Maxima Function
mod (x, y)
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