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version 1.14, 2001/01/03 00:14:47 version 1.125, 2008/03/03 19:14:51
Line 1 Line 1
 # file name (temp): default_homework   # The LearningOnline Network with CAPA 
 # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()  # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
 #   
 #  #
 $RANDOMINIT=0;  # $Id$
   #
   # Copyright Michigan State University Board of Trustees
   #
   # This file is part of the LearningOnline Network with CAPA (LON-CAPA).
   #
   # LON-CAPA is free software; you can redistribute it and/or modify
   # it under the terms of the GNU General Public License as published by
   # the Free Software Foundation; either version 2 of the License, or
   # (at your option) any later version.
   #
   # LON-CAPA is distributed in the hope that it will be useful,
   # but WITHOUT ANY WARRANTY; without even the implied warranty of
   # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   # GNU General Public License for more details.
   #
   # You should have received a copy of the GNU General Public License
   # along with LON-CAPA; if not, write to the Free Software
   # Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
   #
   # /home/httpd/html/adm/gpl.txt
   #
   # http://www.lon-capa.org/
   #
   #
   
   #init some globals
   $hidden::RANDOMINIT=0;
   $pi=atan2(1,1)*4;
   $rad2deg=180.0/$pi;
   $deg2rad=$pi/180.0;
   $"=' ';
   use strict;
   {
       my $n = 0;
       my $total = 0;
       my $num_left = 0;
       my @order;
       my $type;
   
       sub init_permutation {
    my ($size,$requested_type) = @_;
    @order = (0..$size-1);
    $n = $size;
    $type = $requested_type;
    if ($type eq 'ordered') {
       $total = $num_left = 1;
    } elsif ($type eq 'unordered') {
       $total = $num_left = &factorial($size);
    } else {
       die("Unkown type: $type");
    }
       }
   
       sub get_next_permutation {
    if ($num_left == $total) {
       $num_left--;
       return \@order;
    }
   
    # Find largest index j with a[j] < a[j+1]
   
    my $j = scalar(@order) - 2;
    while ($order[$j] > $order[$j+1]) {
       $j--;
    }
   
    # Find index k such that a[k] is smallest integer
    # greater than a[j] to the right of a[j]
   
    my $k = scalar(@order) - 1;
    while ($order[$j] > $order[$k]) {
       $k--;
    }
   
    # Interchange a[j] and a[k]
   
    @order[($k,$j)] = @order[($j,$k)];
   
    # Put tail end of permutation after jth position in increasing order
   
    my $r = scalar(@order) - 1;
    my $s = $j + 1;
   
    while ($r > $s) {
       @order[($s,$r)]=@order[($r,$s)];
       $r--;
       $s++;
    }
   
    $num_left--;
    return(\@order);
       }
       
       sub get_permutations_left {
    return $num_left;
       }
   }
   
   sub check_commas {
       my ($response)=@_;
       #print("$response ");
       my @numbers=split(',',$response);
       #print(" numbers ".join('-',@numbers)." ");
       if (scalar(@numbers) > 1) {
           #print(" numbers[0] ".$numbers[0]." "); 
    if (length($numbers[0]) > 3 || length($numbers[0]) == 0) { return -1; }
    shift(@numbers);
    #print(" numbers ".scalar(@numbers)." ");
    while (scalar(@numbers) > 1) {
       #print(" numbers ".join('-',@numbers)." ");
       if (length($numbers[0]) != 3) { return -2; }
       shift(@numbers);
    }
    my ($number)=split('\.',$numbers[0]);
    #print(" number ".$number." ");
    #print(" numbers[0] ".$numbers[0]." ");
    if (length($number) != 3) { return -3; }
       } else {
    my ($number)=split('\.',$numbers[0]);
    if (length($number) > 3) { return -4; }
       }
       return 1;
   }
   
   
 sub caparesponse_check {  sub caparesponse_check {
   my $answer='';  #done      my ($answer,$response)=@_;
   my $type='';    #done      #not properly used yet: calc
   my $tol_type=''; # gets it's value from whether tol has a % or not done      #not to be used: $ans_fmt
   my $tol='';     #done      my $type=$LONCAPA::CAPAresponse_args{'type'};
   my $sig='';      my $tol=$LONCAPA::CAPAresponse_args{'tol'};
   my $sig_lbound='';      my $sig=$LONCAPA::CAPAresponse_args{'sig'};
   my $sig_ubound='';      my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'};
   my $ans_fmt='';      my $unit=$LONCAPA::CAPAresponse_args{'unit'};
   my $units='';      my $calc=$LONCAPA::CAPAresponse_args{'calc'};
   my $calc='';      my $samples=$LONCAPA::CAPAresponse_args{'samples'};
   my ($response,$expr)=@_;      
         my $tol_type=''; # gets it's value from whether tol has a % or not done
   ($answer,$type,$tol,$sig,$ans_fmt,      my $sig_lbound=''; #done
    $units,$calc) = eval $expr.';return $answer,$type,$tol,$sig,$ans_fmt,$units,$calc';      my $sig_ubound=''; #done
   #type's definitons come from capaParser.h  
   if ($type eq '' ) {  
     if ( $answer eq ($answer *1.0)) { $type = 2;      #type's definitons come from capaParser.h
     } else { $type = 3; }  
   } else {      #remove leading and trailing whitespace
          if ($type eq 'cs')    { $type = 4;      if (!defined($response)) {
     } elsif ($type eq 'ci')    { $type = 3;   $response='';
     } elsif ($type eq 'mc')    { $type = 5;      }
     } elsif ($type eq 'fml')   { $type = 8;      if ($response=~ /^\s|\s$/) {
     } elsif ($type eq 'subj')  { $type = 7;   $response=~ s:^\s+|\s+$::g;
     } else { return "ERROR: Unknown type of answer: $type" }   &LONCAPA_INTERNAL_DEBUG("Removed ws now :$response:");
   }      }
   
   if ($tol eq '') {      #&LONCAPA_INTERNAL_DEBUG(" type is $type ");
     $tol=0.0;      if ($type eq 'cs' || $type eq 'ci') {
     $tol_type=1; #TOL_ABSOLUTE   #for string answers make surec all places spaces occur, there is 
   } else {          #really only 1 space, in both the answer and the response
     if ($tol =~ /%$/) {   $answer=~s/ +/ /g;
       chop $tol;   $response=~s/ +/ /g;
       $tol_type=2; #TOL_PERCENTAGE      } elsif ($type eq 'mc') {
     } else {   $answer=~s/[\s,]//g;
       $tol_type=1; #TOL_ABSOLUTE   $response=~s/[\s,]//g;
     }      }
   }      if ($type eq 'float' && $unit=~/\$/) {
    if ($response!~/^\$/)  { return ('NO_UNIT', undef); }
   if ($sig eq '') {   $response=~s/\$//g;
     $sig_lbound = 0; #SIG_LB_DEFAULT      }
     $sig_ubound =15; #SIG_UB_DEFAULT      if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
   } else {   return "COMMA_FAIL:";
     ($sig_lbound,$sig_ubound) = split /,/,$sig;      }
   }      $ans_fmt=~s/\W//g;
   my $result = &caparesponse_capa_check_answer($response,$answer,$type,      $unit=~s/[\$,]//g;
        $tol_type,$tol,      if ($type eq 'float') { $response=~s/,//g; }
        $sig_lbound,$sig_ubound,  
        $ans_fmt,$units,$calc);      if (length($response) > 500) { return ('TOO_LONG',undef); }
   
   if    ($result == '1') { $result='EXACT_ANS'; }       if ($type eq '' ) {
   elsif ($result == '2') { $result='APPROX_ANS'; }   &LONCAPA_INTERNAL_DEBUG("Didn't find a type :$type: defaulting");
   elsif ($result == '3') { $result='SIG_FAIL'; }   if ( $answer eq ($answer *1.0)) { $type = 2;
   elsif ($result == '4') { $result='UNIT_FAIL'; }        } else { $type = 3; }
   elsif ($result == '5') { $result='NO_UNIT'; }      } else {
   elsif ($result == '6') { $result='UNIT_OK'; }   if    ($type eq 'cs')    { $type = 4; }
   elsif ($result == '7') { $result='INCORRECT'; }   elsif ($type eq 'ci')    { $type = 3 }
   elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }   elsif ($type eq 'mc')    { $type = 5; }
   elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }   elsif ($type eq 'fml')   { $type = 8; }
   elsif ($result =='10') { $result='SUB_RECORDED'; }          elsif ($type eq 'math')  { $type = 9; }
   elsif ($result =='11') { $result='BAD_FORMULA'; }   elsif ($type eq 'subj')  { $type = 7; }
   elsif ($result =='12') { $result='WANTED_NUMERIC'; }   elsif ($type eq 'float') { $type = 2; }
   else  {$result = "ERROR: Unknown Result:$result:$@:";}   elsif ($type eq 'int')   { $type = 1; }
    else { return ('ERROR', "Unknown type of answer: $type") }
       }
   
       my $points;
       my $id_list;
       #formula type setup the sample points
       if ($type eq '8') {
    ($id_list,$points)=split(/@/,$samples);
    &LONCAPA_INTERNAL_DEBUG("Found :$id_list:$points: points in $samples");
       }
       if ($tol eq '') {
    $tol=0.0;
    $tol_type=1; #TOL_ABSOLUTE
       } else {
    if ($tol =~ /%$/) {
       chop $tol;
       $tol_type=2; #TOL_PERCENTAGE
    } else {
       $tol_type=1; #TOL_ABSOLUTE
    }
       }
   
       ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig);
   
   return "$result:$error:$answer:$response:$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$units";      my $reterror="";
       my $result;
       if ((($type eq '9') || ($type eq '8')) && ($response=~/\=/)) { return ('BAD_FORMULA','Please submit just an expression, not an equation.'); }
       if ($type eq '9') {
         $result = &maxima_check(&maxima_cas_formula_fix($response),&maxima_cas_formula_fix($answer),\$reterror);
       } else {
    if ($type eq '8') { # fml type
       $response = &capa_formula_fix($response);
       $answer   = &capa_formula_fix($answer);
    }
          $result = &caparesponse_capa_check_answer($response,$answer,$type,
    $tol_type,$tol,
    $sig_lbound,$sig_ubound,
    $ans_fmt,$unit,$calc,$id_list,
    $points,$external::randomseed,
    \$reterror);
       }
       if    ($result == '1') { $result='EXACT_ANS'; } 
       elsif ($result == '2') { $result='APPROX_ANS'; }
       elsif ($result == '3') { $result='SIG_FAIL'; }
       elsif ($result == '4') { $result='UNIT_FAIL'; }
       elsif ($result == '5') { $result='NO_UNIT'; }
       elsif ($result == '6') { $result='UNIT_OK'; }
       elsif ($result == '7') { $result='INCORRECT'; }
       elsif ($result == '8') { $result='UNIT_NOTNEEDED'; }
       elsif ($result == '9') { $result='ANS_CNT_NOT_MATCH'; }
       elsif ($result =='10') { $result='SUB_RECORDED'; }
       elsif ($result =='11') { $result='BAD_FORMULA'; }
       elsif ($result =='12' && !$response) { $result='MISSING_ANSWER'; }
       elsif ($result =='12') { $result='WANTED_NUMERIC'; }
       elsif ($result =='13') { $result='UNIT_INVALID_INSTRUCTOR'; }
       elsif ($result =='141') { $result='UNIT_INVALID_STUDENT'; }
       elsif ($result =='142') { $result='UNIT_INVALID_STUDENT'; }
       elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
       elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
       else  {$result = "ERROR: Unknown Result:$result:$@:";}
   
       &LONCAPA_INTERNAL_DEBUG("RetError $reterror: Answer $answer: Response $response:  type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|");
       &LONCAPA_INTERNAL_DEBUG(" $answer $response $result ");
       return ($result,$reterror)
 }  }
   
   
 sub caparesponse_check_list {  sub caparesponse_check_list {
   my ($response,$expr)=@_;      my $responses=$LONCAPA::CAPAresponse_args{'response'};
   my $result='';  #    &LONCAPA_INTERNAL_DEBUG(" answer is ".
   my $current_answer;  #    &LONCAPA_INTERNAL_Dumper($LONCAPA::CAPAresponse_answer).":\n");
   my $answer = eval $expr.';return $answer';  #    &LONCAPA_INTERNAL_DEBUG(" respons is ".
   my (@list) = eval $answer;  #    &LONCAPA_INTERNAL_Dumper($responses).":\n");
   my (@responselist)=split /,/,$response;      &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
   ($responselist['-1'],my $unit)= split /\s/, $responselist['-1'], 2;      my $type = $LONCAPA::CAPAresponse_args{'type'};
   $unit=~s/\s//;      &LONCAPA_INTERNAL_DEBUG("Got type :$type:\n");
   my $i=0;      
   my $awards='';      my $num_input_lines =
   for ($i=0; $i<@list;$i++) {   scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
     $result.=&caparesponse_check($responselist[$i]." $unit",      
  $expr.';my $answer='.$list[$i].';');      if ($type ne '' ) {
     my ($temp)=split /:/, $result;   if (scalar(@$responses) < $num_input_lines) {
     $awards.="$temp,";      return 'MISSING_ANSWER';
   }   }
   chop $awards;   if (scalar(@$responses) > $num_input_lines) {
   return "$awards:$result";      return 'EXTRA_ANSWER';
    }
   
       }
   
       foreach my $which (0..($num_input_lines-1)) {
    my $answer_size = 
       scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
    if ($type ne '' 
       && $answer_size > 1) {
       $responses->[$which]=[split(/,/,$responses->[$which])];
    } else {
       $responses->[$which]=[$responses->[$which]];
    }
       }
   #    &LONCAPA_INTERNAL_DEBUG(" parsed response is ".
   #    &LONCAPA_INTERNAL_Dumper($responses).":\n");
       foreach my $which (0..($num_input_lines-1)) {
    my $answer_size = 
       scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}[$which]});
    my $response_size = 
       scalar(@{$responses->[$which]});
    if ($answer_size > $response_size) {
       return 'MISSING_ANSWER';
    }
    if ($answer_size < $response_size) {
       return 'EXTRA_ANSWER';
    }
       }
   
       &LONCAPA_INTERNAL_DEBUG("Initial final response :$responses->[0][-1]:");
       my $unit;
       if ($type eq '' || $type eq 'float') {
    #for numerical problems split off the unit
    if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
       $responses->[0][-1]=$1;
       $unit=$2;
    }
       }
       &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
       $unit=~s/\s//;
       if ($unit ne '') {
    foreach my $response (@$responses) {
       foreach my $element (@$response) {    
    $element .= " $unit";
       }
    }
       }
       
       foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
    if (!defined($thisanswer)) {
       return ('ERROR','answer was undefined');
    }
       }
   
   
   #    &LONCAPA_INTERNAL_DEBUG(&LONCAPA_INTERNAL_Dumper($responses));
       my %memoized;
       if ($LONCAPA::CAPAresponse_answer->{'type'}  eq 'ordered') {
    for (my $i=0; $i<scalar(@$responses);$i++) {
       my $answer   = $LONCAPA::CAPAresponse_answer->{'answers'}[$i];
       my $response = $responses->[$i];
       my $key = "$answer\0$response";
       my (@awards,@msgs);
       for (my $j=0; $j<scalar(@$response); $j++) { 
    my ($award,$msg) = &caparesponse_check($answer->[$j],
          $response->[$j]);
    push(@awards,$award);
    push(@msgs,  $msg);
       }
       my ($award,$msg) = 
    &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
       $memoized{$key} = [$award,$msg];
    }
       } else {
    #FIXME broken with unorder responses where one is a <value>
           #      and the other is a <vector> (need to delay parse til
           #      inside the loop?)
    foreach my $response (@$responses) {
       my $response_size = scalar(@{$response});
       foreach my $answer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
    my $key = "$answer\0$response";
    my $answer_size =  scalar(@{$answer});
    my ($award,$msg);
    if ($answer_size > $response_size) {
       $award = 'MISSING_ANSWER';
    } elsif ($answer_size < $response_size) {
       $award = 'EXTRA_ANSWER';
    } else {
       my (@awards,@msgs);
       for (my $j=0; $j<scalar(@$response); $j++) {
    my ($award,$msg) = &caparesponse_check($answer->[$j],
          $response->[$j]);
    push(@awards,$award);
    push(@msgs,  $msg);
       }
       ($award,$msg) = 
    &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
    }
    $memoized{$key} = [$award,$msg];
       }
    }
       }
   
       my ($final_award,$final_msg);
       &init_permutation(scalar(@$responses),
         $LONCAPA::CAPAresponse_answer->{'type'});
   
       # possible FIXMEs
       # - significant time is spent calling non-safe space routine
       #   from safe space
       # - early outs could be possible with classifying awards is to stratas
       #   and stopping as so as hitting the top strata 
       # - some early outs also might be possible with check ing the 
       #   memoized hash of results (is correct even possible? etc.)
   
       my (@final_awards,@final_msg);
       while( &get_permutations_left() ) {
    my $order = &get_next_permutation();
    my (@awards, @msgs, $i);
    foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
       my $key = "$thisanswer\0".$responses->[$order->[$i]];
       push(@awards,$memoized{$key}[0]);
       push(@msgs,$memoized{$key}[1]);
       $i++;
   
    }
    &LONCAPA_INTERNAL_DEBUG(" all awards ".join(':',@awards));
   
    my ($possible_award,$possible_msg) = 
       &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
    &LONCAPA_INTERNAL_DEBUG(" pos awards ".$possible_award);
    push(@final_awards,$possible_award);
    push(@final_msg,$possible_msg);
       }
   
       &LONCAPA_INTERNAL_DEBUG(" all final_awards ".join(':',@final_awards));
       my ($final_award,$final_msg) = 
    &LONCAPA_INTERNAL_FINALIZEAWARDS(\@final_awards,\@final_msg,undef,1);
       return ($final_award,$final_msg);
   }
   
   sub cas {
       my ($system,$input)=@_;
       my $output;
       if ($system eq 'maxima') {
          $output=&maxima_eval($input);
       }
       return $output;
 }  }
   
 sub tex {  sub tex {
   if ( $external::target eq "tex" ) {      if ( $external::target eq "tex" ) {
     return @_[0];   return $_[0];
   } else {      } else {
     return @_[1];   return $_[1];
   }      }
   }
   
   sub var_in_tex {
       if ( $external::target eq "tex" ) {
    return $_[0];
       } else {
    return "";
       }
 }  }
   
 sub web {  sub web {
   if ( $external::target eq "tex" ) {      if ( $external::target eq "tex" ) {
     return @_[1];   return $_[1];
   } else {  
     if ( $external::target eq "web") {  
       return @_[0];  
     } else {      } else {
       return @_[2];   if ( $external::target eq "web" || $external::target eq "answer") {
       return $_[2];
    } else {
       return $_[0];
    }
     }      }
   }  
 }  }
   
 sub problem {  sub html {
   return '1';      if ( $external::target eq "web" ) {
    return shift;
       }
 }  }
   
 sub hinton {  sub hinton {
   return 0;      return 0;
 }  }
   
 sub random {  sub random {
   my ($start,$end,$step)=@_;      my ($start,$end,$step)=@_;
   if ( ! $RANDOMINIT ) { srand($external::randomseed); $RANDOMINIT=1; }      if ( ! $hidden::RANDOMINIT ) {
   my $num=1+int(($end-$start)/$step);   if ($external::randomseed == 0) { $external::randomseed=1; }
   my $result=$start + int(rand() * $num)*$step;   if ($external::randomseed =~/,/) {
   return $result;      my ($num1,$num2)=split(/,/,$external::randomseed);
       &random_set_seed(1,abs($num1));
    } elsif ($external::randomseed =~/:/) {
       my ($num1,$num2)=split(/:/,$external::randomseed);
       &random_set_seed(abs($num1),abs($num2));
    } else {
       &random_set_seed(1,int(abs($external::randomseed)));
    }
    &math_random_uniform();
    $hidden::RANDOMINIT=1;
       }
       if (!defined($step)) { $step=1; }
       my $num=1+int(($end-$start)/$step);
       my $result=$start + int(&math_random_uniform() * $num)*$step;
       return $result;
   }
   
   sub random_normal {
       my ($item_cnt,$seed,$av,$std_dev) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_normal($item_cnt,$av,$std_dev);
       &random_set_seed(@oldseed);
       return @retArray;
 }  }
   
 sub tan  { sin($_[0]) / cos($_[0]) }  sub random_beta {
 sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }      my ($item_cnt,$seed,$aa,$bb) = @_;
 sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }      my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_beta($item_cnt,$aa,$bb);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
 sub html {  sub random_gamma {
   if ( $external::target eq "web" ) {      my ($item_cnt,$seed,$a,$r) = @_;
     return @_[0];      my @oldseed=&random_get_seed();
   }      my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_gamma($item_cnt,$a,$r);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_exponential {
       my ($item_cnt,$seed,$av) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_exponential($item_cnt,$av);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_poisson {
       my ($item_cnt,$seed,$mu) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_poisson($item_cnt,$mu);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_chi {
       my ($item_cnt,$seed,$df) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_chi_square($item_cnt,$df);
       &random_set_seed(@oldseed);
       return @retArray;
 }  }
   
   sub random_noncentral_chi {
       my ($item_cnt,$seed,$df,$nonc) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_noncentral_chi_square($item_cnt,$df,$nonc);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_f {
       my ($item_cnt,$seed,$dfn,$dfd) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_f($item_cnt,$dfn,$dfd);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_noncentral_f {
       my ($item_cnt,$seed,$dfn,$dfd,$nonc) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_noncentral_f($item_cnt,$dfn,$dfd,$nonc);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_multivariate_normal {
       my ($item_cnt,$seed,$mean,$covar) = @_;
       my @oldseed=&random_get_seed();
       &random_set_seed_from_phrase($seed);
       my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_multinomial {
       my ($item_cnt,$seed,@p) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       my @retArray=&math_random_multinomial($item_cnt,@p);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_permutation {
       my ($seed,@inArray) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_permutation(@inArray);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_uniform {
       my ($item_cnt,$seed,$low,$high) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_uniform($item_cnt,$low,$high);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_uniform_integer {
       my ($item_cnt,$seed,$low,$high) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_uniform_integer($item_cnt,$low,$high);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_binomial {
       my ($item_cnt,$seed,$nt,$p) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_binomial($item_cnt,$nt,$p);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub random_negative_binomial {
       my ($item_cnt,$seed,$ne,$p) = @_;
       my @oldseed=&random_get_seed();
       my @retArray;
       &random_set_seed_from_phrase($seed);
       @retArray=&math_random_negative_binomial($item_cnt,$ne,$p);
       &random_set_seed(@oldseed);
       return @retArray;
   }
   
   sub abs { CORE::abs(shift) }
   sub sin { CORE::sin(shift) }
   sub cos { CORE::cos(shift) }
   sub exp { CORE::exp(shift) }
   sub int { CORE::int(shift) }
   sub log { CORE::log(shift) }
   sub atan2 { CORE::atan2($_[0],$_[1]) }
   sub sqrt { CORE::sqrt(shift) }
   
   sub tan  { CORE::sin($_[0]) / CORE::cos($_[0]) }
   #sub atan { atan2($_[0], 1); }
   #sub acos { atan2(sqrt(1 - $_[0] * $_[0]), $_[0] ); }
   #sub asin { atan2($_[0], sqrt(1- $_[0] * $_[0]) );  }
   
   sub log10 { CORE::log($_[0])/CORE::log(10); }
   
   sub factorial {
       my $input = CORE::int(shift);
       return "Error - unable to take factorial of an negative number ($input)" if $input < 0;
       return "Error - factorial result is greater than system limit ($input)" if $input > 170;
       return 1 if $input == 0;
       my $result = 1; 
       for (my $i=2; $i<=$input; $i++) { $result *= $i }
       return $result;
   }
   
   sub sgn {
       return -1 if $_[0] < 0;
       return 0 if $_[0] == 0;
       return 1 if $_[0] > 0;
   }
   
   sub min {
       my @sorted = sort { $a <=> $b || $a cmp $b } @_;
       return shift @sorted;
   }
   
   sub max {
       my @sorted = sort { $a <=> $b || $a cmp $b } @_;
       return pop @sorted;
   }
   
   sub roundto {
       my ($input,$n) = @_;
       return sprintf('%.'.$n.'f',$input);
   }
   
   sub to_string {
       my ($input,$n) = @_;
       return sprintf($input) if $n eq "";
       $n = '.'.$n if $n !~ /^\./;
       return sprintf('%'.$n,$input) if $n ne "";
   }
   
   sub sub_string {
       my ($str,$start,$len) = @_;
       return substr($str,$start-1,$len);
   }
   
 sub pow   {return $_[0] ** $_[1]; }  sub pow   {return $_[0] ** $_[1]; }
 sub ceil  {return (($_[0]-int($_[0]))== 0.0) ? $_[0] : (int($_[0])+ 1); }  sub ceil  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? (CORE::int($_[0])+ 1) : CORE::int($_[0])); }
 sub floor {return int($_[0]);  }  sub floor  {return (($_[0]-CORE::int($_[0]))== 0.0) ? $_[0] : (($_[0] > 0) ? CORE::int($_[0]) : (CORE::int($_[0])-1)); }
   #sub floor {return int($_[0]); }
   
 sub format {  sub format {
   my ($value,$fmt)=@_;      my ($value,$fmt)=@_;
   return sprintf('%.'.$fmt,$value);      my ($dollarmode,$commamode,$alwaysperiod,$options);
       if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
       #if ($options =~ /\$/) { $dollamode=1; }
       #if ($options =~ /,/)  { $commamode=1; }
       if ($options =~ /\./) { $alwaysperiod=1; }
       my $result;
       if ($fmt=~/s$/i) {
    $result=&format_significant_figures($value,$fmt);
       } else {
    $fmt=~s/e/E/g;
    $result=sprintf('%.'.$fmt,$value);
    if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
    $result=~s/(E[+-]*)0/$1/;
       }
       #if ($dollarmode) {$result=&dollarformat($result);}
       #if ($commamode) {$result=&commaformat($result);}
       return $result;
   }
   
   sub chemparse {
       my ($reaction) = @_;
       my @tokens = split(/(\s\+|\->|<=>|<\-|\.)/,$reaction);
       my $formula = '';
       foreach my $token (@tokens) {
    if ($token eq '->' ) {
       $formula .= '<m>\ensuremath{\rightarrow}</m> ';
       next;
    }
    if ($token eq '<-' ) {
       $formula .= '<m>\ensuremath{\leftarrow}</m> ';
       next;
    }  
    if ($token eq '<=>') {
       if ($external::target eq 'web' &&
    &EXT('request.browser.unicode')) {
    $formula .= '&#8652; ';
       } else {
    $formula .= &web('<=> ','<m>\ensuremath{\rightleftharpoons}</m> ',
    '&lt;=&gt; ');
       }
       next;
    }
    if ($token eq '.') {
     $formula =~ s/(\&nbsp\;| )$//;
     $formula .= '&middot;';
     next;
    }
    $token =~ /^\s*([\d|\/]*(?:&frac\d\d)?)(.*)/;
           $formula .= $1 if ($1 ne '1');  # stoichiometric coefficient
   
    my $molecule = $2;
    # subscripts
    $molecule =~ s|(?<=[a-zA-Z\)\]\s])(\d+)|<sub>$1</sub>|g;
    # superscripts
    $molecule =~ s|\^(\d*[+\-]*)|<sup>$1</sup>|g;
    # strip whitespace
    $molecule =~ s/\s*//g;
    # forced space
    $molecule =~ s/_/ /g;
    $molecule =~ s/-/&minus;/g;
    $formula .= $molecule.'&nbsp;';
       }
       # get rid of trailing space
       $formula =~ s/(\&nbsp\;| )$//;
       return &xmlparse($formula);
   }
   
   sub prettyprint {
       my ($value,$fmt,$target)=@_;
       my $result;
       if (!$target) { $target = $external::target; }
       if ($fmt =~ /chem/i) { return(&chemparse($value)); }
       my ($dollarmode,$commamode,$alwaysperiod,$options);
       if ($fmt =~ /^([^\d]*)(.*)/) { $options=$1; $fmt=$2; } 
       if ($options =~ /\$/) { $dollarmode=1; }
       if ($options =~ /,/)  { $commamode=1; }
       if ($options =~ /\./) { $alwaysperiod=1; }
       if ($fmt=~/s$/i) {
    $value=&format_significant_figures($value,$fmt);
       } elsif ($fmt) {
    $value=sprintf('%.'.$fmt,$value);
       }
       if ($alwaysperiod && $fmt eq '0f') {
    if ($target eq 'tex') {
       $value .='\\ensuremath{.}';
    } else {
       $value .='.';
    }
       }
       if ($value =~ /([0-9\.\-\+]+)E([0-9\-\+]+)/i ) {
    my $frac=$1;
    if ($dollarmode) { $frac=&dollarformat($frac); }
    if ($commamode) { $frac=&commaformat($frac); }
    my $exponent=$2;
    $exponent=~s/^\+0*//;
    $exponent=~s/^-0*/-/;
    $exponent=~s/^-0*/-/;
    if ($exponent eq '-') { undef($exponent); }
    if ($exponent) {
       if ($target eq 'web') {
    $result=$frac.'&#215;10<sup>'.$exponent.'</sup>';
       } elsif ($target eq 'tex') {
    $result='\ensuremath{'.$frac.'\times 10^{'.$exponent.'}}';
       } else {
    $result=$value;
       }
    } else {
       $result=$frac;
    }
       } else {
    $result=$value;
    if    ($dollarmode) { $result=&dollarformat($result,$target); }
    elsif ($commamode)  { $result=&commaformat($result,$target); }
       }
       return $result;
   }
   
   sub commaformat {
       my ($number,$target) = @_;
       if ($number =~ /\./) {
    while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
       $number = $1.$2.','.$3.$4;
    }
       } else {
    while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
       $number = $1.$2.','.$3.$4;
    }
       }
       return $number;
   }
   
   sub dollarformat {
       my ($number,$target) = @_;
       if (!$target) { $target = $external::target; }
       $number=&commaformat($number,$target);
       if ($target eq 'tex') {
    $number='\$'.$number; #' stupid emacs
       } else {
    $number='$'.$number; #' stupid emacs
       }
       return $number; 
   }
   
   # format of form ns or nS where n is an integer
   sub format_significant_figures {
       my ($number,$format) = @_; 
       return '0' if ($number == 0);
       # extract number of significant figures needed
       my ($sig) = ($format =~ /(\d+)s/i);
       # arbitrary choice - suggestions ?? or throw error message?
       $sig = 3 if ($sig eq '');
       # save the minus sign
       my $sign = ($number < 0) ? '-' : '';
       $number = abs($number);
       # needed to correct for a number greater than 1 (or
       my $power = ($number < 1) ? 0 : 1;
       # could round up. Take the integer part of log10.
       my $x10 = int(log($number)/log(10));
       # find number with values left of decimal pt = # of sign figs.
       my $xsig = $number*10**($sig-$x10-$power);
       # get just digits left of decimal pt - also rounds off correctly
       my $xint  = sprintf('%.0f',$xsig);
       # save any trailing zero's
       my ($zeros) = ($xint =~ /(0+)$/);
       # return number to original magnitude
       my $numSig = $xint*10**($x10-$sig+$power);
       # insert trailing zero's if have decimal point
       $numSig =~ s/^(\d+)\.(\d+)(\e?(.*)?)$/$1\.$2$zeros$3/;
       # put a decimal pt for number ending with 0 and length = # of sig fig
       $numSig.='.' if (length($numSig) == $sig && $numSig =~ /0$/);
       if (length($numSig) < $sig) {
    $numSig.='.'.substr($zeros,0,($sig-length($numSig)));
       }
       # return number with sign
       return $sign.$numSig;
   
 }  }
   
 sub map {  sub map {
   my $num = $#_/2;      my ($phrase,$dest,$source)=@_;
   my $i;      my @oldseed=&random_get_seed();
   my @used;      my @seed = &random_seed_from_phrase($phrase);
   my @permutation;      &random_set_seed(@seed);
   for ($i=0; $i < $num;) {      my $destct = scalar(@$dest);
     $rand = &random(1,$num,1);      if (!$source) {
     if ( $used[$rand] == '0' ) {   my @output;
       $i++;   my @idx = &math_random_permuted_index($destct);
       $used[$rand]='1';   my $ctr = 0;
       $permutation[$i]=$rand;   while ($ctr < $destct) {
     }      $output[$ctr] = $$dest[$idx[$ctr]];
   }      $ctr++;
   for ( $i=1 ; $i<$num+1 ; $i++ ) {   }
     ${$_[$permutation[$i]]}=$_[$i+$num]          &random_set_seed(@oldseed);
   }   return @output;
       } else {
    my $num = scalar(@$source);
    my @idx = &math_random_permuted_index($num);
    my $ctr = 0;
    my $tot = $num;
    $tot = $destct if $destct < $num;
    if (ref($$dest[0])) {
       while ($ctr < $tot) {
    ${$$dest[$ctr]} = $$source[$idx[$ctr]];
           $ctr++;
               }
           } else {
       while ($ctr < $tot) {
    $$dest[$ctr] = $$source[$idx[$ctr]];
    $ctr++;
       }
    }
       }
       &random_set_seed(@oldseed);
       return '';
   }
   
   sub rmap {
       my ($phrase,$dest,$source)=@_;
       my @oldseed=&random_get_seed();
       my @seed = &random_seed_from_phrase($phrase);
       &random_set_seed(@seed);
       my $destct = scalar(@$dest);
       if (!$source) {
    my @idx = &math_random_permuted_index($destct);
    my $ctr = 0;
    my @r_idx;
    while ($ctr < $destct) {
       $r_idx[$idx[$ctr]] = $ctr;
       $ctr++;
    }
    my @output;
    $ctr = 0;
    while ($ctr < $destct) {
       $output[$ctr] = $$dest[$r_idx[$ctr]];
       $ctr++;
    }
           &random_set_seed(@oldseed);
    return @output;
       } else {
    my $num = scalar(@$source);
    my @idx = &math_random_permuted_index($num);
    my $ctr = 0;
    my $tot = $num;
    $tot = $destct if $destct < $num;
    my @r_idx;
    while ($ctr < $tot) {
       $r_idx[$idx[$ctr]] = $ctr;
       $ctr++;
    }
    $ctr = 0;
    if (ref($$dest[0])) {
       while ($ctr < $tot) {
    ${$$dest[$ctr]} = $$source[$r_idx[$ctr]];
           $ctr++;
               }
           } else {
       while ($ctr < $tot) {
    $$dest[$ctr] = $$source[$r_idx[$ctr]];
    $ctr++;
       }
    }
       }
       &random_set_seed(@oldseed);
       return '';
   }
   
   sub capa_id { return }
   
   sub problem { return }
   
   sub name{
       my $fullname = &EXT('environment.lastname').', '.&EXT('environment.firstname').' '.&EXT('environment.middlename');
       $fullname = "" if $fullname eq ",  ";
       $fullname =~ s/\%2d/-/g;
       return $fullname;
   }
   
   sub student_number { 
       my $id = &EXT('environment.id');
       $id = '' if $id eq "";
       return $id;
   }
   
   sub class {
       my $course = &EXT('course.description');
       $course = '' if $course eq "";
       return $course;
   }
   
   sub firstname {
       my $firstname = &EXT('environment.firstname');
       $firstname = '' if $firstname eq "";
       return $firstname;
   }
                                                                                   
   sub lastname {
       my $lastname = &EXT('environment.lastname');
       $lastname = '' if $lastname eq "";
       return $lastname;
   }
   
   sub sec { 
       my $sec = &EXT('request.course.sec');
       $sec = '' if $sec eq "";
       return $sec;
   }
   
   sub open_date { 
       my @dc = split(/\s+/,localtime(&EXT('resource.0.opendate')));
       return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
       my @hm = split(/:/,$dc[3]);
       my $ampm = " am";
       if ($hm[0] > 12) {
    $hm[0]-=12;
    $ampm = " pm";
       }
       return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
   }
   
   sub due_date { 
       my @dc = split(/\s+/,localtime(&EXT('resource.0.duedate')));
       return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
       my @hm = split(/:/,$dc[3]);
       my $ampm = " am";
       if ($hm[0] > 12) {
    $hm[0]-=12;
    $ampm = " pm";
       }
       return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
   }
   
   sub answer_date { 
       my @dc = split(/\s+/,localtime(&EXT('resource.0.answerdate')));
       return '' if ($dc[0] eq "Wed" and $dc[2] == 31 and $dc[4] == 1969);
       my @hm = split(/:/,$dc[3]);
       my $ampm = " am";
       if ($hm[0] > 12) {
    $hm[0]-=12;
    $ampm = " pm";
       }
       return $dc[0].', '.$dc[1].' '.$dc[2].', '.$dc[4].' at '.$hm[0].':'.$hm[1].$ampm;
   }
   
   sub array_moments {
       my @input=@_;
       my (@output,$N);
       $N=scalar (@input);
       $output[0]=$N;
       if ($N <= 1) {
    $output[1]=$input[0];
    $output[1]="Input array not defined" if ($N == 0);
    $output[2]="variance undefined for N<=1";
    $output[3]="skewness undefined for N<=1";
    $output[4]="kurtosis undefined for N<=1";
    return @output;
       }
       my $sum=0;
       foreach my $line (@input) {
    $sum+=$line;
       }
       $output[1] = $sum/$N;
       my ($x,$sdev,$var,$skew,$kurt) = 0;
       foreach my $line (@input) {
    $x=$line-$output[1];
    $var+=$x**2;
    $skew+=$x**3;
    $kurt+=$x**4;
       }
       $output[2]=$var/($N-1);
       $sdev=CORE::sqrt($output[2]);
       if ($sdev == 0) {
    $output[3]="inf-variance=0";
    $output[4]="inf-variance=0";
    return @output;
       }
       $output[3]=$skew/($sdev**3*$N);
       $output[4]=$kurt/($sdev**4*$N)-3;
       return @output;
 }  }
   
 sub choose {  sub choose {
   my $num = $_[0];      my $num = $_[0];
   return $_[$num];      return $_[$num];
   }
   
   #&sum1(1,$x,sub { &sum1($_[0],2*$_[0], sub { fact($_[0])**2 })});
   #sub sum1 {
   #    my ($start,$end,$sub)=@_;
   #    my $sum=0;
   #    for (my $i=$start;$i<=$end;$i++) {
   #        $sum+=&$sub($i);
   #    }
   #    return $sum
   #}
   
   #&sum2('a',1,$x,'&sum2(\'b\',$a,2*$a, \'&factorial($b)**2\')');
   #sub sum2 {
   #    my ($varname,$start,$end,$line)=@_;
   #    my $sum=0;
   #    for (my $i=$start;$i<=$end;$i++) {
   # my $func=sub {
   #    eval("\$".$varname."=$i");
   #    eval($line);
   # };
   #        $sum+=&$func($i);
   #    }
   #    return $sum
   #}
   
   # expiremental idea
   sub proper_path {
       my ($path)=@_;
       if ( $external::target eq "tex" ) {
    return '/home/httpd/html'.$path;
       } else {
    return $path;
       }
 }  }
 #$external::randomseed=time;  
 #$a=2;  
 #$b=2;  
 #$c=2;  
 #&map(1,\$a,\$b,\$c,3,4,5);  
 #print $a."\n".$b."\n";  
Removed from v.1.14  
changed lines
  Added in v.1.125

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