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Added more flexible type checking for MathObject classes. This makes it possible to correctly match types even when the context has specified a different package to handle a given type, for example.

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Fixed typo.

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Update new() and make() methods to accept a context as the first parameter (making it easier to create objects in a given context without having to resort to a separate call to coerce them to the given context after the fact).

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More updates to use the new Value->Package() call. This will make the standard object-creation functions like Real() and Complex() use the new lookup method.

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can't use inContext() with the "fake" make that produces perl reals, so remove it for now. (Perhaps we should just go with the Reals() and not try to be fancy about it, since it will often get converted to a Real anyway). This will need more work.

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Give the MathObjects answer checker a _filter_name so it is easier to recognize.

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Added Value->Package(name[,context]) to look up what package is currently set to handle the named type. E.g., Value->Package("Complex") usually returns "Value::Complex". These can be overridden in the Context so that modified vesions of the MathObjects can be made to replace the existing ones more easily. In particular, the Parser classes should call these (not yet implemented) when they create objects, so that you can override the object they create. Also cleaned up some more context issues (with still more to come).

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More updates for marking MathObjects with the context in which they were created, so they should now work like the Formula objects in that respect. As they are combined via overloaded operators, they should pass on their contexts correctly. Also normalized the use of getFlag() to obtain flags from the MathObject's context rather than looking in the context directly. This allows the math object to override the flag by setting the flag value in the object's hash (e.g., $f->{tolerance} = .001). I've also added the ability to override context flags via the answerHash (e.g., $f->cmp(tolerance => .001)), though some filtering may need to be added to this at some point. Note that ONLY the context flags can be overridden, not other parts of the context.

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Added comparisons for periodic reals and complex numbers (numbers that match up to reduction module some number). This makes contextPeriodic.pl obsolete, but the problems that use it should not need to change. (It would be good to remove the loadMacros() call, however.) Reals and Complex numbers now overload the % operator for the modulo operation.

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This begins some major updates to the Parser and Value libraries. This may make the MathObjects unstable as things shake down, but I'll try to keep that to a minimum. This update reorganizes how the overloading of operations are implemented. The base Value class is now overloaded rather than the individual Value classes. This makes it easier to make subclasses that take advantage of the overloading. The code that handles promoting one MathObject to another has been updated as a part of this. This should also make subclassing the existing MathObjects more flexible. In the past, Formula objects included a pointer to the Context in which the object was created, but other MathObject did not. This update is the first round of updates to include the context in the other MathObjects, but more work needs to be done. The changes here should not affect existing problems; it is possible that some macro files will need to be updated, but none of the standard ones in pg/macros seem to need it at the moment.

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Fixed an error with List answer checking when one of the elements was the constant 0 (a check for whether a value was defined was not properly handling the case when the answer is zero (which counts as false in a boolean check)).

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Allow Real object to override the context's number format by setting its format field. E.g.: Real(1.2345)->with(format=>"%.2f")

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Clear the error message in Context before it is used in an answer checker (prevents bleading of one error into a later answer).

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Format fix

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Formatting changes in documentation

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More format changes to documentation

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Updated documentation in response to comments from Davide. More comments welcome. :-) --Mike

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Added pod documentation for these files

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Only show the adaptive parameters where there actually ARE some, and fix a typo when looking up the adaptive points when there aren't any.

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Improved Formula diagonstics when adaptive parameters are used. They now allow you to graph the functions (they are no longer considered multi-variable functions), and the values reported are the adapted values rather then the unadapted correct answers. This now correctly reflects the tests that are being performed.

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Use zeroLevelTol values when checking answers that have adaptive parameters.

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Avoid an infinite loop when string-values formulas are used in a List. Allow diagonstics to work for complex-valued functions.

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Use Perl reals rather than Parser Reals in matrix for adaptive parameters.

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Added ability to have additional information given when not enough test points can be generated for a function comparison. By default, this information is NOT shown (since it could give students additional information about what answer is expectd). Professors can request it by setting the 'showTestPointErrors' flag in the Context().

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Allow overridden Parser classes to generate error messages that the student will see. (For formulas, error messages are trapped silently by the overridden == and will not be seen. This lets Parser objects force a message to be seen.)

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Fixed problem with checking Matrices of dimension 1 x n. (Fixes bug 1122.)

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Make ijk mode use the TeX definitions from the i, j and k constants as defined in the context, if they exist, otherwise fall back on the defaults.

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Fix problem with formula comparisons involving vector-valued formulas. The coordinates for the vectors used in checking equality were plain Perl reals rather than Parser-based reals, and so the comparisons were being done using exact rather than fuzzy comparisons.

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Add parenthesis around ijk vectors for string concatenation.

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Allow cmp_compare to return an array of answers, if requested (needed by parserMultiPart.pl).

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Fixed spelling errors in error messages.

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Fixed a problem where Set objects could incorrectly complain about the parentheses (braces) used to declare the set.

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Allow matrices to be created from lists of vectors or points, or from formulas returning vectors or points.

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Use tolerance flags from the Real object itself, if available, before looking at the context.

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Fix some problems with the Diagonstics output for Formula objects. (The tolerances using in the diagnostics didn't always match the ones used in the actual testing, and the wrong values were sometimes displayed when a multi-variable function was displayed as a graph.)

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Fixed a problem where a pick screen error was produced if a student entered a vector-valued formula rather than a constant vector when parallel answers are being checked and the student used the Preview button to submit the answer.

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When checking for division by zero, don't do fuzzy check.

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Added ability to supply a code reference (rather than a Value object) for the typeMatch and extra fields for the List answer checker (and the String answer checker). This makes these more useful in overriding the match for specific problems that want better error messages, for example.

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Added a new flag that controls how a list with a single entry that is a list is handled. In the past, the student could not specify such an item, but now the default is to form a list with a single entry that is a list, provided the student has used parens explicitly around his list. So "1,2" will be a list with two items and "(1,2)" will be a list with one item (a list). This improves the ability to use the list checker for lists of arbitrary pairs (like "(1,max)") especially when you want to check for lists of these (e.g., "(1,max),(2,min)"), since otherwise a single pair "(1,max)" entered by the student would become the list "1,max" rather than the list containing the single pair. If you really want "(1,max)" to become the list "1,max", use List("1,max")->cmp(implicitList=>0); to prevent single lists from forming a list of a single item.

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Now that the Parser allows multi-letter variable names, there is no need to handle C0 specially.

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Roll back Mike's change, since this can cause unwanted error messages in list comparisons and other situations where the equality check could compare different types of objects (for example) or where the comparison could legitimately fail. We only want to report errors here when the user-supplied checker code fails. This change would cause errors to be reported, for example, when the user (incorrectly) entered a vector one time and then a formula (correctly) the next time. When the previous answer is checked against the current one, this change would report an error rather than silently ignoring the error, as it should.

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Changes to code checking whether the previous answer is equivalent to the current answer. In this module additional code was answer to check for errors in the overloaded == in case the two Values can't be compared. In PGanswermacros.pl the filter which handles "parse_previous_answer" was modified to make sure the context is the same in the previous answer and the current answer.

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In the past, when Value objects were inserted into strings, they would automatically include parentheses so that if you had $f equal to 1+x and $g equal to 1-x, then Formula("$f/$g") would mean (1+x)/(1-x) rather than 1+(x/1)-x, which is what would happen as a straing string substitution. The problem is that this would also happen for real numbers, vectors, and everything else, even when it wasn't necessary. So if $x=Real(3), then "Let x = $x" would be "Let x = (3)". I have changed the behavior of the string concatenation for Value objects so that parentheses are only added in a few cases: for Formulas, Complex numbers, and Unions. This makes the other Value objects work more like regular variables in strings, but might cause some problems with strings that are used as formulas. For example, if $a = Real(-3), then "x + 2 $a" will become "x + 2 -3", or "x-1" rather than the expected "x - 6". (The old approach would have made it "x + 2 (-3)" which would have worked properly). For the most part, it is easier to use something like "x + 2*$a" or even "x" + 2*$a in this case, so the extra trouble of having to avoid parentheses when you really meant to substitute the value into a string didn't seem worth it.

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Added a new experimental diagonstic function for the function answer checker. When enabled, it will produce graphs of the correct answer, the student answer, and the absolute and relative errors, and will list the data points used in the comparison, plus the numerical values of the results and errors. To enable the diagnostic, use ANS(fun_cmp($f,diagnostics=>1)); Note that only single-variable functions can be graphed at the moment, so if you are using a multi-variable check, you need to disable the graphing. To do this use ANS(fun_cmp($f,vars=>['x','y'],diagnostics=>[showGraphs=>0])); The diagnostic mode is only available for the Parser-based versions of the function checker, and (of course) with the native Parser objects as well: ANS(Formula($f)->cmp(diagnostics=>1)); There are now Context settings to control the diagnostics, which can be set through Context()->diagnostics->set(). For example Context()->diagnostics->set(formulas=>{showGraphs=>0}); would turn off graphs for all functions comparisons. Some of the other values you can set are: formulas => { showTestPoints => 1, # show the test points and function values showRelativeErrors => 1, # show the relative errors for the student answer showAbsoluteErrors => 1, # show the absolute errors for the student answer showGraphs => 1, # show the various graphs graphRelativeErrors => 1, # show the relative error graph graphAbsoluteErrors => 1, # show the absolute error graph clipRelativeError => 5, # don't show relative errors above 5 clipAbsoluteError => 5, # don't show absolute errors above 5 plotTestPoints => 1, # include dots at the test points combineGraphs => 1, # show correct and student graphs in one image }, graphs => { divisions => 75, # the number of data points to plot limits => [-2,2], # the lower and upper limit of the plot # (taken from the function limits if not provided) size => 250, # pixel size of the image (could be [width,height]) grid => [10,10], # number of grid lines in each direction axes => [0,0], # where to put axes relative to origin } Any of these can be set in the Context(), or in the answer checker itself. If you set diagnostics to an array reference, the entries in the array refer to element of the formulas hash. If you set diagonstics to a hash reference, then you can set values in either the formulas or graphs hashes, as in: ANS(Formula($f)->cmp(diagnostics=>{ formulas => {showAbsoluteErrors=>0}, graphs => {size=>300, divisions=>100}, })); If you want all function checkers to show diagnostics, use Context()->diagonstics->set(formulas=>{show=>1}); The image file names are modified to include the current time so that the names will be unique. This avoids problems with the browser cache showing a old image when a new one has been generated. But this also means that the temporary image directory will fill up fast, so you may need to empty it if you use the diagnostic images frequently. This is just a first attempt at a diagnostic feature. I think it will help when you are not sure if the tolerances are set properly, or if you think a student answer should be markes correct but isn't, as it will point out which point(s) are not being accepted.

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Modified context data objects to provide a copy method so that the various types of data can copy themselves (and can provide a more comprehensive copy if necessary).

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Let Parser object's cmp(debug=>1) option set the debug feature of the answer evaluator.

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Add a new context flag that controls how the student answer should be displayed. The formatStudentAnswer flag can be set to 'evaluated' (the default), which shows the final numeric answer; 'parsed', which shows the fully parsed version (including extra parentheses for clarity); or 'reduced', which performs constant operations, but doesn't perform function evaluations or named-constant substitutions. For example, if the student answers 1+2+sqrt(3), then 'evaluated' will produce 4.73205, 'reduced' will show 3+sqrt(3), and 'parsed' will show 1+2+sqrt(3).

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Fixed a bug where correct_ans could not be overridden in the cmp() method for Lists.

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Handle the names of entries in Lists and Formulas returning lists better. Also do better typechecking on these lists. Finally, allow better typechecking for String objects that are being used when a Formula answer is allowed.

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Allow context to override object class used to create formula objects (so that things like ImplicitPlane can create instances of themselves automatically when needed). This mechanism needs to be enlarged to encompass the other Value object classes as well (like the Context()->{parser}{...} hash). The real problem is that the List object probably shouldn't create a formula returning a list when it is passed formulas, since there really isn't much need for a formula returning a list to be autogenerated (you can create one by hand using Formula if needed). Right now, ALL the Value objects make themselves into Formulas when one of their entries is a formula. For example, Point(1,"x") produces the same thing as Formula("(1,x)"), and List(1,"x") is the same as Formula("1,x"). This is good for points, but not so good for lists. And it might sometimes be nice to have a Vector of Formulas, or a Matrix with Formula entries (rather than Formulas returning Vectors or Matrices). But this would require some serious changes internally in the Value objects, which make assumptions about their values being constant. Changing that will be for another day...

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Correctly create Formula returning List when a list has formula entries.

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Added ability to have answers that are empty strings. String("") now will produce a valid string object regardless of the Context's defined string values. (You can prevent this using Context()->flags->set(allowEmptyStrings=>0); if you wish). String("")->cmp will produce an answer checker for an empty string (it removes the blank checker that WW installs).

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Don't allow wrapping in label for ans_array errors.

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The Parser answer checkers used to give the student answer as the parsed but unevaluated answer. This has been changed so that the student answer is now the computed result, no the parsed answer. The answer preview still shows the parsed equation. This is more consistent with the traditional answer checkers, and probably is more valuable to the students.

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Better error messages for unreduced unions.

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Improved error message layout and labeling for when ans_array is used.

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Fixed an error where scalar() was used on a hash ref. Fixed a misfeature where operations on formulas could return Value objects of other classes; they should always return formulas, even when the formula is constant.

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Fixed error in atan2 where second argument was not promoted to a Real.

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Added the ability to put class-specific answer-checker defaults into the Context object. For example, Context("Vector")->{cmpDefaults}{Vector}{promotePoints} = 1; would make all Vector answer checkers include promotePoints=>1 automatically. (Note however that if a subclass of Vector is used, it will not get this defaults, since its class name would be different. Perhaps something more sophisticated will be needed in the future.)

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Fixed problem with Context's not properly initializing themselves with the WW environment parameters (like zeroLevelTol and useBaseTenLog). The copy method and the method that did an initialized copy used to be separate routines, but that turned out to be unnecessary, so they have now been merged (copy always tries to initialize the WW values when it can, and when the copied context doesn't already have them). The reason this is complicated is that a number contexts are set up before the global.conf data is available, so these can't be initialized with the WW values. Also, these default contexts are stored in the persistant processes, and we don't want to leave possibly course-specific values lying around in them, so whenever a context is selected, it is copied from the standard version and the WW parameters are inserted into it. The problem author can only modify the copy, not the original, so this is OK with mod_perl. The context's copy method now always tries to initialize (we used to have to call initCoopy to get a copy that has the WW parameters inserted). That turned out to cause trouble with code that handled contexts without the usual Context() command.

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Changed stringify to check for an answer that is zero by using the zeroLevelTol value directly (rather than use the fuzzy equality check for zero, which depends on the tolType in a bad way).

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Added methods for testing containment of one set in another, and so on. These include: $A->contains($B) Test if $B is a subset of $A (or an element of $A if $B$ is a real number). $A->isSubsetOf($B) Test if $A is a subset of $B. $A->isEmpty True if $A is the empty set. $A->intersects($B) True if $A and $B have numbers in common. $A->intersect($B) The set of numbers common to both $A and $B. Be careful of the difference between "intersect" and "intersects". One is a set the other a true/false value.

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Added canBeInUnion and isSetOfReals methods to the Parser package (similar to the ones in the Value package), replacing the canBeInterval flag and other ad hoc checks. Removed ability to form interval like [a] now that we have sets.

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Allow a list of numbers to be converted to a set.

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Pass the canBeInUnion call on to the Formula's root node

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Added isSetOfReals and canBeInUnion methods to the Value objects, and replaced the ad hoc tests for these conditions to call these routines. Cleaned up the make() methods for Intervals, Sets and Unions, and improved the new() methods to handle more cases better. Fixed Value::makeValue() to handle an array reference correctly. I don't THINK any of this will break anything. :-)

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Make formulas that produce lists get default open and close parens, and have them retained in Formula() results.

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Make sure the singletons are sorted before comparing them to the intervals (and each other).

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Can't use the length check when reducing unions, since it could contain a single set that is not reduced, and we need to check that, too.

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Fixed reduction warnings for individual sets, intervals and unions (in making it work for lists, I broke it for the single items).

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Fixed a problem with redefine when used with classes that store their data in a on-standard form (i.e., by overridding the create() method). Now they can define uncreate() to get the original data back for use with redefine().

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Added isReduced method to tell if a Union, Set or Interval is already reduced. Fixed up sort to use CORE::sort, and added sort and reduce to Intervals, which do nothing, but are there for consistency.

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Fixed error in testing is a union is reduced (didn't test if sets within a union were reduced properly).

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Added sort methods to Union and Set that return objects with their data sorted.

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Moved the union and set reduction checks from cmp_equal to cmp_compare so that the messages can be produced even in lists of unions. Improved the message facilities for the list comparison so that cmp_compare can make errors that refer to the number of the entry in the student's answer (otherwise an extra "There was a problem with your nth value" message needs to be prepended, which looks bad if it can be avoided). Use the "extra" answer checker to report syntax error messages in unordered lists.

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Fixed a typo in an error message.

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Added ability for Unions and Sets to simplify themselves (automatically or on demand), and added flags to the Context and answer checkers to control these features. The new Context flags are reduceUnions tells whether unions are automatically reduced when they are created. reduceUnionsForComparison tells whether unions are reduced before comparing them for equality or inequality (etc) if they aren't reduced already. reduceSets tells whether redundent elements are removed from sets as they are created. reduceSetsForComparison tells whether sets are reduced before comparing them. All of these default to true. The Interval, Set, Union, and List answer checkers not have two new flags for controlling these values: studentsMustReduceUnions tells whether unions and sets will be counted as incorrect when they are not reduced to non-overlapping intervals and at most one set with no repeated entries. showUnionReduceWarnings tells whether an error message will be produced for non-reduced unions and sets, or if they will be marked wrong silently. (Not available in Lists.) Both of these are true by default, since most professors probably want their students to write intervals in reduced form. (Is this true?) This corresponds the the current behavior of the interval checkers, which require the student's answer to be the same set of intervals as in the professor's, but with the addition of an error message when the student answer is not reduced.

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Detect preview mode correctly for either WW1 or WW2.

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Adjust spacing.

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Avoid problem with undefined value being passed to protectHTML.

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Changed how Intervals implement the requireParenMatch flag for the interval and union answer checker. (Use a Context flag rather than a flag on the interval itself.) Moved the getFlag method from Formula.pm to Value.pm so it can be used by any object class. New feature where classes can add more context flags to set (and reset after the answer checker runs).

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Removed erroneous dollar sign.

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Added redefine() function to complement undefine() for various Context() values. For example Context()->operators->undefine('+'); makes '+' undefined, but Context()->operators->redefine('+'); will put it back. You can specify a context from which to take the redefinition, and a name in that context, as in Context()->operators->redefine('U',from=>"Interval"); Context()->operators->redefine('u',from=>"Interval",using=>"U"); Context()->operators->redefine('U',from=>$content); where $content is a reference to a Context object. The undefine() function lets you undefine several items at once, as in Context()->operators->undefine('+','-'); For redefine, you must put multiple names in square brackets because of the optional parmeters: Context()->operators->redefine(['+','-']);

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Added ability to subtract intervals, sets and unions. Adjusted the precedence of the union 'U' to be above _ and + so that things like (1,5) U (7,10) - {8} U (2,3) will do ((1,5) U (7,10)) - ({8} U (2,3)) rather than the previous (1,5) U ((7,10) - {8}) U (2,3). Finally, added a constant 'R' to the Interval context that is equivalent to (-inf,inf), so you can do things like R-{0} now. Still need to work out reducing unions so that things like (1,3)U(2,4) can become (1,4).

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Changes needed to Set object. Also, use Parser to handle unions defined as strings rather than doing it by hand (that's the whole point, isn't it?). Added object promotion from lower-precedence classes (for better error messages), and fixed up the comparison routine.

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Changes needed for Set object, better handling of an interval given as a string, and a few misc. fixes.

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Changes needed for new Set object, and moving of string, TeX and perl methods to Value.pm

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Added changes needed for the new Set object.

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Added new Set object class to the Parser. It implements a finite set of real numbers, for use with unions and intervals. E.g., (1,2) U {3} or (1,2) U {3,4,5}. You can created Set objects in your perl code via the Set() command, e.g, Set(3,4,5) or Set("{1,2,3}"). You should set the Context to Context("Interval") if you plan to use Set objects, as this defined the braces to form sets (rather than using them as parentheses, which is the default WW behavior). Note that in Interval context, you can NOT use braces as parentheses. Current, Set objects are only allowed to be sets of numbers. It would be possible to extend that in the future.

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Interval (and Union) checker now accepts requireParenMatch flag for deciding whether the interval type must match. Setting requireParenMatch to 0 will let (1,2) match (1,2] or [1,2], etc.

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Make List("1,2,3") work like List("1","2","3") rather than produce a list with one element that is a list.

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Fixed typo that caused hilighting of the position of errors to be lost.

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Fixed typo related to useBaseTenLog.

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A first pass at making parser error messages localizable. The Context()->{error}{msg} hash can be used to specify translations of the standard messages. For example, Context()->{error}{msg}{'Division by zero'} = "Don't divide by zero, dude!"; Context()->{error}{msg}{'Function '%s' has too many inputs'} = "You passed too many arguments to '%s'"; (I didn't translate into another language, here, but you could do that, too.) The msg hash could also be used within answer checkers to make certain answer messages more appropriate for the given type of expected answer.

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Fixed various perl compiler warnings (due to extra "my", and so on).

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Better messages when adaptive parameters are too big.

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Implement "remove trailing zeros" format, like in prfmt(). I still think '%g' works better in most cases ('%f#' will print larger values without using scientific notation, which is nice, but will print small numbers like .000000005 as 0, even though the fuzzy comparison of this to zero will not be true.)

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Don't use the overloaded Real class for doing adaptive parameter checks (use non-fuzzy checks, since we are checking the fuzziness by hand).

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Change so as not to use raw HTML in the error messages.

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Updates to allow string matches to be case-insensitive. This is now the default, and can be overridden in the Context by setting the string's "caseSensitive" attribute. e.g.: Context()->strings->add("FooBar"=>{caseSensitive=>1}); would rewuire "FooBar" to be entered exactly as typed.

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Adjusted some spacing

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New flag showAllErrors for when a custom checker is supplied. This will cause all errors generated in the user's code to be reported (normally, messages from the Value and Parser packages are ignored).

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Fixed a problem with auto-generated functions getting an incomplete variable list.

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Forgot to check hardcopy mode. Fixed some problems with that. The answer array items have to turn off verbatim mode that is used when answer are included in the hardcopy. This causes paragraph breaks between entries in a singleResult MultiPart that includes ans_arrays, which make the output less pretty, but at least they show up.

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Added ability to have Matrix, Vector and Point objects produce input arrays similar to the ones available in PGmatrixmacros.pg. This provides some substantial new functionality, and it may still have some shaking down to do, but it should not affect the existing functionality of the answer checkers. To create an answer array for a matrix, vector or point, use the new ans_array() or named_ans_array() methods of these objects. For example: Context("Matrix"); $M = Matrix([1,2],[3,4]); BEGIN_TEXT \{$M->TeX\} = \{$M->ans_array\} END_TEXT ANS($M->cmp); This creates a matrix, then prints it ans creates an answer array of the appropriate size for the matrix. The answer checker will automatically know to handle the multiple entry blanks. To used a named answer rule, use: Context("Matrix"); $M = Matrix([1,2],[3,4]); BEGIN_TEXT \{$M->TeX\} = \{$M->named_ans_array('fred')\} END_TEXT NAMED_ANS(fred => $M->cmp); Both methods also take an optional argument that specifies the width of the answer rules. The default is 5. You can get a multi-input point or vector array as well, and you can make column vectors as follows: Context("Vector"); $V = ColumnVector("1+x","3x","1-x"); BEGIN_TEXT \{$V->TeX\} = \{$V->ans_array\} END_TEXT ANS($V->cmp); Note that you can make answer arrays for matrices and vectors of formulas as well as constants, provided the formula is an explicit matrix or vector of formulas, and is not obtained by matrix arithmatic. For concistencey, all objets now have ans_rule and named_ans_rule methods as well. The default width is 20 for these.

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Better handling of delimiters that are explicitly set byt he user. Fixed an incorrect call during object class promotion. Added ability to sepcify that a vector is a Column Vector.

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Better handling of open and close delimiters that are explicitly set.

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Fix some incorrect calls when the promoting types to higher precedence object types.

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Avoid possible infinite loop with length and typeref calls.

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Remove unneeded comment.

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Better control over number of points that can be undefined, and new ability to specify required test points plus additional random ones. (Previously, if you set the test points, no random points were generated.) For example: $f = Formula("(x^2-1)/(x-1)"); $f->{test_at} = [[1]]; # test at x=1 plus random points as opposed to $f->{test_points} = [[-1],[0],[1]]; which tests only the points x = -1, x = 0 and x = 1.

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Modified the Formula answer checker to allow checking of points where the functions are undefined (i.e., attempt to check that the domains agree). This can be enabled by setting the checkundefinedPoints flag in the Context(), or in the formula itself. Test points where the function is undefined will be retained and the student's answer will have to be undefined at the same points. If the points are selected at random, the points where the function is undefined are kept in addition to the ones where it is defined, so the required number of test points where the function IS defined will still need to be found. The number of undefined points can be up to the number of defined points. This number can be reduced by setting the max_undefined flag. If you want to guarantee that a specific undefined point be tested, you can provide that point using the test_points field of the formula. For example: Context()->flags->set(checkUndefinedPoints=>1); $f = Formula("(x^2-1)/(x-1)"); $f->{test_points} = [[-1],[0],[1],[2]]; ANS($f->cmp); will guarantee that the singularity at x=1 is tested, so the answer x+1 will not be marked as correct. If an answer matches at all the test points where the functions are both defined, but some of the undefind points differ between the two functions, the answer checker will generate an error message indicating that the domains of the functions don't agree. (This is ONLY generated with the functions match except for that.) This can be controlled by setting the showDomainErrors flag in the formula's cmp() call: ANS($f->cmp(showDomainErrors=>0)); The default is to show these errors.

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Fixed an accidental hard-coded operation from always being "add" to being the correct operation when promoting the operations to an object of higher precedence. (But since formulas are normally the highest precedence, this will never have occurred.)

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Fixed a bug with adaptive parameters where the relative tolerance was not being properly computed. This allowed large constants to be treated as correct when they shouldn't be.

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Copy parameters like limits, etc, to the newly created formula when 'C0' is added by the "upToConstant=>1" option in formula cmp().

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Use correct form of "x" with lists (rather than hack using split()).

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Handle error messages in the list checker better. In particular, make the error messages generated by custom checkers called on elements in the list look better. Also, in an ordered list, if the student enters extra values, call an answer checker to do a syntax check. (By default, use the first element again, but the user can supply a separate object to use for the checker using the extra=>object option.)

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Compartmentalize the equality check one step further. The cmp_equal method now calls a new cmp_compare method to perform the actual comparison (rather than use == directly). The cmp_compare method either calls a user-supplied checker routine, or defaults to using the == operator. The list checker also uses cmp_compare to check the individual items in the list. The list checker also calls a new cmp_list_checker method to perform the list check. This can be overridden by a user-supplied list-checking routine. To supply an alternate checking routine, use the "checker" option to the cmp() method of the correct answer object. For example: sub check { my ($correct,$student,$ans) = @_; return 0 unless $correct->length == $student->length; my ($x,$y) = $student->value; # break up a point; return $x**2 - $y**2 = 1; # check if it is on a hyperbola } Point(1,0)->cmp(checker=>~~&check); This will check if the student's point lies on the given hyperbola. All the usual error messages will be issued if the student's answer is not a point, or is of the wrong dimension, etc. You can use sub list_check { my ($correct,$student,$ans) = @_; my @correct = @{$correct}; my @student = @{$student}; ... return ($score,@errors); } List(...)->cmp(list_checker=>~~&list_check); to replace the list-checking routine with your own custom one. The $correct and $student values are array references to the elements in the lists provided by the professor and student. (Note that you do NOT get a List() object; this allows you to handle lists of formulas, since a List of formulas becomes a formula returning a list). The checker routine should return the number of correct elements in the student's list ($score), and a list of error messages produced while checking the two lists (@errors). (This is a list of messages, since you might want to include an error for each entry in the list, for example). If your checker or list_checker routine wants to die with an error message, use Value::Error(message). This will put the message in the WeBWorK display area at the top of the page. If you use die(message), or if the code fails due to a runtime error, then "pink screen of death" will be produced indicating the error and asking the student to report the error to the professor.

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Properly handle string values in postprocessing of vectors and other related lists. (It used to report a dimension error for things like 'NONE').

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Update the overloaded operators so that they can be overridden by subclasses of the predefined object classes. This involves calling the objects method rather than using a hard reference to the routine in the parent class. Also, change the name of the string comparison routine to compare_string to avoid conflicts with cmp that is used to produce the answer checker for the class. Finally, in Value.pm, promotePrecedence no longer has to do fancy footwork to get "special" precedence to work (this was a hack to get around the misfeature of the overloaded operators -- now that that is being handled correctly, there is no need for it).

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Missed one situation when making the previous update. Fixed it.

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Fixed it so that direct calls to the add, sub, mult, etc functions would work as expected (even though there is no need to call them directly).

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Updated the answer checkers so that you can more easily specify how the correct answer shoudl be displayed. In the past, you could use something like Real(sqrt(2))->cmp(correct_ans=>"sqrt(2)") to do this, but that is awkward. Now the Compute() function (which parses and then evaluates a string) sets things up so that the original string will be what is used as the correct answer. That means Compute("sqrt(2)")->cmp will have the same result as the example above. You can also set the {correct_ans} properly of any Parser object to have that value used as the correct answer. For example $x = Real(sqrt(2)); $x->{correct_ans} = "sqrt(2)"; ANS($x->cmp) would also produce the same answer checker as the two previous examples. All three methods should work. Use the one that is most convenient for you.

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Improved the Real(), Complex(), Point(), Vector(), Matrix() and String() constructors so that they will process formulas passed to them as strings rather than requiring perl objects for these. For example, you can use Real("2/3") rather than Real(2/3) if you want. Also, Real("1+x") will return a formula returning a real (essentially the same as Formula("1+x") in this case).

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Fixed an error with Matrix() that could cause it to loop infinitely when bad data is passed to it. Also, allow Matrix(), Point(), Vector(), and Real() to accept string values that are evaluated to produce the value returned. (Sorry, accidentally committed with a blank message.)

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*** empty log message ***

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Fixed index problem with matrix multiplciation. (It was returning the transpose!)

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Added "areParallel" method as a synonym for "isParallel".

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Clear error messages before doing the answer check (this clears old messages left over inclass this checker is called by another one, e.g. when using UNORDERD_ANS()).

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Added support for useBaseTenLogs to make log() work like ln() or log10() depending on the value in the course.conf file. Also fixed a bug that caused the WeBWorK parameters not to be copied into contexts by initCopy().

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Report errors for powers of negative numbers rather than return 'nan'. Don't allow 'nan' to be made into a Real object.

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Don't give coordinate hints during parallel vector checks. Also fixed a typo.

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Added isZero and isOne checks for Parser::Value objects (i.e., for constants within formulas). These now correctly handle vector and matrices, in particular. The isOne and isZero checks are used in the reduce() method to simplify formulas.

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Added a new flag to the Formula()->cmp answer checker that allows a constant-valued formula to be evaluated and then use the checker for the resulting type. This is useful when you want the correct answer for a numeric check to be shown in a symbolic form (like "pi/4") rather than as a decimal number. To do this, use Formula("pi/4")->cmp(eval=>1); rather than Real(pi/4)->cmp, which would show the correct answer as 0.785398. Note that Formula("pi/4")->cmp would also match against pi/4, but it does it as a function rather than a number, so error messages might be issued indicating that the checker is expecting a formula that returns a number, rather than just a number; this might be confusing to a student. It would also accept answers like "pi/4-x+x" as correct, whereas with eval=>1 this would produce an error message saying that the answer was supposed to be a number not a formula returning a number. Similarly, if you want to show sqrt(2)/2 as the correct answer, use Context()->flags->set(reduceConstants=>0, reduceConstantFunctions=>0); Formula("sqrt(2)/2")->cmp(eval=>1); The first line tells the parser not to automatically reduce expressions that only involve constants, so that the value of the formula in the second line will not be reduced to a decimal before the cmp method is called.

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Don't reduce constants in the display of student answers (so they can tell how the parser interprets their answer). The drawback is that the final number is not displayed. (We may need to add more columns to the results display.)

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Use extra parens in the string version of the student's answer, but not in the professor's (unless the problem sets the showExtraParens flag).

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Make partial credit in list answer checkers be the default (now that WeBWorK can handle this).

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Fixed a bug with constants where the values were being cached so that changes in the context were not being reflected in the formulas that use them.

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No longer produces the message that there are too many answers if hints are being shown about individual entries in a list. (This gave away the answer about which ones to remove.)

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Use the current context if the answer doesn't have one itself (like with Value objects).

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Added in functMaxConstantOfIntegration support in the adaptive parameter answer checking. Also added a flag to the formula answer checker that allows checking a formula up to a constant (for integration problems). This really just adds a new parameter to the context and adds that to the formula, so there is nothing deep about this. ANS(Formula("2x")->cmp(upToConstant=>1)); Finally, don't look for adaptive parameters if they aren't actually used in the professor's formula (even if they are defined).

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Added ability to have linear adaptive parameters in the function answer checker. It only works for real-valued functions, though. To use a parameter, use Context()->variables->add(a=>'Parameter'); and then use 'a' as a variable within your answer. The student will not be allowed to enter the parameter, but the professor will. Note that the correct answer will show the full professor's answer, including the parameters, even though the student can't type it. Is this the right behaviour?

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Modified the parser so that the classes for the various object constructors are stored in the context table rather than hard-coded into the parser. That way, you can override the default classes with your own. This gives you even more complete control to modify the parser. (You had been able to replace the definitions of operators, functions and list-like objects, but could not override the behaviour of numbers, strings, variables, and so on. Now you can.) This effects most of the files, but only by changing the name of the calls that create the various objects. There are also a couple of other minor fixes.

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Remove more lines in error messages produced while evaluation student answers.

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Moved WW-specific routines from Parser.pm to WeBWorK.pm. Changed error reporting when the error message was not generated by the parser directly. (The stack trace and line number references are removed before the error is reported.)

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Fixed some inconsistencies between handing of matrices within the parser and Value packages. Added a predefined Matrix context.

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Made the granularity of the test-point intervals be a parameter that can be set on a global or variable-by-variable basis, so this is now controlable from the .pg file. For example: Context("Numeric")->variables->are( k=>{limits=>[1,10], resolution=>1}, x=>{limits=>[-2,2], granularity=>1000}, ); will make k be a variable that will only take on integer values between 1 and 10, and x a variable that will take on one of 1000 different values evenly spaced between -2 and 2 (so resolution is 4/1000 in this case). These parameters can also be set for an individual formula: $f = Formula("k^2-1"); $f->{resolution} = 1; $f->{limits} = [0,10];

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Fixed TeX output of Matrices to use \array rather than \matrix for matrices with formulas as entries (this had already been fixed for constant matrices). Made intervals produce formulas when of of the endpoints is a formula. Removed unneeded comment.

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Added support for dimension warnings in the answer checker for formulas that return points, vectors or matrices.

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Formulas can now be compared even if their variables are complex numbers, or even points or vectors! This makes it possible to ask students for complex functions like z^2+i and so on. You can specify limits for variables either via Context()->variables->set(x=>{limits=>[0,1]}) (for reals) or Context()->variables->set(z=>{limits=>[[-2,2],[0,1]]}) (for complexes). Similarly for points and vectors (where the number of sub arrays depends on the dimension). You can also give the limits for a specific formula by assigning to its ->{limits} field: $f = Formula("sqrt(x-10)"); $f->{limits} = [10,12]; There are now named variable types for 'Point2D', 'Point3D', 'Vector2D' and 'Vector3D', in addition to 'Real' and 'Complex'. You can also specify a variable type by giving an explicit instance of a value of the given type. E.g. Context()->variables->add(x=>'Real',y=>0); # two real variables Context()->variables->add(z=>'Complex',w=>i); # two complexes Context()->variables->add(r=>Vector(0,0,0)); # a vector in R^3 Context()->variables->add(X=>'Vector3D'); # a vector in R^3 There still needs to be more error checking in processing user-supplied limits, but I'm not sure how much overhead is worth it.

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Added a file to perform WeBWorK-specific modifications to the Parser/Value packages. (I've tried to make these independent of WeBWorK, so you can use them in other perl code if you want to.) The parameters for fuzzy reals and some of the other parameters now are taken from the pg->{ansEvalDefaults} values (as defined in global.conf or course.conf). More still needs to be done with this, however.

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A number of fixes to make handing lists work better. In particular, you can now specify checks for whether the right kinds of parentheses (or none at all) are used on the student's answer. Some of the flags for the list checker have been changed to accommodate this.

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A number of adjustments to get negative infinities to work better. They used to be stored as separate Parser strings, but now they are flagged versions of a single string. All of the problems are really due to the fact that there is no Infinity class in the Parser (only a Value version). That should be changed, but will require some work, and can be put off for now. It would be best if the classes within the two packages would match up nearly 1-to-1, but for historical reasons, they don't. Since the introduction of Real, String and Infinity classes to the Value package, The Infinity class is the one main difference between the two, and once that is fixed, everything needs to be looked over to check for unnecessary complications due to the historical lack of classes in one or the other package.

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Make blank patterns be ^$ (which should never match) rather than empty (which always matches). this fixes a problem where if a context has no functions, for example, the parser would attempt to create function calls to a function named ''.

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We need to protect the HTML in the professor's answer so that if it contains <, for example, it won't disappear.

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Fixed an error in the generation of regexp patterns for the various data types.

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The answer checkers now work with subclasses of Formulas that are not part of the Value:: package tree itself (we call Value::isFormula() rather than checking the class directly). I also removed the various cmp_* flags that stored method names as they ended up not needing to be used (they were intended as a means of overriding the default method names, but subclassing turned out to be a better approach). I moved some initialization of the answer checker out of the anonymous subroutine that is installed in the checker and just have that subroutine call the correct answer's main checker (which I renamed). Finally, I changed the student_ans value to be an HTMLized version of the student answer, since the student could include things like < in his answer (e.g., for vectors), in which case his whole answer might disappear. I wonder if this couldn't be handled better at a higher level, as it seems wrong to make the student_ans be HTML rather than the parsed string. I originally thought Problem.pm could do the protecting of HTML special characters, but this won't work without additional changes, since some answer checkers put HTML into student_ans to mark sytanx errors in the student answer, and you DON'T want to protect those HTML characters. The student_ans field is probably being misused in this, and there might want to be another field that gets used by Problem.pm in place of student_ans (which can be HTML protected) when it is non-empty; say student_HTML or something like that. The answer checkers could use that field if it wants to add HTML to the student answer, and student_ans otherwise, with the assurance that it's HTML characters will be protected. That way, if a second answer checker calls the first (like some list checkers do), then the second checker doesn't have to worry about removing HTML from the student ans, and doesn't ahve to wonder whether the student_ans actually contains an error message or syntax markings rather than the actual student answer.

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Changed the string used for the student answer to be taken from the unevaluated formula rather than the fully-evaluated one. This leaves constants unreplaced, for one thing. Currently the parser combines constants automatically during the parse [which should be controllable by a flag], so student answers that produce numbers are fully evaluated at this point already, except for constant substitution. This could be changed so that even for numberic results, the student sees the parsed expression (rather than the numeric result), which might help them identify where they and the parser differ in their interpretation. It is still nice to see the final computed result, however, but there is no place to show the parsed input as well as the final result. One solution would be to add another column (wasting space). Another would be to make the value shown be "parsed-value = computed-value" when they are not the same thing. A bit ugly, but works within the current framework.

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Fixed typo in name of random generator.

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Fixed a number of minor problems with creating perl functions from formulas (this is done automatically as part of the function answer checker, so is showing up now that I have that checker in place). Also improved error messages in the function answer checker, and fixed a bug when students enter a constant list or union when the answer checker expects formulas.

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Removed unwanted side-effects of some type-match checks, and moved the ignoreStrings flag so that it is available for the checkers of ANY type.

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One more fix for handling intervals properly (I think it's really right this time). Also, named constants that end in numbers will produce TeX output with the number as a subscript (this was already true for variable names).

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Added string comparison to all Value object classes (to compare the string value of an object to another string). Overloaded perl '.' operator to do dot product when the operands are formulas returning vectors. (Part of the auto-generation of formulas). A few improvements to real and complex class output results. Made Union class slightly more robust and removed need for makeUnion method other than in the Union itself.

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Added support for unorderd list or formulas with partial credit. Fixed type mismatch reporting in formula answer checker. Fixed an error with Unions producing incorrect perl versions under some circumstances.

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Created the first draft of the Parser's function answer checker. Some work still needs to be done, in particular, type mismatches are not being reported, and lists are being processed only as ordered lists with no partial credit. This doesn't implement everything from fun_cmp. In particular, there is no support for parameter matching at the moment. This will have to be added, but I'm not quite sure how to do it when the function's return value is not a real number (e.g., an interval). On the other hand, this checker is more forgiving about domain errors: if tries a point where the professor's function is not defined, it ignores that one and looks for another (until it decides it can't find one). Once it has these points, it tries them on the student's answer, and if the student's function is undefined, then the student answer is wrong (since it is not defined somewhere that the professor's funciton is). This avoids the "Error evaluating student function at ..." messages, which just confused most students anyway.

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Improved error messages, particularly when the student enters a formula in an answer that should be constant, and also for incorrect answers in lists of answers. There are a few other miscellaneous output improvements as well.

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The Union answer checker now uses the generic List checker, so that it will be able to produce partial credit and hints about which Intervals are correct.

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*** empty log message ***

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Fixed some bugs in the handle of the context in ->string and ->TeX methods of Value objects.

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Fixed a typo in one of the parser answer checkers. Added a line that was incorrecctly removed in the parser.

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The class file for the Value::String object. (Forgot to add it before the last commit. Sorry!)

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Added a String type to the Value package. Mostly this is to make it possible to generate an answer checker for it that uses the parser. It also makes it more consistent for handling things like stringify, especially when they are recursively called internally. Added new default strings "NONE" and "DNE", since these get used a lot. Modified how the default parameters are set up for the answer checkers, and how the answer checker reports the expected answer type in type mismatch error messages.

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Can now specify that the objects stringify themselfs in their TeX forms rather than their answer-string forms. This makes it easier to use the objects in the text of a problem (without having to call ->TeX explicitly each reference). Use Context()->texStrings to start outputting TeX strings, and Context()->normalStrings to switch back.

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Incorporated infinities into Parser package better. They have been stored as String objects (with extra data) in the parser, and I've left it that way, but now they convert to/from Vallue::Infinity objects correctly, and these are used for generating the output. Also added the Infinity answer checker, and adjusted the error messages produces by type mismatches in the answer checkers and elsewhere.

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Fixed some output issues with intervals and unions.

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Added an Infinite object class for the Value package. Still need to add it to the Parser package.

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Added ability to report incorrect coordinates in point and vector answers, and incorrect endpoints and endpoint types in intervals. Separated these kinds of checks from the typeMatch check, where they didn't really belong. Added ability to specify intervals and unions as strings in Interval() and Union(), which makes it easier to make constants of these types. There are still problems comparing intervals that contain infinities; I really need to make the infinity object to solve this, so have put off trying to fix that for now.

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Handle list entries that are not Value objects better.

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The List object's answer checker is now considerably improved. It will allow you to specify an unorderd or ordered check, and whether to print various kinds of hints for wrong answers. The checker can return partial credit, but WW doesn't deal well with this at the moment (some small changes to Problem.pm can take care of that). Partial credit should be based on $showPartialCorrectAnswers, but it is disabled for now. The list answer checker probably still needs some work, especially with non-numeric lists.

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Added answer checker for parallel vectors. Added option to number checker to have it not report type mismatches for the known strings (like 'infinity'). (Really need a class for infinities, and a Value.pm class for strings.)

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Have parser handle infinities better.

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Fixes for handling intervals better. In particular, deal better with ambiguous situations, like (1,2) that could be a point. You can use [a,a] to specify the single point a. I'd like to make {a} represent this (and maybe even {a,b,c} to form finite sets), but this would interfere with the use of { and } as alternative parentheses. (Does anyone really use these?) Do we need a cross product for intervals (and sets) as a means of representing regions in R^2 (or higher)?

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This is a preliminary attempt at adding answer checkers that use the parser. If you have a parser object (like a formula or a vector), you can use the ->cmp method to get an answer checker appropriate for the object. For example: Context('Vector'); $v = Vector(1,2,3); # print text of problem ANS($v->cmp); would produce an answer checker that matched against the vector <1,2,3>. Most of the parameters are set in the Context, but additional ones can be passed to the checker (this still needs work). See the sample problems for more examples. The checkers for Reals, Complexes, Points, Vectors, Matrices and Intervals work pretty well. The ones for List and Union objects need more work, as they only do an ORDERED check at the moment (the student answers must be in the same order). This needs to be fixed. The checker for Formula objects (which corresponds to fun_cmp) still needs to be written.

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A number of small fixes. Most were to fix minor bugs in string and TeX output, particulary for the various list-based objects (like vectors, intervals, etc.). There were also some bug fixes in the comparison routines. Some additional checks were added for valid intervals when the coordinates are formulas.

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Forgot to add this file. It implements the "fuzzy real" class.

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Significant update to new parser. New features include: Better control over format of vector output (you can now specify ijk-format rather than <...> format) "Fuzzy" reals, where the relations like == return true when the two values are "close enough". (This is controlable using parameters similar to those used in NUM_CMP). The fuzzy reals are now used in vectors/points/matrices/complexes/intervals and so on so that their relations will also be fuzzy. E.g., (1E-13,2) == (0,3) will be true, and norm(Vector(0,1E-13)) will equal 0. The two main portions of the parser (the Parser and Value packages) now share a common context object for configuration purposes.

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merged changes from rel-2-1-a1 -- stop using that branch.

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