Writing interactive exercises

[Stephan Boltzmann]

The "Active Calculus" textbook is great and it's interactive exercises great for teaching!

How could I generate an exercises like the ones on https://runestone.academy/ns/books/published/ac-single/sec-2-1-elem-rules.html?mode=browsing?

Is this a webwork exercise?

I realized that the system is quite elaborate, because it recognizes algebraic equivalence of the answers entered in the text input fields?

How is this technically done (i.e. via a computer algebra system [CAS] in the background)?

[Alex Jordan]

The Preview Activity on that page is a WeBWorK/PG exercise whose code
is included directly in the PreTeXt source of the book. The exercises
at the bottom of the page come from the WeBWorK Open Problem Library
and are just called directly from the OPL.

PG assesses formula expressions as equivalent by taking a bunch of
random input values and checking that the outputs match. Additional
things can be done if you actually want to distinguish between
different forms for equivalent expressions. So it is not a CAS,
although it is possible to tie questions into Sage. It just adds a lot
of processing overhead.

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[Alex Jordan]

Actually on that page, the Preview Activity is also an OPL question. I
was thinking of a later chapter where we wrote some exercises
specifically for AC.