## WeBWorK Main Forum

### Avoid zero denominator ### Avoid zero denominator

Number of replies: 9

Hello all:

these are answers of the one of the probelm i just created. all are random variables:

$ans3 = ($c/$a)-(($f*$a*$b-$c*$b*$d)/($e*$a*$a-$b*$d*$a));$ans4 = ($f*$a-$c*$d)/($e*$a-$b*$d);

$a is defined already to be non zero random My question is how to avoid having zero in the denominator for these :$e*$a*$a-$b*$d*$a , and$e*$a-$b*$d canot be zero? Best In reply to Adam Z ### Re: Avoid zero denominator by Andras Balogh - You can regenerate the random variables in a do-while loop. Something like do{$e=random...; $a=random...; ... }while($e*$a*$a-$b*$d*$a == 0); In reply to Andras Balogh ### Re: Avoid zero denominator by Adam Z - Thank you for this, it is helpful. In reply to Adam Z ### Re: Avoid zero denominator by Alex Jordan - For example, if you had:$a = non_zero_random(-9,9,1);
$b = non_zero_random(-9,9,1);$d = non_zero_random(-9,9,1);
$e = non_zero_random(-9,9,1);$ans3 = ($c/$a)-(($f*$a*$b-$c*$b*$d)/($e*$a*$a-$b*$d*$a));
$ans4 = ($f*$a-$c*$d)/($e*$a-$b*$d); You could change it to do {$a = non_zero_random(-9,9,1);

$b = non_zero_random(-9,9,1);$d = non_zero_random(-9,9,1);
$e = non_zero_random(-9,9,1); } until ($e*$a -$b*$d != 0);$ans3 = ($c/$a)-(($f*$a*$b-$c*$b*$d)/($e*$a*$a-$b*$d*$a));
$ans4 = ($f*$a-$c*$d)/($e*$a-$b*$d); That will re-loop the variable initializations until neither denominator is 0. Or an alternative is to define$a in a way that guarantees these denominators to be nonzero. It seems that if $a is nonzero, not ±1, and also relatively prime to$b*$d, that would prevent the denominators from being 0. So the line that makes$a could be:

do {$a = list_random(-9,..-2,2..9)} until (gcd($a,$b*$d) == 1);

With more information about how/why you are making $a,$b, $d, and$e, you could possibly define them all deterministically to avoid division by 0. (As opposed to these approaches above which are probabilistic and introduce some inefficiency because of running a loop.) ### Re: Avoid zero denominator

Thank you very much. This is so clear. I will fix it and come back since I still have another question :) ### Re: Avoid zero denominator

What I am trying to do here is create a problem of solving system of linear equations of this format
$ax+$by=$c$dx+$ey=$f

I am still learning this language. I am also stuck with the no solution or infinity many solution cases, I am trying to use IF else but generates errors. ### Re: Avoid zero denominator

by Alex Jordan -

In case it is helpful, let me recommend against coding a problem where for some random versions there is one solution, and for some random versions there are no solutions, and for some random versions there are infinitely many.

Once upon a time that is how I coded WeBWorK questions. Just randomize the parameters that are displayed to the student, and code the rest of it to handle whatever happened next. But after time I came to decide this was a mistake. It is a different pedagogical experience for the student who encounters this system with one solution than it is for the student who encounters a version with no solutions (or infinitely many).

So if it were me, I'd code three problem files. And rest knowing that I had exposed each student to each of the three situations in an exercise set. ### Re: Avoid zero denominator

by Andras Balogh -
I agree that it is better to cover all special cases instead of randomly choosing one.
Regarding learning the language l usually use existing library problems as examples.  