# Examples

## Example programs

FLINT comes with example programs to demonstrate current and future FLINT features. To build the example programs run:

    make examples

The example programs are built in the `build/examples` directory.

For Arb and Calcium there are separate example pages Arb example programs and Calcium example programs. Below are some general examples.

- `partitions` Demonstrates the partition counting code, e.g. `build/examples/partitions 1000000000` will compute the number of partitions of `10^9`.

- `delta_qexp` Computes the \(n\)-th term of the delta function, e.g. `build/examples/delta_qexp 1000000` will compute the one million-th term of the \(q\)-expansion of delta.

- `crt` Demonstrates the integer Chinese Remainder code, e.g. `build/examples/crt 10382788` will build up the given integer from its value mod various primes.

- `multi_crt` Demonstrates the fast tree version of the integer Chinese Remainder code, e.g. `build/examples/multi_crt 100493287498239 13` will build up the given integer from its value mod the given number of primes.

- `stirling_matrix` Generates Stirling number matrices of the first and second kind and computes their product, which should come out as the identity matrix. The matrices are printed to standard output. For example `build/examples/stirling_matrix 10` does this with 10 by 10 matrices.

- `fmpz_poly_factor_zassenhaus` Demonstrates the factorisation of a small polynomial. A larger polynomial is also provided on disk and a small (obvious) change to the example program will read this file instead of using the hard coded polynomial.

- `padic` Gives examples of the usage of many functions in the padic module.

- `fmpz_poly_q` Gives a very simple example of the `fmpz_poly_q` module.

- `fmpq_poly` Gives a very simple example of the `fmpq_poly` module.