--- loncom/homework/default_homework.lcpm	2005/02/17 21:42:37	1.92
+++ loncom/homework/default_homework.lcpm	2006/11/10 17:45:52	1.120
@@ -1,7 +1,7 @@
 # The LearningOnline Network with CAPA 
 # used by lonxml::xmlparse() as input variable $safeinit to Apache::run::run()
 #
-# $Id: default_homework.lcpm,v 1.92 2005/02/17 21:42:37 albertel Exp $
+# $Id: default_homework.lcpm,v 1.120 2006/11/10 17:45:52 albertel Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -33,6 +33,72 @@ $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)=@_;
@@ -60,6 +126,7 @@ sub check_commas {
     return 1;
 }
 
+
 sub caparesponse_check {
     my ($answer,$response)=@_;
     #not properly used yet: calc
@@ -78,25 +145,28 @@ sub caparesponse_check {
 
 
     #type's definitons come from capaParser.h
-    my $message='';
+
     #remove leading and trailing whitespace
     if (!defined($response)) {
 	$response='';
     }
     if ($response=~ /^\s|\s$/) {
 	$response=~ s:^\s+|\s+$::g;
-	$message .="Removed ws now :$response:\n";
-    } else {
-	$message .="no ws in :$response:\n";
+	&LONCAPA_INTERNAL_DEBUG("Removed ws now :$response:");
     }
-    if ($type eq 'cs' || $type eq 'ci' || $type eq 'mc') {
+
+    #&LONCAPA_INTERNAL_DEBUG(" type is $type ");
+    if ($type eq 'cs' || $type eq 'ci') {
 	#for string answers make surec all places spaces occur, there is 
         #really only 1 space, in both the answer and the response
 	$answer=~s/ +/ /g;
 	$response=~s/ +/ /g;
+    } elsif ($type eq 'mc') {
+	$answer=~s/[\s,]//g;
+	$response=~s/[\s,]//g;
     }
     if ($type eq 'float' && $unit=~/\$/) {
-	if ($response!~/^\$/)  { return "NO_UNIT: Missing \$ "; }
+	if ($response!~/^\$/)  { return ('NO_UNIT', undef); }
 	$response=~s/\$//g;
     }
     if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
@@ -106,21 +176,22 @@ sub caparesponse_check {
     $unit=~s/[\$,]//g;
     if ($type eq 'float') { $response=~s/,//g; }
 
-    if (length($response) > 500) { return "TOO_LONG: Answer too long"; }
+    if (length($response) > 500) { return ('TOO_LONG',undef); }
 
     if ($type eq '' ) {
-	$message .= "Didn't find a type :$type: defaulting\n";
+	&LONCAPA_INTERNAL_DEBUG("Didn't find a type :$type: defaulting");
 	if ( $answer eq ($answer *1.0)) { $type = 2;
 				      } else { $type = 3; }
     } else {
-	if ($type eq 'cs')    { $type = 4; }
+	if    ($type eq 'cs')    { $type = 4; }
 	elsif ($type eq 'ci')    { $type = 3 }
 	elsif ($type eq 'mc')    { $type = 5; }
 	elsif ($type eq 'fml')   { $type = 8; }
+        elsif ($type eq 'math')  { $type = 9; }
 	elsif ($type eq 'subj')  { $type = 7; }
 	elsif ($type eq 'float') { $type = 2; }
 	elsif ($type eq 'int')   { $type = 1; }
-	else { return "ERROR: Unknown type of answer: $type" }
+	else { return ('ERROR', "Unknown type of answer: $type") }
     }
 
     my $points;
@@ -128,7 +199,7 @@ sub caparesponse_check {
     #formula type setup the sample points
     if ($type eq '8') {
 	($id_list,$points)=split(/@/,$samples);
-	$message.="Found :$id_list:$points: points in $samples\n";
+	&LONCAPA_INTERNAL_DEBUG("Found :$id_list:$points: points in $samples");
     }
     if ($tol eq '') {
 	$tol=0.0;
@@ -145,13 +216,21 @@ sub caparesponse_check {
     ($sig_ubound,$sig_lbound)=&LONCAPA_INTERNAL_get_sigrange($sig);
 
     my $reterror="";
-    my $result = &caparesponse_capa_check_answer($response,$answer,$type,
+    my $result;
+    if ($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') { $result='SIG_FAIL'; }
@@ -163,6 +242,8 @@ sub caparesponse_check {
     elsif ($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') { $result='UNIT_INVALID_STUDENT'; }
@@ -170,60 +251,204 @@ sub caparesponse_check {
     elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
     else  {$result = "ERROR: Unknown Result:$result:$@:";}
 
-    return ("$result:\nRetError $reterror:\nAnswer $answer:\nResponse $response:\n type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|\n$message",$reterror);
+    &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,$reterror)
+}
+
+sub maxima_cas_formula_fix {
+   my ($expression)=@_;
+   return &implicit_multiplication($expression);
+}
+
+sub capa_formula_fix {
+   my ($expression)=@_;
+   return &implicit_multiplication($expression);
+}
+
+sub implicit_multiplication {
+    my ($expression)=@_;
+# Escape scientific notation, so 3e8 does not become 3*e*8
+# 3e8 -> 3&8; 3e-8 -> 3&-8; 3E+8 -> e&+8
+    $expression=~s/(\d+)e([\+\-]*\d+)/$1\&\($2\)/gsi;
+# 3x10^8 -> 3&8; 3*10^-8 -> 3&-8
+    $expression=~s/(\d+)(?:x|\*)10(?:\^|\*\*)([\+\-]*\d+)/$1\&\($2\)/gsi;
+# Fill in multiplication signs
+# a b -> a*b;3 b -> 3*b;3 4 -> 3*4
+    $expression=~s/(\w)\s+(\w)/$1\*$2/gs;
+# )( -> )*(; ) ( -> )*(
+    $expression=~s/\)\s*\(/\)\*\(/gs;
+# 3a -> 3*a; 3( -> 3*(; 3 ( -> 3*(; 3A -> 3*A
+    $expression=~s/(\d)\s*([a-zA-Z\(])/$1\*$2/gs;
+# a ( -> a*(
+    $expression=~s/(\w)\s+\(/$1\*\(/gs;
+# a3 -> a*3;
+    $expression=~s/([a-zA-Z])(\d)/$1\*$2/gs;
+# )a -> )*a; )3 -> )*3; ) 3 -> )*3
+    $expression=~s/\)\s*(\w)/\)\*$1/gs;
+# 3&8 -> 3e8; 3&-4 -> 3e-4
+    $expression=~s/(\d+)\&\(([\+\-]*\d+)\)/$1e$2/gs;
+    return $expression;
 }
 
-
 sub caparesponse_check_list {
-    my $response=$LONCAPA::CAPAresponse_args{'response'};
-    my ($result,@list);
-    @list=@LONCAPA::CAPAresponse_answer;
-    my $aresult='';
-    my $current_answer;
-    my $answers=join(':',@list);
-    $result.="Got response :$answers:\n";
-    &LONCAPA_INTERNAL_DEBUG("<blink>Yo!</blink> got ".join(':',%LONCAPA::CAPAresponse_args));
-    my @responselist;
+    my $responses=$LONCAPA::CAPAresponse_args{'response'};
+    &LONCAPA_INTERNAL_DEBUG(" answer is ".
+			    &LONCAPA_INTERNAL_Dumper($LONCAPA::CAPAresponse_answer).":\n");
+    &LONCAPA_INTERNAL_DEBUG(" respons is ".
+			    &LONCAPA_INTERNAL_Dumper($responses).":\n");
+    &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
     my $type = $LONCAPA::CAPAresponse_args{'type'};
-    $result.="Got type :$type:\n";
-    if ($type ne '' && $#list > 0) {
-	(@responselist)=split /,/,$response;
-    } else {
-	(@responselist)=($response);
+    &LONCAPA_INTERNAL_DEBUG("Got type :$type:\n");
+    
+    my $num_input_lines =
+	scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
+    
+    if ($type ne '' ) {
+	if (scalar(@$responses) < $num_input_lines) {
+	    return 'MISSING_ANSWER';
+	}
+	if (scalar(@$responses) > $num_input_lines) {
+	    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';
+	}
     }
-    my $unit='';
-    $result.="Initial final response :$responselist['-1']:\n";
+
+    &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 ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
-	    $responselist['-1']=$1;
+	if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
+	    $responses->[0][-1]=$1;
 	    $unit=$2;
 	}
     }
-    $result.="Final final response :$responselist['-1']:$unit:\n";
-    $result.=":$#list: answers\n";
+    &LONCAPA_INTERNAL_DEBUG("Final final response :$responses->[0][-1]:$unit:");
     $unit=~s/\s//;
-    my $i=0;
-    my $awards='';
-    my @msgs;
-    for ($i=0; $i<@list;$i++) {
-	my $msg;
-	$result.="trying answer :$list[$i]:\n";
-	my $thisanswer=$list[$i];
-	$result.="trying answer :$thisanswer:\n";
-	if ($unit eq '') {
-	    ($aresult,$msg)=&caparesponse_check($thisanswer,$responselist[$i]);
-	} else {
-	    ($aresult,$msg)=&caparesponse_check($thisanswer,
-						$responselist[$i]." $unit");
+    if ($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 ($temp)=split /:/, $aresult;
-	$awards.="$temp,";
-	$result.=$aresult;
-	push(@msgs,$msg);
     }
-    chop $awards;
-    return ("$awards:\n$result",@msgs);
+
+    my ($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 tex {
@@ -445,14 +670,14 @@ sub random_negative_binomial {
     return @retArray;
 }
 
-sub abs { abs(shift) }
-sub sin { sin(shift) }
-sub cos { cos(shift) }
-sub exp { exp(shift) }
-sub int { int(shift) }
-sub log { log(shift) }
-sub atan2 { atan2($_[0],$_[1]) }
-sub sqrt { sqrt(shift) }
+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($_[0], 1); }
@@ -516,10 +741,15 @@ sub format {
     #if ($options =~ /\$/) { $dollamode=1; }
     #if ($options =~ /,/)  { $commamode=1; }
     if ($options =~ /\./) { $alwaysperiod=1; }
-    $fmt=~s/e/E/g;
-    my $result=sprintf('%.'.$fmt,$value);
-    if ($alwaysperiod && $fmt eq '0f') { $result .='.'; }
-    $result=~s/(E[+-]*)0/$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;
@@ -527,24 +757,33 @@ sub format {
 
 sub chemparse {
     my ($reaction) = @_;
-    my @tokens = split(/(\s\+|\->|<=>)/,$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; ');
+				 '&lt;=&gt; ');
 	    }
 	    next;
 	}
-	$token =~ /^\s*(\d*(?:&frac\d\d)?)(.*)/;
+	if ($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;
@@ -556,11 +795,11 @@ sub chemparse {
 	$molecule =~ s/\s*//g;
 	# forced space
 	$molecule =~ s/_/ /g;
+	$molecule =~ s/-/&minus;/g;
 	$formula .= $molecule.'&nbsp;';
     }
     # get rid of trailing space
     $formula =~ s/(\&nbsp\;| )$//;
-    if ($external::target eq 'web') { return $formula; }
     return &xmlparse($formula);
 }
 
@@ -574,7 +813,11 @@ sub prettyprint {
     if ($options =~ /\$/) { $dollarmode=1; }
     if ($options =~ /,/)  { $commamode=1; }
     if ($options =~ /\./) { $alwaysperiod=1; }
-    if ($fmt) { $value=sprintf('%.'.$fmt,$value); }
+    if ($fmt=~/s$/i) {
+	$value=&format_significant_figures($value,$fmt);
+    } elsif ($fmt) {
+	$value=sprintf('%.'.$fmt,$value);
+    }
     if ($alwaysperiod && $fmt eq '0f') {
 	if ($target eq 'tex') {
 	    $value .='\\ensuremath{.}';
@@ -613,12 +856,12 @@ sub prettyprint {
 sub commaformat {
     my ($number,$target) = @_;
     if ($number =~ /\./) {
-	while ($number =~ /([^\.,]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
-	    $number = $1.','.$2.$3;
+	while ($number =~ /([^0-9]*)([0-9]+)([^\.,][^\.,][^\.,])([,0-9]*\.[0-9]*)$/) {
+	    $number = $1.$2.','.$3.$4;
 	}
     } else {
-	while ($number =~ /([^,]+)([^,][^,][^,])([,0-9]*)$/) {
-	    $number = $1.','.$2.$3;
+	while ($number =~ /^([^0-9]*)([0-9]+)([^,][^,][^,])([,0-9]*)$/) {
+	    $number = $1.$2.','.$3.$4;
 	}
     }
     return $number;
@@ -636,6 +879,41 @@ sub dollarformat {
     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 {
     my ($phrase,$dest,$source)=@_;
     my @oldseed=&random_get_seed();
@@ -747,6 +1025,18 @@ sub class {
     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 "";
@@ -831,6 +1121,30 @@ sub choose {
     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)=@_;
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
<html><head>
<title>500 Internal Server Error</title>
</head><body>
<h1>Internal Server Error</h1>
<p>The server encountered an internal error or
misconfiguration and was unable to complete
your request.</p>
<p>Please contact the server administrator at 
 root@localhost to inform them of the time this error occurred,
 and the actions you performed just before this error.</p>
<p>More information about this error may be available
in the server error log.</p>
</body></html>