using variable values in mathematical expression pattern restrictions

[merryn....@gmail.com]

How do I add numbas variable values into pattern restrictions?

I want to get students to fully factorise an expression like (8x+12xy), i.e. 4x(2+3y)

To do this I am trying to use pattern restriction, where the pattern needs to have the numerical gcd . x out the front. The gcd is a randomly selected number held in a variable and I cannot figure out how to make this work.

In order to try to figure it out I set up a simpler problem: the answer should be 6 + k, where 6 is held in a number variable {tc}

I tried $n;c + k `where c={tc} and other variations but I haven't succeeded so far in getting the pattern match to work, and would appreciate some help.

[Christian Lawson-Perfect]

I don't think you need to use the value of the gcd in the pattern.

If the greatest common factor has been extracted, then the coefficients inside the brackets must be coprime. Use the `where operator to add this condition.

I've written an example at https://numbas.mathcentre.ac.uk/question/123498/pattern-match-pull-common-factors-out/.

Here's the pattern:

// a number times...
$n`? *
(
  // the constant term:
  //   either a number 'a',
  //   or 'a' is implicitly zero if no constant term is given
  ($n;a `| $z;a:0)
 
  +
 
  // the x term:
  //   either a number 'b' times x,
  //   or x on its own, and 'b' is implicitly 1
  ($n;b * x `| x;b:1)
)

// a and b must be coprime
`where

(gcd(a,b)=1)

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[Merryn Horrocks]

Ok, many thanks Christian

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[merryn....@gmail.com]

Hi Christian,

Thank you for your solution - it works a treat!

However, I have quickly run into another problem, namely, "factorise 6ab + 8bc" where 6 and 8 are randomly chosen, and a, b, and c are randomly chosen letters (so that the questions don't always use the same variables.) Again, the way I am thinking is to use the variable containing b in the pattern match. If so, how do I go about this, or is there a different smart way to do this? 

Thanks again,

Merryn