bezout
======

Bezout equation for polynomials or integers



Calling Sequence
~~~~~~~~~~~~~~~~


::

    [thegcd,U]=bezout(p1,p2)




Arguments
~~~~~~~~~

:p1, p2 two real polynomials or two integer scalars (type equal to 8)
:



Description
~~~~~~~~~~~

`[thegcd,U]=bezout(p1,p2)` computes GCD `thegcd` of `p1` and `p2` and
in addition a (2x2) unimodular matrix `U` such that:

`[p1,p2]*U = [thegcd,0]`

The lcm of `p1` and `p2` is given by:

`p1*U(1,2)` (or `-p2*U(2,2)`)



Examples
~~~~~~~~


::

    // polynomial case
    x=`poly`_(0,'x');
    p1=(x+1)*(x-3)^5;p2=(x-2)*(x-3)^3;
    [thegcd,U]=bezout(p1,p2)
    `det`_(U)
    `clean`_([p1,p2]*U)
    thelcm=p1*U(1,2)
    `lcm`_([p1,p2])
    
    // integer case
    i1=`int32`_(2*3^5); i2=`int32`_(2^3*3^2);
    [thegcd,U]=bezout(i1,i2)
    V=`int32`_([2^2*3^5, 2^3*3^2,2^2*3^4*5]);
    [thegcd,U]=`gcd`_(V)
    V*U
    `lcm`_(V)




See Also
~~~~~~~~


+ `poly`_ polynomial definition
+ `roots`_ roots of polynomials
+ `simp`_ rational simplification
+ `clean`_ cleans matrices (round to zero small entries)
+ `lcm`_ least common multiple


.. _lcm: lcm.html
.. _clean: clean.html
.. _roots: roots.html
.. _simp: simp.html
.. _poly: poly.html