polylib::primpart

Primitive part of a polynomial

Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

Syntax

polylib::primpart(f)
polylib::primpart(q)
polylib::primpart({xpr}, <{inds}>)

Description

polylib::primpart(f) returns the primitive part of the polynomial f.

If the input is a polynomial, the greatest common divisor of its coefficients is removed. The function gcd must be able to calculate this gcd.

If the first argument is an expression, it is converted into a polynomial in the indeterminates specified by the second argument, or in all of its indeterminates if no second argument is given. polylib::primpart returns FAIL if the expression cannot be converted into a polynomial.

For a rational number, its sign is returned.

Examples

Example 1

In the following example, a bivariate polynomial is given. Its coefficients are the integers 3, 6, and 9; the primitive part is obtained by dividing the polynomial by their gcd.

polylib::primpart(poly(6*x^3*y + 3*x*y + 9*y, [x, y]));

However, consider the same polynomial viewed as a univariate polynomial in x. Its coefficients are polynomials in y in this case, and their gcd 3*y is divided off.

polylib::primpart(poly(6*x^3*y + 3*x*y + 9*y, [x]));

Example 2

polylib::primpart divides the coefficients by their gcd, but does not normalize the result. This must be done explicitly:

polylib::primpart(4*x*y + 6*x^3 + 6*x*y^2 + 9*x^3*y, [x])

normal(polylib::primpart(4*x*y + 6*x^3 + 6*x*y^2 + 9*x^3*y, [x]))

Parameters

f

Polynomial

q

Rational number

xpr

Expression

inds

List of identifiers

Return Values

polylib::primpart returns an object of the same type as the input, or FAIL.

Overloaded By

f

Algorithms

The primitive part of a polynomial f is a polynomial g whose coefficients are relatively prime such that f = rg for some element r of the coefficient ring.

See Also

MuPAD Functions

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