input_case nil$

% Calculating limits
% ------------------
limit(sin(x)/x,x,0);  % x -> 0
limit!+(e^(1/x),x,0); % x -> 0 from the right
limit!-(e^(1/x),x,0); % x -> 0 from the left

% Calculating sums and products
% -----------------------------
sum(n,n);       % indefinite sum
sum(n^2,n,0,m); % sum from 0 to m
sum(x^n,n,0,m);
sum(1/n,n,1,m); % cannot be found
sum(1/n/(n+2),n);
sum(sin(n*x),n);
sum(cos((2*k-1)*pi/n),k,1,n);

operator fac;
for all n,m such that fixp(m) let fac(n+m)=
    if m>0 then fac(n+m-1)*(n+m) else fac(n+m+1)/(n+m+1);
sum(n/fac(n+1),n); % sum with factorial
for all n,m such that fixp(m) clear fac(n+m);
clear fac;

prod(n/(n+2),n,1,m); % product from 1 to m
prod(x^n,n);         % indefinite product

end;