interesting ideas, but there is no unifying framework. I haven't even mentioned lists and matrices. Hope this helps all the same.