import jscl.math.Generic;
static import jscl.math.Predef.*;

manager = new javax.script.ScriptEngineManager();
engine = manager.getEngineByName("jscl");
importObject(engine);

x = variable("x");
y = variable("y");

assert(eval("groebner({x^2 + y^2 - 4, x*y - 1}, {x, y})")
.equals($\left(\begin{array}{c}1-4x^2+x^4\\ 4x-x^3-y\end{array}\right)$));

a = matrix("a", 2);
b = vector("b", 2);
x = vector("x", 2);

assert(eval("matrix({{a[0][0], a[0][1]},"+
                    "{a[1][0], a[1][1]}}, {x[0],"+
                                          "x[1]})-{b[0],"+
                                                  "b[1]}")
.equals($\left(\begin{array}{c}-b_0+a_{00}{x}_0+a_{01}{x}_1\\ -b_1+a_{10}{x}_0+a_{11}{x}_1\end{array}\right)$));

a = variable("a");
b = variable("b");
c = variable("c");
x = variable("x");

assert(eval("solve(c+b*x+a*x^2,x)")
.equals(${\mathrm{root}}_0(c, b, a)$));

assert(eval("subst(1/x^2,x,a)")
.equals($\frac{1}{a^2}$));

assert(eval("simplify(exp(sqrt(-1)*pi))")
.equals($-1$));

assert(eval("simplify(elementary(cos(x)^2+sin(x)^2))")
.equals($1$));

assert(eval("numeric(exp(1))")
.equals($2.718281828459045$));

f = function("f", 0);
f_ = function("f", 1);

assert(eval("d(cos(f(x)),x)")
.equals($-(f^{\prime }(x)\sin f(x))$));

z = variable("z");
f = function("f", new int[] {0,0,0});
f_1_0_0 = function("f", new int[] {1,0,0});
f_0_1_0 = function("f", new int[] {0,1,0});
f_0_0_1 = function("f", new int[] {0,0,1});

assert(eval("curl(grad(f(x,y,z),{x,y,z}),{x,y,z})")
.equals($\left(\begin{array}{c}0\\ 0\\ 0\end{array}\right)$));

assert(eval("taylor(exp(x),x,0,4)")
.equals($1+x+\frac{1}{2}x^2+\frac{1}{6}x^3+\frac{1}{24}x^4$));

assert(eval("integral(1/(1+x^2),x)")
.equals(${\mathrm{root}}_0(1, 0, 4)\ln (1-2x{\mathrm{root}}_0(1, 0, 4))+{\mathrm{root}}_1(1, 0, 4)\ln (1-2x{\mathrm{root}}_1(1, 0, 4))$));

assert(eval("quote(integral(1/(1+x^2),x))")
.equals($\int \frac{1}{1+x^2}\,d x$));

man = variable("man");
mortal = variable("mortal");
sokrates = variable("sokrates");

assert(eval("groebner({sokrates*(1+man), man*(1+mortal)}, {man, mortal, sokrates}, lex, 2)")
.equals($\left(\begin{array}{c}\mathrm{man}+\mathrm{man}\mathrm{mortal}\\ \mathrm{sokrates}+\mathrm{man}\mathrm{sokrates}\\ \mathrm{sokrates}+\mathrm{mortal}\mathrm{sokrates}\end{array}\right)$));

assert(eval("factorize(sokrates+mortal*sokrates)").expand()
.equals($\mathrm{sokrates}(1+\mathrm{mortal})$));