div -- the integer part of a
quotient
Introductionx div m represents the integer q satisfying
x = q * m + r with 0 <= r < |m|.
Call(s)
x div m _div(x, m)
Parametersx, m |
- | integers or symbolic arithmetical expressions; m must not be
zero. |
Returnsan integer or an arithmetical expression of type
"_div".
x, m
Related
Functions_mod, /, divide, mod, modp, mods
Detailsx and m, q =
x div m is the integer part of the quotient
x/m, i.e., q = trunc(x/m).x div m is equivalent to the function call
_div(x, m).x and m
evaluate to integers. A symbolic expression of type "_div"
is returned if either x or m does not
evaluate to a number. An error is raised if x or
m evaluates to a number that is not an integer.div does not operate on polynomials. Use divide.div is a function of the system kernel.
Example
1With the default setting for mod, the identity (x div m) * m +
(x mod m) = x holds for integer numbers x and
m:
>> 43 div 13 = trunc(43/13), 43 mod 13 = frac(43/13) * 13
3 = 3, 4 = 4
>> (43 div 13) * 13 + (43 mod 13) = 43
43 = 43
Example
2Symbolic expressions of type "_div" are
returned, if either x or m does not evaluate
to a number:
>> 43 div m, x div 13, x div m
43 div m, x div 13, x div m
>> type(x div m)
"_div"
If x or m are numbers, they
must be integer numbers:
>> 1/2 div 2
Error: Illegal argument in div or mod
>> x div 2.0
Error: Illegal operand [_mod]