dynamic fill-in exercise allowed operations

[Hunter Lehmann]

Hi,

I am trying to create a dynamic exercise to compute the Hamming weight of a random vector in F_p^n, say with entries x_1,...,x_6 in {0,1,..p-1}.  Is it possible to use a mod operator somehow in the computation of dynamic values in PreTeXT?

The computation I would like to do is (x_1^4+x_2^4+...+x_6^4) mod 5.  I tried using % to invoke the mod operator but that just breaks the code.

Current exercise code below also.

Best,

Hunter

<exercise xml:id="daily-prep-fp-hamming-weight">
      <setup seed="123456">
        <de-object name="x1" context="number">
          <de-random distribution="discrete" min="0" max="4" by="1" />
        </de-object>
        <de-object name="x2" context="number">
          <de-random distribution="discrete" min="0" max="4" by="1" />
        </de-object>
        <de-object name="x3" context="number">
          <de-random distribution="discrete" min="0" max="4" by="1" />
        </de-object>
        <de-object name="x4" context="number">
          <de-random distribution="discrete" min="0" max="4" by="1" />
        </de-object>
        <de-object name="x5" context="number">
          <de-random distribution="discrete" min="0" max="4" by="1" />
        </de-object>
        <de-object name="x6" context="number">
          <de-random distribution="discrete" min="0" max="4" by="1" />
        </de-object>
        <de-object name="wt" context="number">
          <de-number>(x1^4+x2^4+x3^4+x4^4+x5^4+x6^4)%5</de-number>
        </de-object>
      </setup>
      <statement>
        <p>
          Compute the Hamming weight of <m>(<eval obj="x1"/>,<eval obj="x2"/>,<eval obj="x3"/>,<eval obj="x4"/>,<eval obj="x5"/>,<eval obj="x6"/>)</m>.
        </p>
        <p>
          <fillin mode="math" name="hamming_wt" ansobj="wt" width="4"></fillin>
        </p>
      </statement>
      <evaluation>
        <evaluate name="hamming_wt">
          <test correct="yes">
          <mathcmp obj="wt" />
          </test>
        </evaluate>
      </evaluation>
    </exercise>

[D. Brian Walton]

Hunter,

The mod operator has not been implemented. It could be possible but would require a dependent package is updated and could take some time. Note that the library was designed for floating point arithmetic, and I haven't thought about what happens with the modulus. Also, there is no integer division implemented.

I do need to get back to that and will see about implementing that operator.

Brian

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[Rob Beezer]

Nothing here should be construed as minimizing Hunter's request.

The possible requests for supported operators is vast. How about polynomial multiplication with coefficients over a finite field? ;-) Yes, I know, out of scope right now.

Years ago, the WeBWorK folks added for me a function to pass computations to Sage and get back the results. It was a bit cumbersome to use (nobody's fault). Suppose there was a dedicated Sage Cell server that FITB problems could utilize? Imagine randomized questions about non-commutative rings for an abstract algebra course.

Not sure what markup, or much else, would look like. Just dreamin'.

Rob

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[D. Brian Walton]

Hunter,

There was a post to the pretext development list that triggered my memory enough to realize that there IS a solution to your problem, it just requires that you code directly in javascript instead of the expression library markdown. Making a test about the formula as an expression is what I was thinking about in my earlier answer. But the system is already capable of adding arbitrary javascript calculations and tests from the original design — just not many have gone this route.

If you go to this section of the documentation Subsection 4.12.7: Fill-in-the-Blanks Exercises there is a reference to a `jscmp` method that you can use to define your own comparison based on any valid javascript that evaluates to a boolean. Because the modulus operator is a first-class operator in javascript, you could use that for your test if you just want to check a numerical answer for comparison.  It also mentions `setupScript` which allows arbitrary javascript (encapsulated in a function) to generate additional values.

All objects are stored as local variables within an object named `v` for the actual javascript. So having defined your values, instead of defining "wt" as a de-object (where the operator is not defined), you can instead compute "wt" in the setupScript.

<setup>

... same as before except defining wt ...

  <setupScript> <!-- This is pure javascript executed within a function -->

  v.wt = (v.x1^4 + v.x2^4 + v.x3^4 + v.x4^4 + v.x5^4 + v.x6^4) % 5;

  </setupScript>

</setup>

And then instead of <mathcmp> you would try:

<jscmp>answer == wt</jscmp>

(At the comparison step, all of the "v" variables are made 1st class variables in their own right so that we don't need v.{...})

I have not attempted if this works as is, but it should be close. 

Brian