NAME

Macros for complex numbers for the PG language

SYNPOSIS

DESCRIPTION

cplx_cmp

#      This subroutine compares complex numbers.
#      Available prefilters include:
#      each of these are called by cplx_cmp( answer, mode => '(prefilter name)' )
#      'std'                   The standard comparison method for complex numbers. This option it the default
#                              and works with any combination of cartesian numbers, polar numbers, and
#                              functions. The default display method is cartesian, for all methods, but if
#                              the student answer is polar, even in part, then their answer will be displayed
#                              that way.
#      'strict_polar'          This is still under developement. The idea is to check to make sure that there
#                              only a single term in front of the e and after it... but the method does not
#                              check to make sure that the i is in the exponent, nor does it handle cases
#                              where the polar has e** coefficients.
#      'strict_num_cartesian'  This prefilter allows only complex numbers of the form "a+bi" where a and b
#                              are strictly numbers.
#      'strict_num_polar'      This prefilter allows only complex numbers of the form "ae^(bi)" where a and b
#                              are strictly numbers.
#      'strict'                This is a combination of strict_num_cartesian and strict_num_polar, so it
#                              allows complex numbers of either the form "a+bi" or "ae^(bi)" where a and b
#                              are strictly numbers.

compare_cplx

#      This is a filter: it accepts and returns an AnswerHash object.
#
#              Usage:  compare_cplx(ans_hash, %options)
#
#      Compares two complex numbers by comparing their real and imaginary parts

multi_cmp

#      
#      Checks a comma separated string of  items against an array of evaluators.
#      For example this is useful for checking all of the complex roots of an equation.
#      Each student answer must be evaluated as correct by a DISTINCT answer evalutor.
#      
#      This answer checker will only work reliably if each answer checker corresponds
#      to a distinct correct answer.  For example if one answer checker requires
#      any positive number, and the second requires the answer 1, then 1,2 might
#      be judged incorrect since 1, satisifes the first answer checker, but 2 doesn't
#      satisfy the second.  2,1 would work however. Avoid this type of use!!
#      
#      Including backtracking to fit the answers as best possible to each answer evaluator
#      in the best possible way, is beyond the ambitions of this evaluator.

Utility functions

#      for checking the form of a number or of the C<student_ans> field in an answer hash

single_term()

#      This subroutine takes in a string, which is a mathematical expresion, and determines whether or not
#      it is a single term. This is accoplished using a stack. Open parenthesis pluses and minuses are all
#      added onto the stack, and when a closed parenthesis is reached, the stack is popped untill the open
#      parenthesis is found. If the original was a single term, the stack should be empty after
#      evaluation. If there is anything left ( + or - ) then false is returned.
#      Of course, the unary operator "-" must be handled... if it is a unary operator, and not a regular -
#      the only place it could occur unambiguously without being surrounded by parenthesis, is the very
#      first position. So that case is checked before the loop begins.