icontent

Content of a polynomial with rational coefficients

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Syntax

icontent(p)

Description

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.

Examples

Example 1

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]))

Example 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)

The polynomial divided by its content has integral coefficients whose greatest common divisor is 1:

q/icontent(q)

icontent(%)

Parameters

p

A polynomial or polynomial expression with integer or rational number coefficients

Return Values

Nonnegative integer or rational number, or FAIL

See Also

MuPAD Functions