First to load the new function you need to unpack the library, and be sure the path is in your libname, then type:

> readlib(DGCD):

The usage of DGCD is identical to that of gcd (i.e. the additional arguments for the cofactors, etc.)

Now for the comparison, we choose two dense degree 20 polynomials in 2 variables as cofactors with a degree 20 gcd (usually the worst case):

> a:=randpoly([x,y],degree=20,dense):

> b:=randpoly([x,y],degree=20,dense):

> g:=randpoly([x,y],degree=20,dense):

> A:=expand(a*g): B:=expand(b*g):

> t:=time(): g1:=DGCD(A,B): time()-t;

> t:=time(): g2:=gcd(A,B): time()-t;

So not much difference. Try three variables, degree 10:

> a:=randpoly([x,y,z],degree=10,dense):

> b:=randpoly([x,y,z],degree=10,dense):

> g:=randpoly([x,y,z],degree=10,dense):

> A:=expand(a*g): B:=expand(b*g):

> t:=time(): g1:=DGCD(A,B): time()-t;

> t:=time(): g2:=gcd(A,B): time()-t;

Improvement is much more noticeable here.

In general the new algorithm will out perform the old whenever the inputs are dense in the input variables.
 
 

A more general fast gcd algorithm is in progress that will improve both dense and sparse gcd computation.