Question: Polynomials extension, create "polynomial" from student's answer

[Ulrich Goertz]

Hi, I would like to have students enter a polynomial, and to create an instance of the JME polynomial type provided by the Polynomials extension. (Specifically, I want to ask my students to "Find a polynomial that annihilates the following matrix." I wrote some JME functions to evaluate a polynomial on a matrix, but I need to get my hands on the polynomial entered by the student, to use it in my custom marking algorithm, and failed to do so, so far.)

I see there is a JavaScript from_string method in polynomials.js, but I am not sure how to reach out to that. I'd be grateful for any suggestions ... Thanks!

Best regards, Ulrich

[Christian Lawson-Perfect]

There wasn't a straightforward way of constructing a polynomial from a string in JME. I've fixed that. Now you can call for example polynomial("x^2+3x+2").

I've made an example question at https://numbas.mathcentre.ac.uk/question/94245/answer-is-a-polynomial/.

While I was doing that, I noticed that the equality test for polynomials didn't properly cope with zero coefficients, so I've fixed that too. The polynomials extension hasn't been very rigorously tested, so please be careful when using it with student input, and let me know if you spot any more bugs or missing features.

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[Ulrich Goertz]

Thanks, Christian, that's very helpful!

I used the extension for several problems and am happy with it :-)

One thing that I wasn't able to do in a completely straight-forward way is to retrieve a LaTeX representation of a polynomial in a JME function. (I need this in the advice section of this problem on the euclidean algorithm in the polynomial ring over the rationals.) For now, I worked around this by adding a JavaScript function which takes a polynomial p and returns p.toLaTeX(); This feels a bit like a hack. Maybe I am missing something? In any case, it's not an actual problem for me, it's more a question of making the polynomials extension more user-friendly.

[Christian Lawson-Perfect]

Good point! I've added functions `string(p)` and `latex(p)` which produce plain string and LaTeX renderings of a polynomial.

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