PolynomialLCM

PolynomialLCM[poly1,poly2,]

gives the least common multiple of the polynomials polyi.

PolynomialLCM[poly1,poly2,,Modulusp]

evaluates the LCM modulo the prime p.

Details and Options

  • PolynomialLCM[poly1,poly2,] will by default treat algebraic numbers that appear in the polyi as independent variables.
  • PolynomialLCM[poly1,poly2,,Extension->Automatic] extends the coefficient field to include algebraic numbers that appear in the polyi.

Examples

open allclose all

Basic Examples  (1)

The least common multiple of polynomials:

Scope  (3)

The LCM of univariate polynomials:

The LCM of multivariate polynomials:

The LCM of more than two polynomials:

Generalizations & Extensions  (1)

The LCM of rational functions:

Options  (3)

Extension  (1)

By default, algebraic numbers are treated as independent variables:

With Extension->Automatic, PolynomialLCM detects algebraically dependent coefficients:

Modulus  (1)

Compute the LCM over the integers modulo 2:

Trig  (1)

By default, PolynomialLCM treats trigonometric functions as independent variables:

With Trig->True, PolynomialLCM recognizes dependencies between trigonometric functions:

Properties & Relations  (1)

The LCM of polynomials is divisible by the polynomials; use PolynomialMod to prove it:

PolynomialGCD finds the greatest common divisor of polynomials:

Introduced in 1991
 (2.0)
 |
Updated in 1996
 (3.0)