--- loncom/homework/default_homework.lcpm	2004/10/11 16:31:34	1.90
+++ loncom/homework/default_homework.lcpm	2006/06/30 21:24:27	1.108
@@ -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 1.90 2004/10/11 16:31:34 albertel Exp $
+# $Id: default_homework.lcpm,v 1.108 2006/06/30 21:24:27 www Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -34,6 +34,32 @@ $rad2deg=180.0/$pi;
 $deg2rad=$pi/180.0;
 $"=' ';
 
+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($number) > 3) { return -4; }
+    }
+    return 1;
+}
+
 sub caparesponse_check {
     my ($answer,$response)=@_;
     #not properly used yet: calc
@@ -63,18 +89,26 @@ sub caparesponse_check {
     } else {
 	$message .="no ws in :$response:\n";
     }
-    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') { $response=~s/,//g; }
-    if ($type eq 'float' && $ans_fmt=~/\$/) {
+    if ($type eq 'float' && $unit=~/\$/) {
 	if ($response!~/^\$/)  { return "NO_UNIT: Missing \$ "; }
 	$response=~s/\$//g;
     }
+    if ($type eq 'float' && $unit=~/\,/ && (&check_commas($response)<0)) {
+	return "COMMA_FAIL:";
+    }
     $ans_fmt=~s/\W//g;
+    $unit=~s/[\$,]//g;
+    if ($type eq 'float') { $response=~s/,//g; }
 
     if (length($response) > 500) { return "TOO_LONG: Answer too long"; }
 
@@ -83,10 +117,11 @@ sub caparesponse_check {
 	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')   { $type = 1; }
@@ -115,13 +150,17 @@ sub caparesponse_check {
     ($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 {
+       $result = &caparesponse_capa_check_answer(&capa_formula_fix($response),&capa_formula_fix($answer),$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') { $result='SIG_FAIL'; }
@@ -133,6 +172,8 @@ sub caparesponse_check {
     elsif ($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') { $result='UNIT_INVALID_STUDENT'; }
@@ -143,26 +184,44 @@ sub caparesponse_check {
     return ("$result:\nRetError $reterror:\nAnswer $answer:\nResponse $response:\n type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|\n$message",$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)=@_;
+    $expression=~s/\s+/\*/g;
+    $expression=~s/(\d)([a-zA-Z\(])/$1\*$2/g;
+    $expression=~s/\)(\w)/\)\*$1/g;
+    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;
+    if ($type ne '' && $#LONCAPA::CAPAresponse_answer > 0) {
+	(@responselist)=split(/,/,$response);
+	if (@responselist < @LONCAPA::CAPAresponse_answer) {
+	    return 'MISSING_ANSWER';
+	}
+	if (@responselist > @LONCAPA::CAPAresponse_answer) {
+	    return 'EXTRA_ANSWER';
+	}
     } else {
 	(@responselist)=($response);
     }
-    my $unit='';
     $result.="Initial final response :$responselist['-1']:\n";
+    my $unit;
     if ($type eq '' || $type eq 'float') {
 	#for numerical problems split off the unit
 	if ( $responselist['-1']=~ /(.*[^\s])\s+([^\s]+)/ ) {
@@ -171,28 +230,32 @@ sub caparesponse_check_list {
 	}
     }
     $result.="Final final response :$responselist['-1']:$unit:\n";
-    $result.=":$#list: answers\n";
     $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[$i];
+
+    my ($awards, @msgs, $i);
+    foreach my $thisanswer (@LONCAPA::CAPAresponse_answer) {
+	my ($msg,$aresult);
 	$result.="trying answer :$thisanswer:\n";
-	if ($unit eq '') {
-	    ($aresult,$msg)=&caparesponse_check($thisanswer,$responselist[$i]);
+	if (defined($thisanswer)) {
+	    if ($unit eq '') {
+		($aresult,$msg)=&caparesponse_check($thisanswer,
+						    $responselist[$i]);
+	    } else {
+		($aresult,$msg)=&caparesponse_check($thisanswer,
+						    $responselist[$i]." $unit");
+	    }
 	} else {
-	    ($aresult,$msg)=&caparesponse_check($thisanswer,
-						$responselist[$i]." $unit");
+	    $aresult='ERROR';
+	    $msg='answer was undefined';
 	}
-	my ($temp)=split /:/, $aresult;
+	&LONCAPA_INTERNAL_DEBUG("after if $aresult -- $msg");
+	my ($temp)=split(/:/, $aresult);
 	$awards.="$temp,";
 	$result.=$aresult;
 	push(@msgs,$msg);
+	$i++;
     }
-    chop $awards;
+    chop($awards);
     return ("$awards:\n$result",@msgs);
 }
 
@@ -415,14 +478,14 @@ 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($_[0], 1); }
@@ -486,10 +549,15 @@ sub format {
     #if ($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;
@@ -497,24 +565,33 @@ 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;
@@ -526,11 +603,11 @@ sub chemparse {
 	$molecule =~ s/\s*//g;
 	# forced space
 	$molecule =~ s/_/ /g;
+	$molecule =~ s/-/&minus;/g;
 	$formula .= $molecule.'&nbsp;';
     }
     # get rid of trailing space
     $formula =~ s/(\&nbsp\;| )$//;
-    
     return &xmlparse($formula);
 }
 
@@ -544,7 +621,11 @@ 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') {
 	    $value .='\\ensuremath{.}';
@@ -583,12 +664,12 @@ sub prettyprint {
 sub commaformat {
     my ($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;
@@ -606,6 +687,41 @@ 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();
@@ -801,6 +917,30 @@ 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>