•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $m ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 39426).
• ##

• at (eval 39317) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $m ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 39428).
• ##

• at (eval 39317) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . cyclic( $n1 ) . " \\times " . cyclic( $m1 ) . " \\)", "\\( ($a1, $b1 ) \\)", ans_rule(10) )
• ##Undefined subroutine &main::cyclic called at line 3 of (eval 39979).
• ##

• at (eval 39868) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . cyclic( $n1 ) . " \\times " . cyclic( $m1 ) . " \\)", "\\( ($b2, $a1 ) \\)", ans_rule(10) )
• ##Undefined subroutine &main::cyclic called at line 3 of (eval 39981).
• ##

• at (eval 39868) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . cyclic( $n1 ) . " \\times U($m1) \\)", "\\( ( $a1, $b1 ) \\)", ans_rule(10) )
• ##Undefined subroutine &main::cyclic called at line 3 of (eval 39983).
• ##

• at (eval 39868) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . dihedral( $n2 ) . " \\times U($m1) \\)", "\\( ( a^{$e1}b^{$e2}, $b1) \\)", ans_rule(10) )
• ##Undefined subroutine &main::dihedral called at line 3 of (eval 39985).
• ##

• at (eval 39868) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . dihedral( $n2 ) . " \\times " . quaternions( ) . " \\)", "\\( ( a^{$e3}b^{$e4}, $e ) \\)", ans_rule(10) )
• ##Undefined subroutine &main::dihedral called at line 3 of (eval 39987).
• ##

• at (eval 39868) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## dihedral( $m )
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 40548).
• ##

• at (eval 40439) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . cyclic( $u1 ) . " \\)", "\\( " . cyclic( $w1 ) . " \\)", "\\( $z1 \\)", ans_rule(10) )
• ##Undefined subroutine &main::cyclic called at line 3 of (eval 40552).
• ##

• at (eval 40439) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## 
• row( "\\( " . dihedral( $m ) . " \\)", "\\( " . quaternions( ) . " \\)", "\\( $k2 \\)", ans_rule(10) )
• ##Undefined subroutine &main::dihedral called at line 3 of (eval 40555).
• ##

• at (eval 40439) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## dihedral( $m ) 
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 41675).
• ##

• at (eval 41552) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $n ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 41677).
• ##

• at (eval 41552) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## dihedral( $m ) 
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 41681).
• ##

• at (eval 41552) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## quaternions( ) 
• ##Undefined subroutine &main::quaternions called at line 2 of (eval 41684).
• ##

• at (eval 41552) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## dihedral( $m ) 
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 42242).
• ##

• at (eval 42133) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $x \\pmod{$m}, $y \\pmod{$n} ) \\)", 
• "\\(" . cyclic( $m ) . "\\times " . cyclic($n) . "\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 42246).
• ##

• at (eval 42133) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $x \\pmod{$m}, $y \\pmod{$n} ) \\)", 
• "\\(" . cyclic( $m ) . "\\times U($n)\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 42248).
• ##

• at (eval 42133) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $z \\pmod{$m}, a^{$u} ) \\)", 
• "\\( U( $m ) \\times " . dihedral( $n ) . "\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 42250).
• ##

• at (eval 42133) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## dihedral( $m ) 
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 42807).
• ##

• at (eval 42696) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( $a \\) + \\( \\langle $b \\pmod{$n} \\rangle\\)", 
• "\\(" . cyclic( $n ) . "/\\langle $b \\pmod{$n}\\rangle \\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 42811).
• ##

• at (eval 42696) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( a^{$u} \\langle a^{$i} \\rangle \\)", 
• "\\(" . dihedral( $m ) . "/\\langle a^{$i} \\rangle\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 42814).
• ##

• at (eval 42696) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( a^{$u} b \\langle a^{$i} \\rangle \\)", 
• "\\(" . dihedral( $m ) . "/\\langle a^{$i} \\rangle\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::dihedral called at line 2 of (eval 42816).
• ##

• at (eval 42696) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $ax, $ay ) \\)", 
• "\\(" . cyclic( $am ) . "\\times" . cyclic($an) . "/ \\langle ( $au, $aw ) \\rangle\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 43930).
• ##

• at (eval 43819) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $bx, $by ) \\)", 
• "\\(" . cyclic( $bm ) . "\\times" . cyclic($bn) . "/ \\langle ( $bu, $bw ) \\rangle\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 43932).
• ##

• at (eval 43819) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $mx, $my ) \\)", 
• "\\(" . cyclic( $mm ) . "\\times U($mn)/\\langle ( $mu, $mw ) \\rangle\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 43934).
• ##

• at (eval 43819) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## row( "\\( ( $kx, $ky ) \\)", 
• "\\(" . cyclic( $km ) . "\\times U($kn)/\\langle ( $ku, $kw ) \\rangle\\)", 
• ans_rule(21))
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 43936).
• ##

• at (eval 43819) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
•Use of uninitialized value in numeric le (<=) at /opt/webwork/pg/lib/WeBWorK/PG/Translator.pm line 1009
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $m ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 44966).
• ##

• at (eval 44904) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $n ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 44968).
• ##

• at (eval 44904) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $a ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 44971).
• ##

• at (eval 44904) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $b ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 44973).
• ##

• at (eval 44904) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $k ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 44976).
• ##

• at (eval 44904) line 1671
•Can't locate macro file |algebraMacros.pl| via path: |.|, |/opt/webwork/courses/admin/templates/macros|, |/opt/webwork/pg/macros|, |/opt/webwork/courses/admin/templates/Library/macros/Union|, |/opt/webwork/courses/admin/templates/Library/macros/Michigan|, |/opt/webwork/courses/admin/templates/Library/macros/CollegeOfIdaho|, |/opt/webwork/courses/admin/templates/Library/macros/FortLewis|, |/opt/webwork/courses/admin/templates/Library/macros/TCNJ|, |/opt/webwork/courses/admin/templates/Library/macros/NAU|, |/opt/webwork/courses/admin/templates/Library/macros/Dartmouth|, |/opt/webwork/courses/admin/templates/Library/macros/WHFreeman| at [PG]/lib/PGloadfiles.pm line 170
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $modulus ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 45492).
• ##

• at (eval 45430) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $modulus ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 45494).
• ##

• at (eval 45430) line 1671
• ERROR in old_safe_ev, PGbasicmacros.pl: 

• ## There is an error occuring inside evaluation brackets \{ ...code... \}
• ## somewhere in an EV2 or EV3 or BEGIN_TEXT block.
• ## Code evaluated:
• ## cyclic( $modulus ) 
• ##Undefined subroutine &main::cyclic called at line 2 of (eval 45497).
• ##

• at (eval 45430) line 1671