icontent
-- the content of a
polynomial with rational coefficientsicontent(
p)
computes the content of the
polynomial p
with integer or rational number coefficients,
i.e., the gcd of its coefficients.
icontent(p)
p |
- | a polynomial or polynomial expression with integer or rational number coefficients |
a nonnegative integer or rational number, or FAIL
coeff
, content
, factor
, gcd
, ifactor
, igcd
, ilcm
, lcm
, poly
, polylib::primpart
icontent(
p)
calculates the content of a
polynomial or polynomial expression with integer or rational
coefficients, i.e., the greatest common divisor of the coefficients,
such that p/
icontent(p)
has integral
coefficients whose greatest common divisor is 1
. In
particular, if p
is itself an integer or a rational
number, then icontent
returns abs(p)
(see example 1).p
is a polynomial or polynomial expression with integer
coefficients, then the content is the greatest common divisor of the
coefficients. If p
is a polynomial or polynomial
expression with rational coefficients, then the content is the greatest
common divisor of the numerators of the coefficients divided by the
least common multiple of the denominators (see example 2).p
is a polynomial
expression, then it is first converted into a polynomial of domain
type DOM_POLY
using
poly
. If this conversion
is not possible, then icontent
returns FAIL
.icontent
returns an error message if not all
coefficients of p
are integers or rational numbers.icontent
is a function of the system kernel.The first argument can be a polynomial or a polynomial
expression. The following two calls of icontent
are
equivalent:
>> p := 6*x*y - 9*y^2 + 21: icontent(poly(p)), icontent(p)
3, 3
The result of icontent
is always
nonnegative:
>> icontent(2*x - 4), icontent(-2*x + 4)
2, 2
The content of a constant polynomial is its absolute value:
>> icontent(0), icontent(-2), icontent(poly(-2, [x]))
0, 2, 2
The content of a polynomial with rational coefficients is a rational number in general:
>> q := 6/7*x*y - 9/4*y + 12: icontent(poly(q)), icontent(q)
3/28, 3/28
The polynomial divided by its content has integral
coefficients whose greatest common divisor is 1
:
>> q/icontent(q)
8 x y - 21 y + 112
>> icontent(%)
1