Function: mspathlog
Section: modular_forms
C-Name: mspathlog
Prototype: GG
Help: mspathlog(M,p): M being a full modular symbol space, as given by
 msinit and p being a path between two elements in P^1(Q), return (p_i)
 in Z[G] such that p = \sum p_i g_i, and the g_i are fixed Z[G]-generators
 for Div^0(P^1 Q), see mspathgens.
Doc: Let $\Delta:=\text{Div}^0(\P^1(\Q))$.
 Let $M$ being a full modular symbol space, as given by \kbd{msinit},
 encoding fixed $\Z[G]$-generators $(g_i)$ of $\Delta$ (see \tet{mspathgens}).
 A path $p=[a,b]$ between two elements in $\P^1(\Q)$ corresponds to
 $[b]-[a]\in \Delta$. The path extremities $a$ and $b$ may be given as
 \typ{INT}, \typ{FRAC} or $\kbd{oo} = (1:0)$.

 Returns $(p_i)$ in $\Z[G]$ such that $p = \sum_i p_i g_i$.
 \bprog
 ? M = msinit(2,8); \\ M_8(Gamma_0(2))
 ? [g,R] = mspathgens(M);
 ? g
 %3 = [[+oo, 0], [0, 1]]
 ? p = mspathlog(M, [1/2,2/3]);
 ? p[1]
 %5 =
 [[1, 0; 2, 1] 1]

 ? p[2]
 %6 =
 [[1, 0; 0, 1] 1]

 [[3, -1; 4, -1] 1]

 @eprog\noindent
 Note that the output depends only on the group $G$, not on the
 representation $V$.
