1. Basic Data Types

The basic data types are numbers: integers, rationals, floats, strings, etc.

>

a := 3;

>

b := 3.0;

>	whattype(a); whattype(b);

The type determines the effect of the operations.

>	a + 10^(-20); b + 10^(-20);

>	s := "x*y + 3*x^3 - 8";

>	whattype(s);

>	p := parse(s); # opposite to convert(p,string)

2. Expression Trees

Let us look into the structure of the polynomial p.  The p is an expression, a composite data type.

>	op(p); whattype(p); nops(p);

We see that p is of type "+" and p consists of 3 operands.

>	p1 := op(1,p); # select the first operand of p

>	op(p1); whattype(p1);

>	p2 := op(2,p); op(p2); whattype(p2);

>	op([2,2],p); # x^3 is the 2nd operand of the 2nd operand of p

>	op([2,2,1],p); op([2,2,2],p); whattype(op([2,2],p));

>	r := convert(p,`*`);  # we convert p from a `+` to a `*`

>

op(r);

>	q := convert(r,`+`);

3. Attributes

Attributes are characteristics of a variable what a user can add to it.  It is mainly for human consumption, we could see it as an annotation or a comment to a variable.

>	p := x^2 + x + 1;

>	alias(alpha=RootOf(p));

>	whattype(alpha);

To associate to alpha the meaning as a formal root we can add a string as an attribute to alpha:

>	alpha := setattribute(alpha,"a formal root of x^2 + x + 1");

>	attributes(alpha); # query the attributes of alpha

4. Properties

A property of a variable is used mainly for simplication purposes in calculations.  Unlike attributes, we use properties for calculating more efficiently, which means in symbolic computation that we may simplify more often.

>	assume(x,real);

>	simplify(sqrt(x^2));

Maple does the simplification because of the assumption, which is indicated by the flag x~.

5. Units

Units give meaning to calculations.

>	convert(1,units,km,miles);

>

evalf(%);

>	with(Units[Standard]);

Warning, the name Unit has been rebound

Warning, the assigned names factor and polar now have a global binding

Warning, these protected names have been redefined and unprotected: *, +, -, /, <, <=, <>, =, Im, Re, ^, abs, add, arccos, arccosh, arccot, arccoth, arccsc, arccsch, arcsec, arcsech, arcsin, arcsinh, arctan, arctanh, argument, ceil, collect, combine, conjugate, convert, cos, cosh, cot, coth, csc, csch, csgn, diff, eval, evalc, evalr, exp, expand, floor, frac, int, ln, log, log10, max, min, mul, normal, root, round, sec, sech, seq, shake, signum, simplify, sin, sinh, sqrt, surd, tan, tanh, trunc, type, verify

>	a := 3*Unit(miles);

>	b := 7*Unit(km);

>

c := a+b;

>

evalf(c);

After loading Units[Standard], Maple automatically converts to the metric system.