1 How to Write Sage in LaTeX
There are two phases to writing sage code using sagetex. The first phase is writing the actual code, which generates all the content you want to utilize, and the second phase is calling parts of the code from the first phase to display or use.
1.1 Phase One
The first phase should almost certainly be written in the “sagesilent” block, which is where you write pure sage code that contains everything from generating the function you want to display, to the answer you want the student to enter.
For example, we would write something like the following:
\begin{sagesilent}
p1f1 = 3*x+1
p1ans = 10
\end{sagesilent}
This generates the sage variable named p1f1 and p1ans. This may seem like an odd
answer scheme but there is a good reason for it (see the “potential pitfalls section
below”. There is also a “sageblock” environment, but this tries to display the running
sage code as if it was being done in a sagecell prompt as you go, which is almost
always a bad idea.
1.2 Phase Two
The second phase is when you want to display the results of something from the sage
code you executed to define all the variables/functions/etc you needed to populate
the problem. In the current Ximera system, the only sage command that loads sage
content for the student to see, is the \sage command. Most importantly, the other
typical sage commands, like \sagestr and \sageplot do not work at all, and should
be avoided. So you will want to only use the \sage command to call content, even
though other commands may work locally - they won’t work on a Ximera page
.
1.3 Example
Consider the following problem:
The above problem is generated with the following code:
\begin{sagesilent}
p2f1 = 3*x+1
p2ans = p2f1(x=4)
\end{sagesilent}
\begin{problem}
Let $f(x) = \sage{p2f1}$. Then $f(4) = \answer{\sage{p2ans}}$
\end{problem}
The composition bit may look a little odd, but you can see why this is necessary in the “Pitfalls and Problems” section below.
2 Potential Pitfalls and Problems
2.1 Composition is a little weird
When doing composition in sage, it (now) requires you to use “x = ()” style notation. For example, if you use something like:
\begin{sagesilent}
## Function for first problem:
p3c1 = 4
p3c2 = 5
p3f1 = p3c1*x+p3c2
# Answer is just f(3)
p3ans = p3f1(3)
\end{sagesilent}
Sage will error and you will get a “spinning wheel of death” that kills everything
after it on the page. Instead, you need to write: \begin{sagesilent}
## Function for first problem:
p3c1 = 4
p3c2 = 5
p3f1 = p3c1*x+p3c2
# Answer is just f(3)
p3ans = p3f1(x=3)# Could also use p3f1(x=(3))
\end{sagesilent}
If the substitution is just one variable, you can use “x=var” but if you need
something more complex, like substituting in you would need to use extra
parentheses, like p3f1( x=(3x+1) ).
2.2 Ximera processes all the Sage code fully before being populated
Unlike when you compile locally (for most editors) all of the sage code is processed independently before it is populated into the page in Ximera. This means that if you accidentally use the same variable for two different problems, the second definition of that variable will overwrite the value for that variable for both problems. In other words, if you had something like:
\begin{sagesilent}
## Function for first problem:
const1 = 4
const2 = 5
func1 = const1*x+const2
## Function for second problem:
const1 = pi
func2 = sin(x=(x - const1))
\end{sagesilent}
Then the first function will come out as not because the const1 sage variable was
overwritten in the second problem’s code and overwrote it for every problem where
that variable is used - including the first problem. Annoyingly, you may compile it
locally, and depending on your editor, it may have shown the first function as
leading to more confusion.
2.3 Strings are tricky to get Ximera to accept...
Since sagetex usually uses the \sagestr command to generate text, and
since the \sage command requires mathemode, it makes strings a little...
interesting.
In particular, trying to actually display strings, you get some weird latex code. Consider the following code:
\begin{sagesilent}
p4str = ’this is a string’
p4ans = ’yes’
\end{sagesilent}
\begin{problem}
Is the following text?
\[
\sage{p4str}
\]
Type ‘‘yes’’ or ‘‘no’’ (without the quotes!)
$\answer{\sage{p4ans}}$
\end{problem}
You get:
The text shows up correctly as a string of text, but it is surrounded by brackets and
the LaTeX command. Moreover, if you type in yes (or even ’yes’) it won’t work.
Indeed, if you were to check the code to see what answer it was expecting, you
would discover that it is expecting \textit{yes} - just like the displayed
string.
But, there is a way to get a string to display correctly, both in actual text and in the validator - by using the “LatexExpr(r’string’)” command. So if we make some minor modifications to our previous code:
\begin{sagesilent}
p5str = LatexExpr(r’\text{this is a string}’)
p5ans = LatexExpr(r’yes’)
\end{sagesilent}
\begin{problem}
Is the following text?
\[
\sage{p5str}
\]
Type ‘‘yes’’ or ‘‘no’’ (without the quotes!)
$\answer{\sage{p5ans}}$
\end{problem}
Then we get:
Which both displays the problem, and accepts the answer, correctly. Notice that we need to use the\text command when we want to display text correctly to the student -
otherwise mathmode will display the provided text as if it were in mathmode (i.e.
without any spaces, and as if all letters were variables). Also note that we didn’t use
“format=string” in the answer command - indeed, doing so makes the validation fail
because of how LaTeX handles fonts in mathmode (this is deep LaTeX magic, so you
probably don’t want details - suffice it to say it isn’t something that can be
easily fixed or worked around with the current system). This means that
the validator is really thinking that the ‘y’, ‘e’, and ‘s’ are variables, so any
permutation of those variables would be accepted. This doesn’t typically
impact student answers however, but it might be worth remembering just in
case.
2024-06-24 13:14:39