div
-- the integer part of a
quotientx div m
represents the integer q satisfying
x = q * m + r with 0 <= r < |m|.
x div m _div(x, m)
x, m |
- | integers or symbolic arithmetical expressions; m must not be
zero. |
an integer or an arithmetical expression of type
"_div"
.
x
, m
_mod
, /
, divide
, mod
, modp
, mods
x
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.With 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
Symbolic 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]