# Pascal's Triangle in LateX

### Table of Contents

### Περιεχόμενα

You need to display Pascal's Triangle in a LaTeX document and whenever
you hear ‘ampersand’ or ‘smallskip’, you go into a homicidal rage, leaving
behind you a trail of viscera and blood-stained Lion Book pages. Also, you're
lazy. Put that chainsaw down, this recipe is for you. Although, really, with
that kind of reaction to ampersands, what *are* you doing using the
world's best Turing-complete typesetting software?

## Solution

This recipe uses a small Python script to generate a Pascal triangle of
arbitrary size in a `tabular`

environment — it's entirely up to you
to make it fit on your page, of course. If you're interested in the pure
Pascal's Triangle code, without typesetting embellishments, there's a
recipe devoted to just this. Here's the
Python code for the script:

```
import sys
def pascal(n):
"""
Yield up to row ``n`` of Pascal's triangle, one row at a time.
The first row is row 0.
"""
if not isinstance (n, int):
raise TypeError ('n must be an integer')
if n < 0:
raise ValueError ('n must be an integer >= 0')
def newrow(row):
"Calculate a row of Pascal's triangle given the previous one."
prev = 0
for x in row:
yield prev + x
prev = x
yield 1
prevrow = [1]
yield prevrow
for x in xrange(n):
prevrow = list(newrow(prevrow))
yield prevrow
def pascal_latex(n, out=sys.stdout):
"""
Generate a Pascal triangle for LaTeX embedding.
Sends output to the file-like object ``out`` (default: sys.stdout).
"""
out.write('\\begin{tabular}{r%s}\n' % ('c' * (2 * n + 1)))
for i, row in enumerate(pascal(n)):
out.write('$n=%d$:& ' % i)
out.write(' & ' * (n - i))
out.write(' & & '.join ('%2d' % coeff for coeff in row))
out.write('\\\\\\noalign{\\smallskip\\smallskip}\n')
out.write ('\\end{tabular}\n')
if __name__ == '__main__':
try:
pascal_latex (int(sys.argv[1]))
except ValueError:
sys.stderr.write ('Please specify a positive integer.\n')
sys.exit (1)
```

## Usage

Turn this into an executable script (this depends on your operating system — on
Unix, `chmod +x some_filename.py`

works well), and run it:

```
python some_filename.py 4
```

If you made this into an executable, you can leave `python`

out of
the command line (unless your Unix installation is very insecure, you'll need
to type `./some_filename.py 4`

though). You'll get something like
this:

```
\begin{tabular}{rccccccccc}
$n=0$:& & & & & 1\\\noalign{\smallskip\smallskip}
$n=1$:& & & & 1 & & 1\\\noalign{\smallskip\smallskip}
$n=2$:& & & 1 & & 2 & & 1\\\noalign{\smallskip\smallskip}
$n=3$:& & 1 & & 3 & & 3 & & 1\\\noalign{\smallskip\smallskip}
$n=4$:& 1 & & 4 & & 6 & & 4 & & 1\\\noalign{\smallskip\smallskip}
\end{tabular}
```

Which, of course, renders this:

You can place the LaTeX code fragment in a `pascals_triangle.tex`

file on its own, and then include it into your other documents by saying:

```
\input{pascals_triangle}
```

Obviously, you can also cut and paste it.

You can also call the triangle-generating routine from another Python program
by saying `pascal_latex(4)`

. Optionally, you may specify a file-like
object to output to: `pascal_latex(4, out=open('some_file', 'w'))`

,
and you'll get output sent to `some_file`

.

## Discussion

The script is written in three, visibly distinct parts. The first part is
the `pascal()`

function. For a better discussion of how this works,
please refer to the *Pascal's Triangle*.

The second function, `pascal_latex()`

, is where we put all the
strings together to build the LaTeX code. It's the usual ugly-looking code
present whenever this kind of string manipulation is needed. The table header
lists all the column alignments (`r`

for the first
column, `c`

for each triangle coefficient). The trickiest bit is
remembering that the tabular form of an *n*-row Pascal's Triangle
has *2n+1* columns because of its symmetry.

The rest of the function merely prints out consecutive rows of the triangle,
prepending `tabular`

alignment characters (`&`

) to align
the triangle's columns properly. Finally, the coefficients are all printed in
one fell swoop, and terminated with `\\`

(end of table row)
and `\noalign{\smallskip\smallskip}`

, to add enough vertical space
between rows (otherwise the triangle looks squashed).

The third and smallest part of the script simply parses (without much checking) the command-line arguments, when the program is used as a script (not a module to be included in another Python program).