** Using WeBWorK **

I endorse Darwyn Cook's proposal (in the Features & Development forum) for a Tips & Tricks forum.  Here is my first contribution.


When I started writing PG problems, I would generate a pair of distinct integers with the pattern

$a = random( -9 , 9 , 1 ) ;
$b = random( -9 , 9 , 1 ) ;
while ($b == $a) {$b = random( -9 , 9 , 1 ) ;} ;

with the awkward extension

$a = random( -9 , 9 , 1 ) ;
$b = random( -9 , 9 , 1 ) ;
while ($b == $a) {$b = random( -9 , 9 , 1 ) ;} ;
$c = random( -9 , 9 , 1 ) ;
while (($c-$a)*($c-$b)==0) {$c = random( -9 , 9 , 1 ) ;} ;


That evolved into a more elegant/efficient form

$a = random( -9 , 9 , 1 ) ;
do {$b = random( -9 , 9 , 1 ) ;}  until ($b != $a) ;
do {$c = random( -9 , 9 , 1 ) ;} until ( ($c != $a) and ($c != $b) ) ;


An alternative using NchooseK is less transparent, but scales better for generating larger sets of distinct integers

loadMacros( “PGchoicemacros.pl” ) ;
@choose = NchooseK( 19 , 3 ) ;  ## values between 0 and (19-1)
$a = @choose[0] - 9 ;                ## indices between 0 and (3-1)
$b = @choose[1] - 9 ;
$c = @choose[2] - 9 ;


More recently, I generated 4 reals with distinct magnitudes (to be Real and Imaginary parts of 2 random complex numbers) using

$Rlo    = 0.5 ;
$Rhi    = 9.5 ;
$Rdelta = 0.5 ;
$a = random($Rlo,$Rhi,$Rdelta);
do {$b = random($Rlo,$Rhi,$Rdelta);} until ($b != $a) ;
do {$c = random($Rlo,$Rhi,$Rdelta);} until (($c != $a) and ($c != $b)) ;
do {$d = random($Rlo,$Rhi,$Rdelta);} until (($d!=$a) and ($d!=$b) and ($d!=$c));
$a = $a * list_random( -1 , 1 ) ;
$b = $b * list_random( -1 , 1 ) ;
$c = $c * list_random( -1 , 1 ) ;
$d = $d * list_random( -1 , 1 ) ;


I would like to learn about alternative (or simpler) techniques to do these (and similar) tasks.