icontent
Content of a polynomial with rational coefficients
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icontent(p
)
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).
If 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).
If 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.
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)
The result of icontent
is always nonnegative:
icontent(2*x - 4), icontent(-2*x + 4)
The content of a constant polynomial is its absolute value:
icontent(0), icontent(-2), icontent(poly(-2, [x]))
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)
The polynomial divided by its content has integral coefficients
whose greatest common divisor is 1
:
q/icontent(q)
icontent(%)
|
A polynomial or polynomial expression with integer or rational number coefficients |
Nonnegative integer or rational number, or FAIL