mnewton SciMax Toolbox mod_big_prime

SciMax Toolbox >> mod

mod

Maxima Function

Calling Sequence

mod (x, y)

Description

If x and y are real numbers and y is nonzero, return x - y * floor(x / y). Further for all real x, we have mod (x, 0) = x. For a discussion of the definition mod (x, 0) = x, see Section 3.4, of "Concrete Mathematics," by Graham, Knuth, and Patashnik. The function mod (x, 1) is a sawtooth function with period 1 with mod (1, 1) = 0 and mod (0, 1) = 0.

To find the principal argument (a number in the interval (-%pi, %pi]) of a complex number, use the function x |-> %pi - mod (%pi - x, 2*%pi), where x is an argument.

When x and y are constant expressions (10 * %pi, for example), mod uses the same big float evaluation scheme that floor and ceiling uses. Again, it's possible, although unlikely, that mod could return an erroneous value in such cases.

For nonnumerical arguments x or y, mod knows several simplification rules:

(%i1) mod (x, 0);
(%o1)                           x
(%i2) mod (a*x, a*y);
(%o2)                      a mod(x, y)
(%i3) mod (0, x);
(%o3)                           0
mnewton SciMax Toolbox mod_big_prime