Name

Notation

Example

symbol

combinations of letters, numbers

and some other characters

x name cons_one

operator

Standard binary operations

+ - / * ^

expression

Combination of symbols, operators and separaters

(x1 + y1)^2/(x1*y1)

assignment

When a symbol is assigned a value :=

v := expr1*expr2

termination

:(no output shown), ;(output shown)

(x1 + expr1*v);

evaluation

automatic but can be forced in some cases with eval

certain forms such as evaln used to get numeric or other results

evaln(sin(1.1));

quote

stops evaluation quote(1+1);

s:=x^2 + 2;t:=quote(s) or

t:= 's

string

use left quotes

read `file1.txt`;

last results

one, two or three double quotes

x1 := """;

equal

used to represent logical statements or equations

5=3;

sequence

expr1, expr2, expr3,

1,5=3,sin(x);

list

[sequence]

[1,5=3,sin(x)]:

set

{sequence with no repeats and no order preserved}

{1,2,3}={1,1,2,3};

substitution

An equation symbol = expr1 used to substitute expr1 for symbol

in another expression, thus subs(sym=expr1,expr2) or subs(set,expr)

where set is a set of substitutions

subs(t=q+1,sin(t));

iteration

for counter from integer1 to integer2 do statement sequence od;

for j from 1 to5 do tot := tot + j od

differentiate

diff(expr,symbol1,symbol2, ....);

diff(x^2*y^2,x,y);

function

symbol -> expression that depends on symbol

cosap:= x-> 1 - x^2/2

map

map(function, list)

map(cosap,[1,2,x]);