MTH 207 Labs

Maple Data Types

Some useful Maple data types are given here.
Note that this is not an exhaustive list, if you want to see them all try
> ?type

You should be aware that data types can overlap. For example, given
f := x -> x^2
then f is an operator, a name, a scalar and a string.

You can check the type of an expression using the Maple type keyword. The syntax is:

type(expression, type)

type returns a boolean value, either true or false. For example
> f := x -> x^2;
> type(f, operator);
> type(f, function);
> type(f, numeric);
> type(14/64, rational);
> type(14/64, float);
> type(evalf(14/64), float);
> type(14/64, numeric);

Data Types

Logical Types
boolean A Boolean expression is an expression of type relation or of type logical or one of the Boolean constants true or false.
relation A relational expression is an expression involving `=`, `<>`, `<` or `<=`.
logical A logical expression is an expression involving and, or, or not.

Numeric Types
complex A complex constant, of type constant and does not involve one of the non-numeric constants (true, false, FAIL, infinity).
constant A complex constant, including ±infinity.
float An object is of type float if it is a floating point number, that is, a sequence of digits and a decimal point.
fraction An object is of type fraction if it is represented by a signed integer divided by a positive integer (posint)
infinity ±infinity, or complex infinity.
integer An expression is of type integer if it is an (optionally signed) sequence of one or more digits.
numeric An object is of type numeric if it is either an integer, a fraction, or a float.
rational An object is of type rational if it is either of type fraction or of type integer.
realcons A real constant is ±infinity or an expression for which evalf will return a float.

Algeraic Types
anything Any valid Maple expression, except an expression sequence (exprseq)
algebraic An expression is of type algebraic if it is one of the following types: integer, fraction, float, string, indexed, series, function, operator (and several more)
equation An equality '=' with a left and right hand side, e.g. 'a = b'
function An uneveluated function call e.g. 'f(x)', where f is undefined. Note that if f is defined f := x -> x^2; this becomes an operator. Usually you want type operator not type function
operator A function defined with the -> operator, e.g. f := x -> x^2, f is of type operator.
range A range defined with ellipsis e.g. 'a..b'.

Indexed Types
array A variable declared with the array keyword (see lesson 6).
exprseq A sequence of expressions, possibly in square brackets or braces. Expression sequences (or simply sequences) are created using the comma operator ','. e.g. s := 1,2,3 assigns s the sequence 1,2,3. In Maple, sequences form the basis of many data types. In particular, they appear in function calls, lists, sets and subscripts.
list A list is an ordered sequence of expressions enclosed in square brackets [..].
set A set is an unordered sequence of distinct expressions enclosed in braces {..}, representing a set in the mathematical sense.
matrix A matrix is defined to be a two-dimensional array with indices starting at 1.
scalar A scalar is anything which is not of type vector or matrix.
vector A vector is defined to be an one-dimensional array indexed from 1.

String Types
name A name is usually a string, which in its simplest form is a letter followed by zero or more letters, digits, and underscores.
string Any text string, not a numeric value.

Logical Types
boolean	A Boolean expression is an expression of type relation or of type logical or one of the Boolean constants true or false.
relation	A relational expression is an expression involving `=`, `<>`, `<` or `<=`.
logical	A logical expression is an expression involving and, or, or not.

Numeric Types
complex	A complex constant, of type constant and does not involve one of the non-numeric constants (true, false, FAIL, infinity).
constant	A complex constant, including ±infinity.
float	An object is of type float if it is a floating point number, that is, a sequence of digits and a decimal point.
fraction	An object is of type fraction if it is represented by a signed integer divided by a positive integer (posint)
infinity	±infinity, or complex infinity.
integer	An expression is of type integer if it is an (optionally signed) sequence of one or more digits.
numeric	An object is of type numeric if it is either an integer, a fraction, or a float.
rational	An object is of type rational if it is either of type fraction or of type integer.
realcons	A real constant is ±infinity or an expression for which evalf will return a float.

Algeraic Types
anything	Any valid Maple expression, except an expression sequence (exprseq)
algebraic	An expression is of type algebraic if it is one of the following types: integer, fraction, float, string, indexed, series, function, operator (and several more)
equation	An equality '=' with a left and right hand side, e.g. 'a = b'
function	An uneveluated function call e.g. 'f(x)', where f is undefined. Note that if f is defined f := x -> x^2; this becomes an operator. Usually you want type operator not type function
operator	A function defined with the -> operator, e.g. f := x -> x^2, f is of type operator.
range	A range defined with ellipsis e.g. 'a..b'.

Indexed Types
array	A variable declared with the array keyword (see lesson 6).
exprseq	A sequence of expressions, possibly in square brackets or braces. Expression sequences (or simply sequences) are created using the comma operator ','. e.g. s := 1,2,3 assigns s the sequence 1,2,3. In Maple, sequences form the basis of many data types. In particular, they appear in function calls, lists, sets and subscripts.
list	A list is an ordered sequence of expressions enclosed in square brackets [..].
set	A set is an unordered sequence of distinct expressions enclosed in braces {..}, representing a set in the mathematical sense.
matrix	A matrix is defined to be a two-dimensional array with indices starting at 1.
scalar	A scalar is anything which is not of type vector or matrix.
vector	A vector is defined to be an one-dimensional array indexed from 1.

String Types
name	A name is usually a string, which in its simplest form is a letter followed by zero or more letters, digits, and underscores.
string	Any text string, not a numeric value.

Some other types are given below.

Function types
arctrig An expression which is one of the inverse trigonometric or hyperbolic functions: arcsin, arccos, arctan, arcsec, arccsc, arccot, arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth.
trig An expression which is one of the trigonometric functions: sin, cos, tan, sec, csc, cot, sinh, cosh, tanh, sech, csch, coth
linear An expression which is linear, i.e. of the form ax + b.
quadratic An expression which is quadratic, i.e. of the form ax² + bx + c.
cubic An expression which is cubic, i.e. of the form ax³ + bx² + cx + d.
quartic An expression which is quartic, i.e. of the form ax⁴ + bx³ + cx² + dx + e.
polynom An expression which is a polynomial.

Integer Types
posint Of type integer and positive (> 0).
negint Of type integer and negative (< 0).
nonnegint Of type integer and not negative (>= 0).
even Of type integer and even.
odd Of type integer and odd.
prime Of type integer and prime (see the function isprime).

Other Types
nothing No valid Maple expression is of this type. That is, this type always returns false.
protected A Maple protected (reserved) word.
procedure A procedure name.
type A valid data type. The call type(a, type) checks to see if a is a valid type. By definition, a type is any expression afor which the command type(expr, a) could succeed. e.g. type(integer, type) is true
uneval An expression is of type uneval if it is enclosed in single quotes, 'x'. Maple will not evaluate expressions in single quotes.

Function types
arctrig	An expression which is one of the inverse trigonometric or hyperbolic functions: arcsin, arccos, arctan, arcsec, arccsc, arccot, arcsinh, arccosh, arctanh, arcsech, arccsch, arccoth.
trig	An expression which is one of the trigonometric functions: sin, cos, tan, sec, csc, cot, sinh, cosh, tanh, sech, csch, coth
linear	An expression which is linear, i.e. of the form `ax + b`.
quadratic	An expression which is quadratic, i.e. of the form `ax`² + `bx + c`.
cubic	An expression which is cubic, i.e. of the form `ax`³ + `bx`² + `cx + d`.
quartic	An expression which is quartic, i.e. of the form `ax`⁴ + `bx`³ + `cx`² + `dx + e`.
polynom	An expression which is a polynomial.

Integer Types
posint	Of type integer and positive (> 0).
negint	Of type integer and negative (< 0).
nonnegint	Of type integer and not negative (>= 0).
even	Of type integer and even.
odd	Of type integer and odd.
prime	Of type integer and prime (see the function isprime).

Other Types
nothing	No valid Maple expression is of this type. That is, this type always returns false.
protected	A Maple protected (reserved) word.
procedure	A procedure name.
type	A valid data type. The call type(`a`, type) checks to see if `a` is a valid type. By definition, a type is any expression `a`for which the command type(`expr, a`) could succeed. e.g. type(integer, type) is true
uneval	An expression is of type uneval if it is enclosed in single quotes, '`x`'. Maple will not evaluate expressions in single quotes.

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Maintained by: P. Danziger, March 1998