Basic Functions
The size of an integer in Axiom is only limited by the amount of computer storage you have available. The usual arithmetic operations are available. There are a number of ways of working with the sign of an integer. Let's use the x as an example. First of all, there is the absolute value function. The sign operation returns -1 if its argument is negative, 0 if zero and 1 if positive. You can determine if an integer is negative in several other ways. Similarly, you can find out if it is positive. This is the recommended way of determining whether an integer is zero.
Use the zero? whenever you are testing any mathematical object for equality with zero. This is usually more efficient than using = (think of matrices: it is easier to tell if a matrix is zero by just checking term by term than constructing another "zero" amtrix and comparing the two matrices term by term) and also avoids the problem that = is usually used for creating equations.
This is the recommended way of determining whether an integer is equal to one. This syntax is used to test equality using =. It says that you want a Boolean (true or false) answer rather than an equation. The operations odd? and even? determine whether an integer is odd or even, respectively. They each return a Boolean object. The operation gcd computes the greatest common divisor of two integers. The operation lcm computes their least common multiple. To determine the maximum of two integers, use max. To determine the minimum, use min. The reduce operation is used to extend binary operations to more than two arguments. For example, you can use reduce to find the maximum integer in a list or compute the least common multiple of all integers in a list. The infix operator "/" is not used to compute the quotient of integers. Rather , it is used to create rational numbers as described in Fractions. The infix operator quo computes the integer quotient. The infix operation rem computes the integer remainder. One integer is evenly divisible by another if the remainder is zero. The operation exquo can also be used. See Unions for an example. The operation divide returns a record of the quotient and remainder and thus is more efficient when both are needed. Records are discussed in detail in Records.