Basic Maple Commands
Command Description
1. General Commands and Conventions
f(a) evaluating a function f at a; e.g. sin(Pi)
; command end/result displayed
: ” ” /result not displayed
% (previously: ”) output of previous line
cursor on name, click on help help for name
settime := time(); expression;
time() − settime;
to get elapsed time for computing an expression
a := expression; assignment
aˆn; n-th power of a
sqrt(a); the (exact) square root of a
evalf(expression, n); numerical value of expression to n-digit accuracy
evalb(a = b); logical comparison (gives true or false)
a[n]; n-th element of list a
plot(expression, x = a..b); 2-dim plot of expression for x between a and b
plot3d(expr, x = a..b, y = c..d); 3-dim plot of expr for x between a and b and y between
c and d
f := x−> expr definition of a one-variable function f(x)
f := [x, y, . . .]−> expr definition of multi-variable function f(x, y, . . .)
a := proc(x, y) local z, w; ...; end; definition of subroutine a
2. Elementary Number Theory
iquo(a, b); or floor(a/b); integral part of the quotient a/b
irem(a, b); or modp(a, b); remainder of division of a by b
frac(x); the fractional part of x
igcd(a, b); the gcd of a and b
igcdex(a, b, x , y ); the extended gcd
x; y; to extract the values of the above extended gcd
ithprime(n); the n-th prime number
isprime(n); test whether or not n is prime (gives true or false)
ifactor(n); factor n into its prime factors
a&∧
n mod m; or Power(a, n) mod m; compute an
mod m efficiently
mpl–1
Command Description
3. Sets and Lists: Basic Structure
s := {1, 2, 3, 4, 5}; defines a set s: an unordered sequence of elements
a := [1, 2, 3, 4, 5]; defines a list a: an ordered sequence of elements
s := {seq(f, i = 1..5)}; create the set s consisting of the elements f(1),. . . ,
f(5); here f is an expression (depending on i)
a := [seq(f, i = 1..5)]; create the list a consisting of the elements f(1), . . . ,
f(5); here f is an expression (depending on i)
nops(a); the number of elements in list a
a[i] the ith element of the list a
[a[i..j]] or [op(i..j, a)] the list consisting of elements i through j (inclusive)
select(k−> k < m or k > n, a); list a with elements m through n dropped
member(e, a); test whether e occurs in list a (true or false)
member(e, a, p ); p; the position(s) at which e occurs in a
type(s, set); check whether s is a set (has type “set”); gives true
or false
type(a, list); check whether s is a list (has type “list”); gives true
or false
4. Operations on Sets and Lists
s := convert(a, set); convert a list to a set
a := convert(s, list); convert a set to a list
s union t; or ‘union‘(s, t, . . .) combine sets s, t, . . . , removing repeated elements
s intersect t; intersection of sets s and t
s minus t the set of elements which are in s but not in t
[op(a), op(b), . . .] concatenate (join) the lists a, b, . . .
a := [e, op(a)]; add element e at the beginning of list a
a := [op(a), e]; add element e at the end of list a
a := subsop(i = e, a); replace the ith element of the list a by e
a := subsop(i = NULL, a); delete ith element from list a
[a[1..n − 1], e, a[n..nops(a)]; insert e at position n in list a
sort(a); sort the elements of list a (into a standard order)
[select(bool, a)]; list consisting of the elements of a for which the
boolean-valued function bool is true
map(f, a); apply the function f to each element of the list a
mpl–2
Command Description
5. Character Strings
str := ”This is a string”; defining a character string
length(str); the number of characters in a string
substring(str, m..n); extract a substring from string str starting with the
mth and ending with the nth character
[seq(substring(str, k..k), k = 1..
length(str)]
give the list of characters in a string
searchtext(st, str) find the place where st occurs in string str
s1.s2. . . . or cat(s1, s2, . . .) join the strings s1, s2, . . . together
convert(expr, string); convert an expression to a string (textual form)
type(str, string) check whether str is a string (true or false)
6. Boolean expressions
b := true; b := false; assigning true/false to the variable b
=, <>, <, <=, >, >= relation operators (equal, not equal, less than, etc.);
can be used to form boolean expressions
and, or, not logical operators (→ boolean expressions)
evalb(bool) evaluate the boolean expression bool (gives true or
false)
type(b, boolean) check whether b is a boolean expression (true or
false)
7. Looping control
for i to m do; expr; od; evaluate expr repeatedly with i varying from 1 to m
in steps of 1
for i from n to m by s do; expr; od; evaluate expr repeatedly with i varying from n to m
in steps of s
while test do; expr; od; evaluate expr until test becomes false
for i from n to m by s while test
do; expr; od;
evaluate expr repeatedly with i varying from n to m
in steps of s as long as test is true
RETURN(expr) (explicit) return from a subroutine, assigning the
value expr to the subroutine
8. Conditionals
if test then statmt fi; execute the statement (sequence) statmt only if test
is true
if test then statmt1 else statmt2 fi; execute the statement (sequence) statmt1 if test is
true, otherwise execute statmt2
mpl–3
Command Description
9. Complex Numbers
z := x + y ∗ I; defining a complex number
abs(expr); the absolute value of expr
argument(expr) the argument of expr
Re(expr); Im(expr); the real and imaginary part of expr
conjugate(expr); the complex conjugate of expr
evalc(expr) evaluating an expression (as a complex number)
convert(expr, polar) convert expr to its polar form
type(expr, complex) check that expr has type “complex”
10. Polynomials
f := x∧
n + a1 ∗ x∧
(n − 1) + . . . ; defining a polynomial f = f(x) (assuming that x has
no value)
type(f, polynom(integer, x)) check that f is an integer polynomial in x
degree(f, x) degree of f in x
coeff(f, x, n) extract the coefficient of xn
in f
coeffs(f, x) list of coefficients of f(x)
lcoeff(f, x) the leading (highest) coefficient of f(x)
tcoeff(f, x) the constant (trailing) coefficient of f(x)
collect(f, x) collect all coefficients of f which have the same powers
in x
expand(expr) distribute products over sums
sort(f) sort into decreasing order
subs(x = a, f) evaluate f(x) at x = a
Eval(f, x = a) mod p; evaluate f(x) (mod p) at x = a
f mod n; reduce the coefficients of f modulo n
quo(f, g, x); rem(f, g, x); the quotient and remainder of division of f by g
(viewed as polynomials in x)
gcd(f, g, x) the greatest common divisor of f(x) and g(x)
gcd(f, g, x, s , t ) the extended Euclidean algorithm of f(x) and g(x);
i.e. s, t satisfy f ∗ s + g ∗ t = g := gcd(f, g)
factor(f) factor f into its irreducible factors
Factor(f) mod p factor f modulo p
roots(f) find the rational roots of f
interp(x, y, t) The Lagrange Interpolation polynomial
mpl–4