--- loncom/homework/default_homework.lcpm	2005/08/02 18:47:24	1.102
+++ loncom/homework/default_homework.lcpm	2008/03/06 14:04:09	1.132
@@ -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 1.102 2005/08/02 18:47:24 albertel Exp $
+# $Id: default_homework.lcpm,v 1.132 2008/03/06 14:04:09 www 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
@@ -78,20 +145,19 @@ 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:");
     }
-    &LONCAPA_INTERNAL_DEBUG(" type is $type ");
+
+    #&LONCAPA_INTERNAL_DEBUG(" type is $type ");
     if ($type eq 'cs' || $type eq 'ci') {
-	#for string answers make surec all places spaces occur, there is 
+	#for string answers make sure all places spaces occur, there is 
         #really only 1 space, in both the answer and the response
 	$answer=~s/ +/ /g;
 	$response=~s/ +/ /g;
@@ -100,7 +166,7 @@ sub caparesponse_check {
 	$response=~s/[\s,]//g;
     }
     if ($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)) {
@@ -110,21 +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 $points;
@@ -132,7 +199,7 @@ sub caparesponse_check {
     #formula type setup the sample points
     if ($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 '') {
 	$tol=0.0;
@@ -149,13 +216,22 @@ sub caparesponse_check {
     ($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') || ($type eq '8')) && ($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') { $result='SIG_FAIL'; }
@@ -176,60 +252,188 @@ sub caparesponse_check {
     elsif ($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 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;
-	    $unit=$2;
+#	if ( $responses->[0][-1]=~ /(.*[^\s])\s+([^\s]+)/ ) {
+        if ( $responses->[0][-1]=~ /^([\d\.\,\s\$]*(?:(?:[xX\*]10[\^\*]*|[eE]*)[\+\-]*\d*)*(?:^|\S)\d+)([\$\s\w\^\*\/\(\)\+\-]*[^\d\.\s\,][\$\s\w\^\*\/\(\)\+\-]*)$/ ) {
+	    $responses->[0][-1]=$1;
+	    $unit=&capa_formula_fix($2);
+            &LONCAPA_INTERNAL_DEBUG("Found unit :$unit:");
 	}
     }
-    $result.="Final final response :$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 =~ s/\s//g;
+                my $appendunit=$unit;
+                if ($unit=~/\%/) {
+                   $element=$element/100;
+                   $appendunit=~s/\%//;
+                }    
+		$element .= " $appendunit";
+                &LONCAPA_INTERNAL_DEBUG("Made response element :$element:");
+	    }
+	}
+    }
+    
+    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 cas {
+    my ($system,$input)=@_;
+    my $output;
+    if ($system eq 'maxima') {
+       $output=&maxima_eval($input);
+    }
+    return $output;
 }
 
 sub tex {
@@ -451,14 +655,14 @@ 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); }
@@ -806,6 +1010,18 @@ 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 "";