--- loncom/homework/default_homework.lcpm	2004/03/16 15:31:52	1.73
+++ loncom/homework/default_homework.lcpm	2006/07/05 19:01:44	1.109
@@ -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 1.73 2004/03/16 15:31:52 albertel Exp $
+# $Id: default_homework.lcpm,v 1.109 2006/07/05 19:01:44 albertel Exp $
 #
 # Copyright Michigan State University Board of Trustees
 #
@@ -26,12 +26,7 @@
 # http://www.lon-capa.org/
 #
 #
-# Guy Albertelli
-#
-# 05/25/2001 H. K. Ng
-# 05/31/2001 H. K. Ng
-# 12/21/2001 Matthew
-#
+
 #init some globals
 $hidden::RANDOMINIT=0;
 $pi=atan2(1,1)*4;
@@ -39,17 +34,47 @@ $rad2deg=180.0/$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
     #not to be used: $ans_fmt
-    my ($type,$tol,$sig,$ans_fmt,$unit,$calc,$samples) =
-	eval $_[2].
-	';return ($__LC__type,$__LC__tol,$__LC__sig,$__LC__ans_fmt,$__LC__unit,$__LC__calc,$__LC__samples);';
+    my $type=$LONCAPA::CAPAresponse_args{'type'};
+    my $tol=$LONCAPA::CAPAresponse_args{'tol'};
+    my $sig=$LONCAPA::CAPAresponse_args{'sig'};
+    my $ans_fmt=$LONCAPA::CAPAresponse_args{'format'};
+    my $unit=$LONCAPA::CAPAresponse_args{'unit'};
+    my $calc=$LONCAPA::CAPAresponse_args{'calc'};
+    my $samples=$LONCAPA::CAPAresponse_args{'samples'};
     
     my $tol_type=''; # gets it's value from whether tol has a % or not done
     my $sig_lbound=''; #done
     my $sig_ubound=''; #done
-    my ($answer,$response,$expr)=@_;
 
 
     #type's definitons come from capaParser.h
@@ -64,18 +89,39 @@ sub caparesponse_check {
     } else {
 	$message .="no ws in :$response:\n";
     }
+    &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 \$ "; }
+	$response=~s/\$//g;
+    }
+    if ($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"; }
 
     if ($type eq '' ) {
-	$message .= "Didn't find a type :$type:$expr: defaulting\n";
+	$message .= "Didn't find a type :$type: defaulting\n";
 	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; }
@@ -101,25 +147,24 @@ sub caparesponse_check {
 	}
     }
 
-    if ($sig eq '') {
-	$sig_lbound = 0; #SIG_LB_DEFAULT
-	$sig_ubound =15; #SIG_UB_DEFAULT
-    } else {
-	($sig_lbound,$sig_ubound) = split /,/,$sig;
-	if (!defined($sig_lbound)) {
-	    $sig_lbound = 0; #SIG_LB_DEFAULT
-	    $sig_ubound =15; #SIG_UB_DEFAULT
-	}
-	if (!defined($sig_ubound)) { $sig_ubound=$sig_lbound; }
-    }
+    ($sig_ubound,$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') { $result='SIG_FAIL'; }
@@ -131,31 +176,56 @@ sub caparesponse_check {
     elsif ($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') { $result='UNIT_INVALID_STUDENT'; }
+    elsif ($result =='143') { $result='UNIT_INVALID_STUDENT'; }
+    elsif ($result =='15') { $result='UNIT_IRRECONCIBLE'; }
     else  {$result = "ERROR: Unknown Result:$result:$@:";}
 
-    return ("$result:\nRetError $reterror:\nError $error:\nAnswer $answer:\nResponse $response:\n type-$type|$tol|$tol_type|$sig:$sig_lbound:$sig_ubound|$unit|\n$message$expr",$reterror);
+    return ("$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 ($response,$expr)=@_;
-    my ($result,@list);
-    @list=@CAPARESPONSE_CHECK_LIST_answer;
-    my $aresult='';
-    my $current_answer;
-    my $answers=join(':',@list);
-    $result.="Got response :$answers:\n";
+    my $response=$LONCAPA::CAPAresponse_args{'response'};
+    my $result="Got response :".join(':',@LONCAPA::CAPAresponse_answer).":\n";
+    &LONCAPA_INTERNAL_DEBUG("args ".join(':',%LONCAPA::CAPAresponse_args));
     my @responselist;
-    my $type =eval $expr.';return $__LC__type;';
+    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]+)/ ) {
@@ -163,31 +233,33 @@ sub caparesponse_check_list {
 	    $unit=$2;
 	}
     }
-    $result.="Final final response :$responselist['-1']:\n";
-    $result.=":$#list: answers\n";
+    $result.="Final final response :$responselist['-1']:$unit:\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],
-						$expr);
+	if (defined($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",
-						$expr);
+	    $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);
 }
 
@@ -234,7 +306,10 @@ sub random {
     if ( ! $hidden::RANDOMINIT ) {
 	if ($external::randomseed == 0) { $external::randomseed=1; }
 	if ($external::randomseed =~/,/) {
-	    my ($num1,$num2)=split(/,/,$seed);
+	    my ($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)));
@@ -342,7 +417,7 @@ sub random_multivariate_normal {
     my ($item_cnt,$seed,$mean,$covar) = @_;
     my @oldseed=&random_get_seed();
     &random_set_seed_from_phrase($seed);
-    @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
+    my @retArray=&math_random_multivariate_normal($item_cnt,@$mean,@$covar);
     &random_set_seed(@oldseed);
     return @retArray;
 }
@@ -352,7 +427,7 @@ sub random_multinomial {
     my @oldseed=&random_get_seed();
     my @retArray;
     &random_set_seed_from_phrase($seed);
-    @retArray=&math_random_multinomial($item_cnt,@p);
+    my @retArray=&math_random_multinomial($item_cnt,@p);
     &random_set_seed(@oldseed);
     return @retArray;
 }
@@ -407,14 +482,14 @@ 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($_[0], 1); }
@@ -473,25 +548,99 @@ sub floor  {return (($_[0]-CORE::int($_[
 
 sub format {
     my ($value,$fmt)=@_;
-    my $dollarmode;
-    if ($fmt =~ /^\$(.*)/) { $fmt=$1; $dollarmode=1; } 
-    $fmt=~s/e/E/g;
-    my $result=sprintf('%.'.$fmt,$value);
-    $result=~s/(E[+-]*)0/$1/;
-    if ($dollarmode) {$result=&dollarmode($result);}
+    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;
-    my $dollarmode;
     if (!$target) { $target = $external::target; }
-    if ($fmt =~ /^\$(.*)/) { $fmt=$1; $dollarmode=1; } 
-    if ($fmt) { $value=sprintf('%.'.$fmt,$value); }
+    if ($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*/-/;
@@ -510,23 +659,30 @@ sub prettyprint {
 	}
     } else {
 	$result=$value;
-	if ($dollarmode) { $result=&dollarformat($result,$target); }
+	if    ($dollarmode) { $result=&dollarformat($result,$target); }
+	elsif ($commamode)  { $result=&commaformat($result,$target); }
     }
     return $result;
 }
 
-sub dollarformat {
+sub commaformat {
     my ($number,$target) = @_;
-    if (!$target) { $target = $external::target; }
     if ($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 $number;
+}
+
+sub dollarformat {
+    my ($number,$target) = @_;
+    if (!$target) { $target = $external::target; }
+    $number=&commaformat($number,$target);
     if ($target eq 'tex') {
 	$number='\$'.$number; #' stupid emacs
     } else {
@@ -535,6 +691,41 @@ 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();
@@ -730,6 +921,30 @@ 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)=@_;