dirmul

Function: dirmul
Section: number_theoretical
C-Name: dirmul
Prototype: GG
Help: dirmul(x,y): multiplication of the Dirichlet series x by the Dirichlet
 series y.
Doc: $x$ and $y$ being vectors of perhaps different lengths representing
 the \idx{Dirichlet series} $\sum_n x_n n^{-s}$ and $\sum_n y_n n^{-s}$,
 computes the product of $x$ by $y$, again as a vector.
 \bprog
 ? dirmul(vector(10,n,1), vector(10,n,moebius(n)))
 %1 = [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
 @eprog\noindent
 The product
 length is the minimum of $\kbd{\#}x\kbd{*}v(y)$ and $\kbd{\#}y\kbd{*}v(x)$,
 where $v(x)$ is the index of the first nonzero coefficient.
 \bprog
 ? dirmul([0,1], [0,1]);
 %2 = [0, 0, 0, 1]
 @eprog