This is a small tour of the capabilities Yacas currently offers. Note that this list of examples is far from complete. Yacas contains a few hundred commands, of which only a few are shown here.
Additional example calculations including the results can be found here:
100!; |
ToBase(16,255); FromBase(16,"2FF"); |
Expand((1+x)^5); |
Apply("+",{2,3}); |
Apply({{x,y},x+y},{2,3}); |
D(x)D(x) Sin(x); |
Solve(a+x*y==z,x); |
Taylor(x,0,5) Sin(x); |
Limit(x,0) Sin(x)/x; |
Newton(Sin(x),x,3,0.0001); |
DiagonalMatrix({a,b,c}); |
Integrate(x,a,b) x*Sin(x); |
Factors(x^2-1); |
Apart(1/(x^2-1),x); |
The function g(q,phi,chi) is defined by
To solve this problem, we prepare a separate file with the following Yacas code:
/* Auxiliary function */ g1(n, q, phi, chi) := [ Local(s); s := q^2-n^2; N(Cos(n*chi) * If(s=0, 1/2, /* Special case of s=0: avoid division by 0 */ Sin(Sqrt(s)*phi)/Sin(2*Sqrt(s)*phi) /* now s != 0 */ /* note that Sqrt(s) may be imaginary here */ ) ); ]; /* Main function */ g(q, phi, chi) := [ Local(M, n); M := 16; /* Exp(-M) will be the precision */ /* Use N() to force numerical evaluation */ N(1/2*Sin(q*phi)/Sin(2*q*phi)) + /* Estimate the necessary number of terms in the series */ Sum(n, 1, N(1+Sqrt(q^2+M^2/phi^2)), g1(n, q, phi, chi)) ; ]; /* Parameters */ q:=3.5; phi:=2; /* Make a function for plotting: it must have only one argument */ f(x) := g(q, phi, x); /* Plot from 0 to 2*Pi with 80 points */ Plot2D(f(x), 0: 2*Pi); |
Name this file "fun1" and execute this script by typing
Load("fun1"); |