Some pretty obvious commands are: simplify, expand, factor

> factor(x^4+4); 2 2 (x - 2 x + 2) (x + 2 x + 2) > expand(sin(x+y)); sin(x) cos(y) + cos(x) sin(y)

Sometimes simplify(expand(expr)) differs from simplify(expr).

The opposite of `expand` is `combine`, in some sense.

For simplification of rational expressions, use `normal`:

> normal((x+1)/y+x/(x+y)); 2 x + 2 x y + x + y ------------------ y (x + y)

> collect(pol,var); returns the multivariate polynomial `pol`
written as a univariate one, in the variable `var`. More advanced uses
are possible.

> collect(y^2*x^2+7*x*y+a*y^2-y+u*x,y); 2 2 (a + x ) y + (7 x - 1) y + u x

SOME MATHEMATICAL FUNCTIONS

> diff(f,x); means ``differentiate `f` with respect to `x`''

> diff(f,x$n); yields the `n`:th derivative.

> grad(f,[x1,x2]); computes the gradient of `f` w.r.t. `[x1,x2]`.

> jacobian(f,[x1,x2]); jacobian matrix of the vector `f`.

> laplace(f,t,s); yields the laplace transform of

> int(f,x); int(f,x=a..b); indefinite and definite integration

For numerical integration apply `evalf`.
For complex integration, apply `evalc`.

> sum(f,i); sum(f,i=a..b); indefinite and definite summation

For products use `product` which has the same syntax as `sum`.

> limit(f,x=a); limit of `f` as `x` goes to `a`

> limit(f,x=a,right); a directional limit

> taylor(f,x=a,n); a Taylor expansion of `f`
about `x=a` to

See also `series` for more general series expansions.

> int(sin(x)*x,x); sin(x) - x cos(x) > evalf(int(sin(x)/x,x=0..1),15); .946083070367183 > sum(binomial(n,k)*x^k,k=0..n); n (1 + x)

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