Thanks to the numerous examples, along with some deep thought, I have some success to report!

reduce.t

#!/usr/bin/env/perl

use strict;
use warnings;

use Test::More 'no_plan';

my $test_path = "C:/Users/Greyhat/PDL_Old/trig/src";
ok( require(  "$test_path/reduce.pl" ), 'Load file correctly.' ) or ex
+it;

# Not implemented
#my $test_2     =   [0,0,0];
#my $answer_2   =   [0,0,0];
#my $note_2     =   "@$test_2 | @$answer_2 | 2. Call with no value.";

my $test_3     =   [180, 59, 58];
my $answer_3   =   [180, 59, 58];
my $note_3     =   "@$test_3 | @$answer_3 | 3. already reduced";

my $test_4     =   [19, 0, 60];
my $answer_4   =   [19, 1,  0];
my $note_4     =   "@$test_4 | @$answer_4 | 4. test if single carry wo
+rks correctly";

my $test_5     =   [179, 59, 60];
my $answer_5   =   [180,  0,  0];
my $note_5     =   "@$test_5 | @$answer_5 | 5. tests if multiple carry
+ works correctly";

my $test_6     =   [-179, 60, 0];
my $answer_6   =   [-178,  0, 0];
my $note_6     =   "@$test_6 | @$answer_6 | 6. test addition with nega
+tives";

my $test_7     =   [ 0, 0, -60];
my $answer_7   =   [-1, 59,  0]; 
my $note_7     =   "@$test_7 | @$answer_7 | 7. test negative borrow wo
+rks correctly";

my $test_8     =   [90, 360, 360];
my $answer_8   =   [96,   6,   0]; 
my $note_8     =   "@$test_8 | @$answer_8 | 8. tests if multiple reduc
+e calls work correct";



sub main { 
    
reduce( @ARGV );
}

# Degree Reduction Tests
# Need to pass array refs to is_deeply
#ok(        &main()           ==  $answer_2, $note_2 );  
# From perl monks test code 
# is_deeply [ reduce(@$ar_args) ], $ar_expected, $full_comment;
is_deeply [ reduce(@$test_3 ) ],  $answer_3, $note_3 ;                
+          
is_deeply [ reduce(@$test_4 ) ],  $answer_4, $note_4 ;                
+                  
is_deeply [ reduce(@$test_5 ) ],  $answer_5, $note_5 ;                
+               
is_deeply [ reduce(@$test_6 ) ],  $answer_6, $note_6 ;                
+                  
is_deeply [ reduce(@$test_7 ) ],  $answer_7, $note_7 ;                
+    
is_deeply [ reduce(@$test_8 ) ],  $answer_8, $note_8 ;

# Degree Subtraction Tests

# Degree Multiplication Tests

# Degree Division Tests
[download]

#!/usr/bin/env/perl

use strict;
use warnings;

   
my ($a, $b, $c) = 0;

print "0. Value of ARGV is @ARGV; Value of magic array var is @_.\n";

# Take list of arguments from any of the 4 other subroutines
 # In principle, should accept variable length arguments
 # and recursively reduce the items in list from right to left.
 #
 # Termination: @angle has 1 length. This is pushed onto @answer array
+.
 # Case 1: reduce negative number by adding 60 to it, and 
 #         subtracting 1 from number on left.
 # Case 2: reduce positive number >= 60 by subtracting 60 and 
 #         adding 1 to number on left.
 #
 # NOTE 1: CHECK BRACKETS AROUND UNTIL LOOP! MAY NEED TO MOVE CLOSING 
+BRACKET!
 # NOTE 2: Add check to test for length of @angle array!  Then it shou
+ld work.
 # NOTE 3: Add elsif to test for case where $c is ok value but scalar(
+@angle) > 1.  
 #         Just push value to answer array.
 # NOTE 4: Does not handle multiples of 60 correctly.  Likely scope is
+sue.

my @answer;         
sub reduce {
# print "0. Value of magic array var is @_.\n"; 
  
  my @angle = @_;
#  @_ = undef;
 my ($b, $c) = ($angle[-2], $angle[-1]); # reduce from end.

  if ($c < 0 && scalar(@angle) > 1) {
   until ($c >= 0 && $c < 60) {
     $c += 60;
     $b -=  1;
     }
     unshift(@answer, $c);
     pop(@angle);
     @angle[-1] = $b;
# Debug print statements
     print "2. b = $b, c = $c\n";
     print "2. Angle array is @angle.\n ";
     print "2. Value of magic array var is @_.\n";
     print "2. Values in answer array: @answer.\n";
####
     
     &reduce(@angle);
    
  } elsif ($c >= 60 && scalar(@angle) > 1 ) {
     until ($c < 60 && $c >= 0) {
     $c -= 60;
     $b += 1;
     }
     unshift(@answer, $c);
     pop(@angle);
     @angle[-1] = $b;
# Debug print statements
     print "3. b = $b, c = $c\n";
     print "3. Angle array is @angle.\n ";
     print "3. Value of magic array var is @_.\n";
     print "3. Values in answer array: @answer.\n";
####
              
     &reduce(@angle);
    
  } elsif ( ($c >= 0 && $c < 60 ) && scalar(@angle) > 1)  {
     unshift(@answer, $c);
     pop(@angle);
     &reduce(@angle); 
  } else {
     unshift(@answer, @angle);            
     print "Reduced answer: @answer \n";
     return $answer[0], $answer[1], $answer[2];
     
 }
 
}

main( @ARGV ) unless caller();

sub main {
    
reduce( @_ );

}
[download]

... the initial goal of getting the tests to run has been met.

I'm looking at your  $test_7: (0, 0, -60) -> (-1, 59, 0) (result: -1° 59' 0"). (There's a similar test 7 here with result (-1, 59, 2).) I would have thought the normalized or reduced result to be  (0 -1 0) (0° -1' 0"). If the required result shown in the code is correct, it suggests a set of sign propagation rules I have yet to see. Can you expand on this?

I notice that you haven't recast your core code into a module yet. Doing so is a good idea for many reasons, including testing. Note that Test::More::use_ok() is available for modules and Test::More::require_ok() for more humble files.

The other point that occurred to me is also in terms of general design. Rather than always reduce()-ing deg/min/sec tuples to other d/m/s tuples, it might be less of a headache to normalize d/m/s tuples to, say, integer or decimal fraction arc-seconds (or maybe radians?) or whatever's most convenient, do all the trig in these standard units, then convert back to the ultimate d/m/s (or whatever) output form just once as a final step. Just a thought...

---

Give a man a fish:  <%-{-{-{-<

Negative numbers are only permitted in the degree column. Any minutes or seconds need to be a positive integer from 0-59 inclusive. Although an angle has a combined decimal and base 60 format, I treat the base 60 components of an angle like the fractional components of a decimal are treated; negatives get propagated to the next highest term. You can find the procedure Albert Klaf's Trigonometry Refresher on page 12; the section is available on google books. As I was going through the tests, I noticed some errors in the tests that I have no idea how they made their way into the code. I suspect they were just typos or search/replace errors I had missed. Regarding extensions to decimals -- that is a planned future extension based upon the problems in the study guide I am going through. Instead of doing the problems manually, I write a program to calculate the solutions, and learn Perl testing in the process :)