alu001.mws

> evalf(exp(20),20);

485165195.40979027797

> 100!;

933262154439441526816992388562667004907159682643816...
933262154439441526816992388562667004907159682643816...

> evalf(Pi,20);

3.1415926535897932385

> 5/3;

5/3

> evalf(5/3,20);

>

1.6666666666666666667

> simplify(1/a+1/b+1/c);

(b*c+a*c+a*b)/(a*b*c)

> simplify(a/b+c/d);

(a*d+b*c)/(b*d)

> expand((1+x+x^2)^2);

1+2*x+3*x^2+2*x^3+x^4

> factor(x^6-1);

(x-1)*(x+1)*(1+x+x^2)*(x^2-x+1)

> factor(x^6-1,{3^(1/2),I});

1/16*(2*x+1-I*sqrt(3))*(2*x+1+I*sqrt(3))*(2*x-1+I*s...

> factor(x^2+x-1,5^(1/2));

1/4*(2*x+1-sqrt(5))*(2*x+1+sqrt(5))

> ifactor(2^(2^5)+1);

``(641)*``(6700417)

> diff(sin(x^2+3*x+1),x);

cos(x^2+3*x+1)*(2*x+3)

> diff(log(x),x$4);

-6*1/(x^4)

> evalf(sin(Pi/8),20);

.38268343236508977173

> int(tan(x),x);

-ln(cos(x))

> int(sin(x)*cos(x),x);

-1/2*cos(x)^2

> int(x^2*cos(x)*exp(x),x);

(1/2*x^2-1/2)*exp(x)*cos(x)-(-1/2*x^2+x-1/2)*exp(x)...

> evalf(int(x^2*cos(x)*exp(x),x=0..1),20);

.50000000000000000000

> series(exp(x),x=1,10);

series(exp(1)+exp(1)*(x-1)+1/2*exp(1)*(x-1)^2+1/6*e...
series(exp(1)+exp(1)*(x-1)+1/2*exp(1)*(x-1)^2+1/6*e...

> combine(sin(x)*sin(x));

1/2-1/2*cos(2*x)

> combine(sin(x)*sin(y));

1/2*cos(x-y)-1/2*cos(x+y)

> expand(tan(x+y+z));

(tan(x)+tan(y)+tan(z)-tan(x)*tan(y)*tan(z))/(1-tan(...

> solve(x^3-1);

1, -1/2+1/2*I*sqrt(3), -1/2-1/2*I*sqrt(3)

> solve({x+y=1,x-y=2});

{y = -1/2, x = 3/2}

> sum(n^3,n=1..k);

1/4*(k+1)^4-1/2*(k+1)^3+1/4*(k+1)^2

> implicitdiff(x^2*y+y^3*x,y,x);

-y*(2*x+y^2)/(x*(x+3*y^2))

> implicitdiff(x^2*y+y^3*x,x,y);

-x*(x+3*y^2)/(y*(2*x+y^2))

>