1.

(%i110) rovnice: x^3 - (a-1)*x^2 - a^2*x - a^3;
realonly:true; reseni:solve(rovnice,x);

Result

(%i122) define(g(a), reseni[3])$ g(1); g(0); bfloat(g(2));

Result

2.

(%i46) f(x):= (if x>=-1 and x<=1 then 1 else 0);

Result

(%i51) wxplot2d(f(x),[x,-3,3],[y,-2,2]);

Result

3.

(%i63) L(n):=(if n = 0 then 1 else if n=1 then x else ratsimp((((2*n-1)*x*L(n-1) - (n-1)*L(n-2))/n)));

Result

(%i64) L(7);

Result

(%i142) load(orthopoly)$ expand(legendre_p(7,x));

Result

4.

(%i145) killall$ reseni:solve([x^2+y^2=5, x*y=y^2-2], [x,y]);

Result

(%i147) ev([x^2+y^2=5, x*y=y^2-2],reseni);

Result

(%i99) killall$ numer:true$ reseni:solve([x^2+y^2=5, x*y=y^2-2], [x,y]); numer:false$

Result

5.

(%i54) load(solve_rat_ineq);

Result

(%i55) solve_rat_ineq(x<(x-3)^2);

Result


Created with wxMaxima.