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extraAnswerEvaluators.pl - Answer evaluators for intervals, lists of numbers, and lists of points.

```
interval_cmp() -- checks answers which are unions of intervals. It can also
be used for checking an ordered pair or list of ordered
pairs.
number_list_cmp() -- checks a comma separated list of numbers. By use of
optional arguments, you can request that order be
important, that complex numbers be allowed, and specify
extra arguments to be sent to num_cmp (or cplx_cmp) for
checking individual entries.
equation_cmp() -- provides a limited facility for checking equations. It
makes no pretense of checking to see if the real locus of
the student's equation matches the real locus of the
instructor's equation. The student's equation must be of
the same general type as the instructors to get credit.
```

This file adds subroutines which create "answer evaluators" for checking student answers of various "exotic" types.

Compares an interval or union of intervals. Typical invocations are

` interval_cmp("(2, 3] U(7, 11)")`

The U is used for union symbol. In fact, any garbage (or nothing at all) can go between intervals. It makes sure open/closed parts of intervals are correct, unless you don't like that. To have it ignore the difference between open and closed endpoints, use

` interval_cmp("(2, 3] U(7, 11)", sloppy=>'yes')`

interval_cmp uses num_cmp on the endpoints. You can pass optional arguments for num_cmp, so to change the tolerance, you can use

` interval_cmp("(2, 3] U(3+4, 11)", relTol=>3)`

The intervals can be listed in any order, unless you want to force a particular order, which is signaled as

` interval_cmp("(2, 3] U(3+4, 11)", ordered=>'strict')`

You can specify infinity as an endpoint. It will do a case-insensitive string match looking for I, Infinity, Infty, or Inf. You can prepend a + or -, as in

` interval_cmp("(-inf, 3] U [e^10, infinity)")`

or

` interval_cmp("(-INF, 3] U [e^10, +I)")`

If the question might have an empty set as the answer, you can use the strings option to allow for it. So

` interval_cmp("$ans", strings=>['empty'])`

will not generate an error message if the student enters the string empty. Better still, it will mark a student answer of "empty" as correct iff this matches $ans.

You can use interval_cmp for ordered pairs, or lists of ordered pairs. Internally, this is just a distinction of whether to put nice union symbols between intervals, or commas. To get commas, use

` interval_cmp("(1,2), (2,3), (4,-1)", unions=>'no')`

Note that interval_cmp makes no attempt at simplifying overlapping intervals. This becomes an important feature when you are really checking lists of ordered pairs.

Now we use the Parser package for checking intervals (or lists of points if unions=>'no'). So, one can specify the Parser options showCoordinateHints, showHints, partialCredit, and/or showLengthHints as optional arguments:

` interval_cmp("(1,2), (2,3), (4,-1)", unions=>'no', partialCredit=>1)`

Also, set differences and 'R' for all real numbers now work too since they work for Parser Intervals and Unions.

Checks an answer which is a comma-separated list of numbers. The actual numbers are fed to num_cmp, so all of the flexibilty of num_cmp carries over (values can be expressions to be evaluated). For example,

` number_list_cmp("1, -2")`

will accept "1, -2", "-2, 1", or "-1-1,sqrt(1)".

` number_list_cmp("1^2 + 1, 2^2 + 1, 3^2 + 1", ordered=>'strict')`

will accept "2, 5, 10", but not "5, 2, 10".

If you want to allow complex number entries, complex=>'ok' will cause it to use cplx_cmp instead:

` number_list_cmp("2, -2, 2i, -2i", complex=>'ok')`

In cases where you set complex=>'ok', be sure the problem file loads PGcomplexmacros.pl.

Optional arguements for num_cmp (resp. cplx_cmp) can be used as well, such as

` number_list_cmp("cos(3), sqrt(111)", relTol => 3)`

The strings=>['hello'] argument is treated specially. It can be used to replace the entire answer. So

` number_list_cmp("cos(3), sqrt(111)", strings=>['none'])`

will mark "none" wrong, but not generate an error. On the other hand,

` number_list_cmp("none", strings=>['none'])`

will mark "none" as correct.

One can also specify optionnal arguments for Parser's List checker: showHints, partialCredit, and showLengthHints, as in:

` number_list_cmp("cos(3), sqrt(111)", partialCredit=>1)`

Compares an equation. This really piggy-backs off of fun_cmp. It looks at LHS-RHS of the equations to see if they agree up to constant multiple. It also guards against an answer of 0=0 (which technically gives a constant multiple of any equation). It is best suited to situations such as checking the equation of a line which might be vertical and you don't want to give that away, or checking equations of ellipses where the students answer should be quadratic.

Typical invocation would be:

` equation_com("x^2+(y-1)^2 = 11", vars=>['x','y'])`