Adrian Mariano

University of Washington

2729 72nd Ave SE

Mercer Island, WA 98040

USA

The program’s source implements four functions, all from the same source file!

Usage:

```
theorem expression x1 x2 h y1
where:
expression - function f(x,y) (see below)
x1 - start of interval
x2 - end of interval
h - step size
y1 - initial value (y(x1) == y1)
```

When you compile theorem.c as is and run with 5 args, it numerically solves the equation y'=f(x,y), with a step size of h, over the interval x=[x1,x2], with the initial condition of y(x1)=y1.

The ‘expression’ f(x,y), is any function of ‘x’ and ‘y’ with the operators:

```
+ - * / ^
```

The symbol ‘^’ is the power operator. Note that it only supports integer powers. Also note that all expressions are evaluated strictly left to right. (i.e., parenthesis aren’t supported).

Try running the program with the following args:

```
theorem y 0 1 0.1 1
theorem 1/x 1 2 0.1 0
theorem 'x^2/y+x' 0 1 0.1 6
```

But wait, there is more! You also get, free of charge, a reversing filter! Try:

```
theorem -r 0 0 0 0 < theorem.c > sorter.c
```

Still not impressed? The author throws in for free, a sort program! Try:

```
cc sorter.c -o sorter
ls | sorter
```

This program is safe for home use as well. The author has included a safety feature in case you misplace the original program source:

```
sorter -r 0 0 0 0 < sorter.c > theorem_bkp.c
```

And finally, as a special offer to users of this entry, the author provides a Fibonacci sequence generator! Try:

```
sorter 0 0 0 0 < theorem.c > fibonacci.c
cc fibonacci.c -o fibonacci
fibonacci 1 1
fibonacci 2 1
```

Program available 9 track and cartridge cassette. Gensu knife not included! :-)

When this program was first shown at the 1990 Summer Usenix conference, it received a standing ovation; a first for a contest entry.

It should be noted that the 4 trailing args ‘0 0 0 0’, are required on systems that dump core when NULL is dereferenced.

Differential equations are solved via the Runge-Kutta method,
which guarantees local error proportional to h^{5}, and total
error across a finite interval is at most a constant times h^{4}.

Sorting is accomplished with a standard shell sort.

Note that the sorting and reversing is limited to files with fewer than 500 lines, each less than 99 characters long.

Copyright © 1990, Landon Curt Noll & Larry Bassel. All Rights Reserved. Permission for personal, educational or non-profit use is granted provided this this copyright and notice are included in its entirety and remains unaltered. All other uses must receive prior permission in writing from both Landon Curt Noll and Larry Bassel.