Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Change language to: English - Français - 日本語 - Русский
Ajuda do Scilab >> Funções Elementares > Matemática discreta > gcd

gcd

Greatest (positive) Common Divisor

Syntax

gpcd = gcd(P)
[gpcd, U] = gcd(P)

Arguments

P

array of decimal integers, encoded integers, or of polynomials.

gpcd

single element of P type: the greatest common divisor of all P components.

U

Square matrix of the P type, with integer components or of minimal degrees. Its last column B = U(:,$) holds Bezout coefficients, such that B(1)*P(1) + B(2)*P(2) + .... + B($)*P($) == gpcd.

Description

[gpcd, U] = gcd(P) computes the greatest common divisor gpcd of components of P, and an unimodular matrix U.

If P components are decimal or encoded integers, they are priorly converted into int64 signed integers.

If P has an unsigned inttype uint8, uint16, uint32 or uint64, U gets the corresponding signed inttype.

When P are integers, the returned GCD is always positive.

When a second output is expected, an unimodular matrix U of the P type is returned, such that

  • size(U) == [length(P) length(P)]
  • matrix(P,1,-1)*U = [0...0 gpcd] with length(P)-1 leading zeros
  • det(U) is 1 or -1.

Its last column provides Bezout coefficients.

gcd([0 0]) returns 0.
For big P values (smaller but of the order of 2^63, depending also on the number of input values), results may be corrupted by integer overflow and wrapping (int8(127)+1 == -128).

Examples

// With polynomials
s = %s;
p = [s  s*(s+1)^2  2*s^2+s^3];
[GCD, U] = gcd(p)
p*u

// With encoded integers
V = uint16([2^2*3^5 2^3*3^2 2^2*3^4*5])
[GCD, U] = gcd(V)
typeof(GCD)
typeof(U)
V*U

// With decimal integers
V = [2^2*3^5 2^3*3^2 2^2*3^4*5];
[GCD, U] = gcd(V)
type(GCD)
type(U)
V*U

gcd([0 60])
gcd([0 0])

See also

  • bezout — Maior Comum Divisor de dois polinômios ou dois inteiros, pelo método Bezout
  • lcm — mínimo múltiplo comum
  • factor — fatoração
  • prod — produto
  • hermit — forma hermitiana

History

VersionDescription
6.0.1
  • int64 and uint64 input integers are now supported.
  • The input P may be any array instead of a row vector.
  • For input integers possibly negative, the returned GCD is now always positive.
Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Mon Feb 12 19:58:35 CET 2018