Help:=proc():print(`Jac(P,x),Comp(P,Q,x)`):
print(`El(x,i,f,y)`):
end:

#Jac(P,x): the Jacobian determinant
#of the trans. x->P(x)
Jac:=proc(P,x)
local i,j,n:
with(linalg):
n:=nops(P):
det(matrix(n,n, [            
seq( seq( diff(P[i],x[j]),j=1..n),i=1..n)
 ] ) ):
end:

#x->P(Q(x))
Comp:=proc(P,Q,x) local i:
 subs({seq(x[i]=Q[i],i=1..nops(P))},P):
end:


#Inouts a list of variables, and a place i
#and a function f of nops(x)-1 variables y
#outputs the transormation x[i]->x[i]+f( not x[i])
El:=proc(x,i,f,y) local n,j:
n:=nops(x):

[op(1..i-1,x),      
x[i]+ subs({ seq(y[j]=x[j],j=1..i-1),
 seq(y[j]=x[j+1], j=i..n-1)},f)
, op(i+1..n,x)]:

end: