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## 4.8 Predicates for Numeric Objects

Since the type of a variable may change during the execution of a program, it can be necessary to do type checking at run-time. Doing this also allows you to change the behavior of a function depending on the type of the input. As an example, this naive implementation of `abs` returns the absolute value of the input if it is a real number, and the length of the input if it is a complex number.

 ```function a = abs (x) if (isreal (x)) a = sign (x) .* x; elseif (iscomplex (x)) a = sqrt (real(x).^2 + imag(x).^2); endif endfunction ```

The following functions are available for determining the type of a variable.

Built-in Function: isnumeric (x)

Return nonzero if x is a numeric object.

Built-in Function: isreal (x)

Return true if x is a real-valued numeric object.

Built-in Function: isfloat (x)

Return true if x is a floating-point numeric object.

Built-in Function: iscomplex (x)

Return true if x is a complex-valued numeric object.

Built-in Function: ismatrix (a)

Return 1 if a is a matrix. Otherwise, return 0.

Function File: isvector (a)

Return 1 if a is a vector. Otherwise, return 0.

Function File: isscalar (a)

Return 1 if a is a scalar. Otherwise, return 0.

Function File: issquare (x)

If x is a square matrix, then return the dimension of x. Otherwise, return 0.

Function File: issymmetric (x, tol)

If x is symmetric within the tolerance specified by tol, then return the dimension of x. Otherwise, return 0. If tol is omitted, use a tolerance equal to the machine precision. Matrix x is considered symmetric if `norm (x - x.', inf) / norm (x, inf) < tol`.

Function File: isdefinite (x, tol)

Return 1 if x is symmetric positive definite within the tolerance specified by tol or 0 if x is symmetric positive semidefinite. Otherwise, return -1. If tol is omitted, use a tolerance equal to 100 times the machine precision.

Built-in Function: islogical (x)

Return true if x is a logical object.

Function File: isprime (n)

Return true if n is a prime number, false otherwise.

Something like the following is much faster if you need to test a lot of small numbers:

 ``` t = ismember (n, primes (max (n (:)))); ```

If max(n) is very large, then you should be using special purpose factorization code.

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