Whitelist package gf for finite field arithmetic

[mminzlaff]

Please whitelist the package "gf" so that "load(gf)" is allowed. This enables STACK questions with finite field arithmetic.

[sangwinc]

I think this is already auto-loaded. Please try the following in the question variables

gf_set_data(2,x^4+x+1);
a:x^3+x;
b:x^3+x^2+1;

Then castext: {@gf_add(a,b)@}. If you need me to add anything else, please re-open this issue and I'll help!

[mminzlaff]

Dear Chris, many thanks for your quick response and offer to help! When I use this I and try to save the question, I get an "CAS failed to return any data due to timeout." error. Do you have any hints?

[sangwinc]

OK, to this problem is documented here: https://docs.stack-assessment.org/en/Developer/Maxima_packages/#maxima-graph-theory-package

Some of the contributed packages, including the very nice graph theory package, have developed their own internal representation for mathematical objects. For example,

gf_set_data(2,x^4+x+1);

returns Structure [GF-DATA]. This internal structures are not compatible with STACK's PHP-Maxima interface without rewriting how those structures are communicated.

That said, since I made that note in 2020, a lot has change in STACK. In particular we now have a "preamble" so we don't need to communicate back and forward with PHP all the time - we can just call this command every time we call Maxima. So, could you try this please as your question variables?

m:x^4+x+1;
p:2;
/* The gf_set_data() function tried to return a LISP structure, which we can't capture.  Return true instead. */
f:(gf_set_data(p,m), true);
%_stack_preamble_end

a : x^3+x;
b : x^3+x^2+1;

ta1:gf_add(a, b);

Then the following question text:

<p>Add \({@a@}\) to \({@b@}\) in \(\mathbb{F}_{@2@}[x]/m(x)\) where \(m(x)={@m@}\).</p><p>[[input:ans1]] [[validation:ans1]]</p>

Could I ask for your help please? Perhaps you could investigate if the approach above (returning true not the LISP structure) really works? I don't work in finite fields, and am pushed for time over the next couple of weeks. If this looks workable, then we can add examples, documentation and test cases to "bake in" this solution as a way to support the "gf" package. (Graph theory is much more difficult, sorry!)

[mminzlaff]

Excellent - that seems to solve the initial problem. Many thanks!

I went ahead and tried all the functions from the gf package as explained in Finite Fields Computations in Maxima up to and including the section "Large fields".

Three commands throw errors when using them in Question Text:

• gf_make_arrays(): The value #(1 2 4 8 3 6 12 11 5 10 7 14 15 13 9 1) is not of type SYMBOL when binding SYMBOL.
• gf_logs[3]: found gf_logs evaluates to false where an array was expected.
• gf_powers[4]): found gf_powers evaluates to false where an array was expected.

The computation for r in the section on the knapsack cryptosystem also didn't work, but that might be an issue with the manual. I didn't investigate further.

All the rest work fine and reproduce the same output as in the manual.

[sangwinc]

Thanks @mminzlaff I very much appreciate you looking into this.

I think the resolution of this issue will be documentation and sample questions in the first instance. If someone would like to look into, and perhaps rewrite the gf package parts which are currently incompatible with STACK then that would be great. But for now, I don't have the capacity to do that myself (sorry!).

I've added a branch here: https://github.com/maths/moodle-qtype_stack/tree/iss1813

Sample questions will live in
https://github.com/maths/moodle-qtype_stack/tree/iss1813/samplequestions/stacklibrary/Topics
and the start of docs are here
https://github.com/maths/moodle-qtype_stack/blob/iss1813/doc/en/Topics/Finite_fields.md
(MathJax is not applied to the github preview, but will be when the docs are published on stack-assessment.org)

If you have a couple of working sample questions, or other comments, you can either send a pull request or an email to me at C.J.Sangwin@ed.ac.uk, and we'll improve the support for gf in the next version.