Books about CAS

[Jonathan Busby]

(01-31-2020 06:44 AM)Nad Wrote:  P.S. Talking about data types and memory representation, how are things like "x", pi, sqrt(2), "x^3 +y" etc. stored in memory in a CAS?

Usually, the CAS has some internal representation for algebraic expressions that's easy to convert to a string. The internal representation could be the AST ( Abstract Syntax Tree ) or something derived from it. In this format it's easy to manipulate the expressions for the purposes of eg. term re-writing and it's also possible to quickly evaluate the expression, assuming all free variables in the expression have been instantiated.

In the case of the 48, the CAS has a stack based, RPN, "meta-object" intermediate representation for symbolic expressions when the CAS needs to transform or manipulate the expression. Such expressions are stored as symbolic objects in another "intermediate representation" which are essentially the same as any other composite object such as lists or secondaries, and, with xEVAL, they're also executable. The symbolic object can contain a mix of variables, functions, and constants etc. basically any RPL word that makes sense in a symbolic. If the CAS needs the value of the symbolic, then EVALing it is quite quick since it can be directly executed like a secondary, assuming that all free variables are bound. In terms of term re-writing and other functions, IIRC, I think that the stack based, RPN, meta-object representation is used.
Regards,

Jonathan

NOTE #1 : The technical definition of a Sys-RPL meta-object is essentially an RPL composite object that has been serialized onto the stack via =INNERCOMP, where the first element on the stack is a system binary integer which indicates the number of objects that have been pushed to the stack.