I find it confusing how certain things in webwork are implemented as Contexts that I would expect to simply be objects. In particular, my understanding is that only one Context can be active at a time, so what do I do if I want to use more than one of those things?

At the moment I am particularly interested in piecewise functions and fractions, each of which is apparently enabled by setting a Context. I want to define a piecewise function that includes fractions (without converting them to decimals); how do I do it?

In reply to Michael Shulman

### Re: combining contexts (piecewise functions and fractions)

by Alex Jordan -
The Fraction context is more for:

Then Formula("1/2 x") will display as "\frac{1}{2}x". (Also Formula("2/4 x") will display as "\frac{2}{4}x and Formula("4/2 x") will display as "\frac{4}{2}x.)

If you additionally want a Formula answer where you force students to enter their answers using fractions, then I think you need to use bizarroArithmetic.pl. Or maybe LimitedRadical.pl would enough.

- enforcing that students enter fraction answers using fractions, not decimals. This is with respect to actual fraction answers, not expressions which happen to have fractions in them.
- a shortcut to make sure that any fraction you generate is automatically reduced.

If what you want to do is create a Formula in some other context where things like "1/2 x" do not display as "0.5x", then you can set the flag which stops arithmetic simplification in formulas:

Context()->flags->set(reduceConstants=>0);Then Formula("1/2 x") will display as "\frac{1}{2}x". (Also Formula("2/4 x") will display as "\frac{2}{4}x and Formula("4/2 x") will display as "\frac{4}{2}x.)

If you additionally want a Formula answer where you force students to enter their answers using fractions, then I think you need to use bizarroArithmetic.pl. Or maybe LimitedRadical.pl would enough.

In reply to Alex Jordan

### Re: combining contexts (piecewise functions and fractions)

by Michael Shulman -
Ideally, what I want is for

Formula("1/2 x") to display as "\frac{1}{2}x".

Formula("2/4 x") to display as "\frac{1}{2}x".

Formula("4/2 x") will display as "2x".

Is that possible?

Formula("1/2 x") to display as "\frac{1}{2}x".

Formula("2/4 x") to display as "\frac{1}{2}x".

Formula("4/2 x") will display as "2x".

Is that possible?

In reply to Michael Shulman

### Re: combining contexts (piecewise functions and fractions)

by Michael Shulman -
I think I figured it out: I set Context("Fraction") and define the pieces of the piecewise function individually, then set Context("PiecewiseFunction") and define the function using a hash of intervals, so that the pieces that were defined in fraction context aren't stringified and re-parsed, and thereby remain fractions.

In reply to Michael Shulman

### Re: combining contexts (piecewise functions and fractions)

by Alex Jordan -
I'm afraid not, at least not with any context I am familiar with. I think that the definition of the / symbol would have to be enhanced to do that. Maybe if its two operands could both be identified as simple integers, then maybe there would be a way to make that happen. But I'm pretty certain that you won't get things like Formula("2x/4") to automatically become "\frac{x}{2}" without external help from a CAS.

But back to those three examples. If I am in a situation where I need to use Formula("$a/$b x"), then along with turning off the reduceConstants flag, I also use the Fraction context to make $frac=Fraction($a,$b), and then make Formula("$frac x"). This will leave each of the three cases that you gave displaying as you want.

Just to be clear, all of this is about how Formulas will be displayed. If you want simplified expressions from students, then other techniques are needed (like bizarroArithmetic.pl).

But back to those three examples. If I am in a situation where I need to use Formula("$a/$b x"), then along with turning off the reduceConstants flag, I also use the Fraction context to make $frac=Fraction($a,$b), and then make Formula("$frac x"). This will leave each of the three cases that you gave displaying as you want.

Just to be clear, all of this is about how Formulas will be displayed. If you want simplified expressions from students, then other techniques are needed (like bizarroArithmetic.pl).