--- loncom/homework/default_homework.lcpm	2005/07/13 20:44:29	1.101
+++ loncom/homework/default_homework.lcpm	2006/09/29 20:55:33	1.116
@@ -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 1.101 2005/07/13 20:44:29 albertel Exp $
+# $Id: default_homework.lcpm,v 1.116 2006/09/29 20:55:33 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)=@_;
@@ -78,17 +144,16 @@ 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_INTENAL_DEBUG("Removed ws now :$response:");
     }
+
     &LONCAPA_INTERNAL_DEBUG(" type is $type ");
     if ($type eq 'cs' || $type eq 'ci') {
 	#for string answers make surec all places spaces occur, there is 
@@ -113,14 +178,15 @@ sub caparesponse_check {
     if (length($response) > 500) { return "TOO_LONG: Answer too long"; }
 
     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')   { $type = 1; }
@@ -132,7 +198,7 @@ sub caparesponse_check {
     #formula type setup the sample points
     if ($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 '') {
 	$tol=0.0;
@@ -149,13 +215,21 @@ sub caparesponse_check {
     ($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') { $result='SIG_FAIL'; }
@@ -176,29 +250,67 @@ sub caparesponse_check {
     elsif ($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|",$reterror);
+    return ($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 $result="Got response :".join(':',@LONCAPA::CAPAresponse_answer).":\n";
+    &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
     my @responselist;
     my $type = $LONCAPA::CAPAresponse_args{'type'};
-    $result.="Got type :$type:\n";
-    if ($type ne '' && $#list > 0) {
-	(@responselist)=split /,/,$response;
+    &LONCAPA_INTERNAL_DEBUG("Got type :$type:\n");
+    my $num_answers = scalar(@{$LONCAPA::CAPAresponse_answer->{'answers'}});
+    if ($type ne '' 
+	&& $num_answers > 1) {
+	(@responselist)=split(/,/,$response);
+	if (@responselist < $num_answers) {
+	    return 'MISSING_ANSWER';
+	}
+	if (@responselist > $num_answers) {
+	    return 'EXTRA_ANSWER';
+	}
     } else {
 	(@responselist)=($response);
     }
-    my $unit='';
-    $result.="Initial final response :$responselist['-1']:\n";
+    &LONCAPA_INTERNAL_DEBUG("Initial final response :$responselist['-1']:");
+    my $unit;
     if ($type eq '' || $type eq 'float') {
 	#for numerical problems split off the unit
 	if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
@@ -206,30 +318,47 @@ sub caparesponse_check_list {
 	    $unit=$2;
 	}
     }
-    $result.="Final final response :$responselist['-1']:$unit:\n";
-    $result.=":$#list: answers\n";
+    &LONCAPA_INTERNAL_DEBUG("Final final response :$responselist['-1']:$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]);
+
+    #&reset_caparesponse_memoization();
+    my ($final_award,$final_msg);
+    &init_permutation(scalar(@responselist),
+		      $LONCAPA::CAPAresponse_answer->{'type'});
+    while( &get_permutations_left() ) {
+	my @responses_ordered = @responselist[&get_next_permutation()];
+	my (@awards, @msgs, $i);
+	foreach my $thisanswer (@{ $LONCAPA::CAPAresponse_answer->{'answers'} }) {
+	    my ($msg,$aresult);
+	    if (defined($thisanswer)) {
+		my $response = $responses_ordered[$i];
+		if ($unit eq '') {
+		    $response .= " $unit";
+		}
+		($aresult,$msg)=&caparesponse_check($thisanswer,$response);
+	    } else {
+		$aresult='ERROR';
+		$msg='answer was undefined';
+	    }
+	    #&LONCAPA_INTERNAL_DEBUG("after if $aresult -- $msg");
+	    my ($temp)=split(/:/, $aresult);
+	    push(@awards,$temp);
+	    push(@msgs,$msg);
+	    $i++;
+	}
+	my ($possible_award,$possible_msg) = 
+	    &LONCAPA_INTERNAL_FINALIZEAWARDS(\@awards,\@msgs);
+	if ($final_award) {
+	    ($final_award,$final_msg) = 
+		&LONCAPA_INTERNAL_FINALIZEAWARDS([$final_award,$possible_award],
+						 [$final_msg,$possible_msg],
+						 undef,1);
 	} else {
-	    ($aresult,$msg)=&caparesponse_check($thisanswer,
-						$responselist[$i]." $unit");
+	    ($final_award,$final_msg) = ($possible_award,$possible_msg);
 	}
-	my ($temp)=split /:/, $aresult;
-	$awards.="$temp,";
-	$result.=$aresult;
-	push(@msgs,$msg);
     }
-    chop $awards;
-    return ("$awards:\n$result",@msgs);
+    #&reset_caparesponse_memoization();
+    return ($final_award,$final_msg);
 }
 
 sub tex {
@@ -451,14 +580,14 @@ 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($_[0], 1); }
@@ -637,12 +766,12 @@ sub prettyprint {
 sub commaformat {
     my ($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;
@@ -806,6 +935,18 @@ 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 "";