Symbolic Expressions

All primitive mathematical procedures are extended to be generic over symbolic arguments. When given symbolic arguments these procedures construct a symbolic representation of the required answer. There are primitive literal numbers. We can make a literal number that is represented as an expression by the symbol 'a as follows:

(literal-number 'a)

The literal number is an object that has the type of a number, but its representation as an expression is the symbol 'a:

(kind (literal-number 'a))
;;=>  :sicmutils.expression/numeric

(freeze (literal-number 'a))
;;=>  a

Literal numbers may be manipulated, using the generic operators:

(sin (+ (literal-number 'a) 3))
;;=> (sin (+ 3 a))

To make it easy to work with literal numbers, Clojure symbols are interpreted by the generic operations as literal numbers:

(sin (+ 'a 3))
;;=>  (sin (+ 3 a))

We can extract the numerical expression from its type-tagged representation with the freeze procedure:

(freeze (sin (+ 'a 3)))
;;=>  (sin (+ 3 a))

but usually we really don’t want to look at raw expressions

(freeze ((D cube) 'x))
;;=>  (+ (* x (+ x x)) (* x x))

because they are unsimplified. We will talk about simplification later, but for now note that simplify will usually give a better form:

(simplify ((D cube) 'x))
;;=>  (* 3 (expt x 2))

and print-expression, which incorporates simplify, will attempt to format the expression nicely.

Besides literal numbers, there are other literal mathematical objects, such as vectors and matrices, that can be constructed with appropriate constructors:

(literal-vector <name>)
(literal-down-tuple <name>)
(literal-up-tuple <name>)
(literal-matrix <name>)
(literal-function <name>)

As of version 0.14.0, these haven’t yet been ported over to Clojure from scmutils. Stay tuned for a future release, as we have all of the machinery in place to do this.

There are currently no simplifiers that can manipulate literal objects of these types into a nice form.