Section 23 Program Listings
Sage cells can be used for Python examples, but Sage uses a mild amount of preparsing, so that might not be a wise decision, especially in instructional settings. We might implement Skulpt or Brython (inbrowser Python) or the Python language argument to the Sage Cell Server. To see examples of authoring Sage cells, have a look at Section 3.
In the meantime, program listings, especially with syntax highlighting, is useful all by itself. The “R” language might not be a bad standin for pseudocode, as it supports assignment with a left arrow and has fairly generic procedural syntax for control structures and data structures. Or maybe Pascal would be a good choice? Here is an example of R. Note in the source that the entire block of code is wrapped in a CDATA section due to the four left angle brackets. We do not recommend this technique for isolated problem characters, but it is a lifesaver for situations like the XSLT code just following.
n_loops < 10
x.means < numeric(n_loops) # create a vector of zeros for results
for (i in 1:n_loops){
x < as.integer(runif(100, 1, 7)) # 1 to 6, uniformly
x.means[i] < mean(x)
}
x.means
And some selfreferential XSL:
<xsl:template match="biblio" mode="number">
<xsl:applytemplates select="." mode="structuralnumber" />
<xsl:text>.</xsl:text>
<xsl:number from="references" level="any" count="biblio" />
</xsl:template>
Matlab is a commercial language for mathematics, while Octave in an open source version. The @language
values of matlab
and octave
are somewhat interchangeable. Following is a very slighlty edited version of an example from “50 Basic Examples for Matlab”^{ 1 }.
a = [0:0.5:5]; % A Matlab comment here
b = 2*a.^2 + 3*a 5;
c = 1.2*a.^2+4*a3;
subplot(1,2,1)
plot(a,b,'or','MarkerFaceColor','g','LineWidth',2)
xlabel('X'); ylabel('Y'); legend('Curve ','Location','NorthWest')
subplot(1,2,2)
plot(a,c,'ok','MarkerFaceColor','c','LineWidth',2)
xlabel('X'); ylabel('Y'); legend('Curve 2','Location','NorthWest')
You can write madeup pseudocode, but you might explain to a reader what your symbols all mean. This routine takes the \(m\times n\) marix \(A\) to reduced rowechelon form. Note that with no language specified, there is no special formatting or use of color. Note in the source the use of escaped characters for the three lessthan symbols.
input m, n and A
r := 0
for j := 1 to n
i := r+1
while i <= m and A[i,j] == 0
i := i+1
if i < m+1
r := r+1
swap rows i and r of A (row op 1)
scale A[r,j] to a leading 1 (row op 2)
for k := 1 to m, k <> r
make A[k,j] zero (row op 3, employing row r)
output r and A
Look in the pretextcommon.xsl
file to see the strings to use to identify languages. Always alllowercase, no symbols, no punctuation.
Note that the above examples all have slightly different widths (theser are very evident in print with the frames). As 2D atomic objects, to place them in the narrative requires the layout features of a sidebyside
element. Then width
and/or margin
attributes will influence the width of the panel.
A program
may also be nested inside a listing
, which behaves similar to a figure
. You can provide a caption
, and the listing will be numbered along with tables and figures. This then makes it possible to crossreference the listing, such as Listing 23.1. It also removes the requirement of wrapping the program
in a sidebyside
. For technical reasons, the three examples above will not split across a page break in PDF output, but the placement inside a listing
will allow splits, as you should see in at least one example following.
If you are discussing algorithms in the abstract (or even concretely), you can set them off like a theorem, with a number, a title and a target for crossreferences. Sometimes you claim an algorithm produces something in particular, or has certain properties, such as a theoretical run time, so a proof may be included. See the discussion just preceding about (limited) options for pseudocode.
Algorithm 23.2. Sieve of Eratosthenes.
On input of a positive integer n
this algorithm will compute all the prime numbers up to, and including, n
. It was named for Eratosthenes of Cyrene (ca. 276 BC–ca. 195/194 BC) by Nicomachus (ca. 60–ca. 120 CE) in Introduction to Arithmetic. ( Wikipedia^{ 2 }, 2015)
Input:
n
Form the list of all integers from
2
ton
Set
p = 2

While
p < sqrt(n)
If present, remove from the list multiples
2p, 3p, ...
If
p
is now the last element of the list, stopOtherwise, set
p
to the element of the list immediately after currentp
Output: the remaining elements of the list
Proof.
Any element removed is a nontrivial product of two integers and hence composite. So no prime is is ever removed from the list.
Each composite number is a multiple of some prime, and since no prime is ever removed, each composite will be removed. Hence the removed elements are precisely the set of composite numbers in the list and thus the remainder are precisely the primes on the list.
If you are writing about systemlevel software, you may need to write numbers in hexadecimal or binary. Here we use a numbered, displayed equation (mathematics) and LaTeX macros such as \texttt
for a monospace text font, and \;
for spacing/grouping the bits of the binary number.
If you use these constructions repeatedly, then some LaTeX macros might be useful. It might also be beneficial for us to add some PreTeXt markup for such numbers used in a paragraph—send us a feature request.
Theorem 23.3.
This is a spurious theorem to break up the run of consecutive listing
so we might test the effect.
And this is a spurious paragraph to prove that the theorem beforehand, and the proof following, are distinct from one another.
Proof.(Theorem 23.3)
This is a proof that is authored “detached.” It is not associated with the theorem above in a way other than simply following it.
A specialized version of a program listing is an interactive command/response session at a commandline, where differing fonts are used to differentiate the system prompt, the user's commands, and the system's reaction. A console
session may be used by itself inside a sidebyside
, or it can be wrapped in a listing to get a number and a caption. As elsewhere, you will need to escape ampersands and angle brackets (such as if you have a command using redirection), using &
, <
, and >
in your source.
Here is the plain version, some layout control. We simply place a small margin on the left (at 4% width).
pi@raspberrypi ~/progs/chap02 $ gcc Wall o intAndFloat intAndFloat.c pi@raspberrypi ~/progs/chap02 $ ./intAndFloat The integer is 19088743 and the float is 19088.742188 pi@raspberrypi ~/progs/chap02 $
If your console input exceeds more than one line, you can author it across several lines and your choice of line breaks will be reflected in the rendering. You can decide to indent lines after the first one for clarity, if desired. You can also decide if your audience needs linecontinuation characters or not.
Notice in the HTML version of the above example that when you highlight all, or a portion, of the listing for a cutandpaste that the prompts are not included.
The next listing is just absurdity, to check various characters from LaTeX that are otherwise employed by the code supporting consoles, and some Latin1 characters. We test each in a prompt, input, and output. We use (*
and *)
as sequences used to escape embedded LaTeX commands, so we test those also.
We conclude this section with a longer example of a program listing, an assembly language program from Bob Plantz, included to test a listing
breaking across pages in PDF output.
www.public.asu.edu/~hhuang38/hph_matlab_basic2013_1.pdf
en.wikipedia.org/wiki/Sieve_of_Eratosthenes