Maxima Function
ceiling (x)
When x is a real number, return the least integer that is greater than or equal to x.
If x is a constant expression (10 * %pi
, for example),
ceiling
evaluates x using big floating point numbers, and
applies ceiling
to the resulting big float. Because ceiling
uses
floating point evaluation, it's possible, although unlikely,
that ceiling
could return an erroneous value for constant
inputs. To guard against errors, the floating point evaluation
is done using three values for fpprec
.
For non-constant inputs, ceiling
tries to return a simplified
value. Here are examples of the simplifications that ceiling
knows about:
(%i1) ceiling (ceiling (x)); (%o1) ceiling(x) (%i2) ceiling (floor (x)); (%o2) floor(x) (%i3) declare (n, integer)$ (%i4) [ceiling (n), ceiling (abs (n)), ceiling (max (n, 6))]; (%o4) [n, abs(n), max(n, 6)] (%i5) assume (x > 0, x < 1)$ (%i6) ceiling (x); (%o6) 1 (%i7) tex (ceiling (a)); $$\left \lceil a \right \rceil$$ (%o7) false
The function ceiling
does not automatically map over lists or matrices.
Finally, for all inputs that are manifestly complex, ceiling
returns
a noun form.
If the range of a function is a subset of the integers, it can be
declared to be integervalued
. Both the ceiling
and floor
functions
can use this information; for example:
(%i1) declare (f, integervalued)$ (%i2) floor (f(x)); (%o2) f(x) (%i3) ceiling (f(x) - 1); (%o3) f(x) - 1