# /home/jaubrey/webwork//pg_TRUNK/macros/PGcomplexmacros.pl

### From WeBWorK

# 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 <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. =cut

sub single_term{ my $term = shift; my @stack; $term = reverse $term; if( length $term >= 1 ) { my $temp = chop $term; if( $temp ne "-" ){ $term .= $temp; } } while( length $term >= 1 ){ my $character = chop $term; if( $character eq "+" || $character eq "-" || $character eq "(" ){ push @stack, $character; }elsif( $character eq ")" ){ while( pop @stack ne "(" ){} } } if( scalar @stack == 0 ){ return 1;}else{ return 0;} }

# changes default to display as a polar sub fix_for_polar_display{ my ($rh_ans, %options) = @_; if( ref( $rh_ans->{student_ans} ) =~ /Complex/ && $rh_ans->{answer_form} eq 'polar' ){ $rh_ans->{student_ans}->display_format( 'polar'); ## these lines of code have the polar displayed as re^(theta) instead of [rho,theta] $rh_ans->{student_ans} =~ s/,/*e^\(/; $rh_ans->{student_ans} =~ s/\[//; $rh_ans->{student_ans} =~ s/\]/i\)/; } $rh_ans; }

# this does not seem to be in use, so I'm commenting it out. Mike Gage 6/27/05

# sub cplx_cmp2 { ####.............########### # }

# this does not seem to be in use, so I'm commenting it out. Mike Gage 6/27/05

# sub cplx_cmp_mult { ####.............########### # }

# this does not seem to be in use, so I'm commenting it out. Mike Gage 6/27/05

# sub answer_mult{ ####.............########### # } # # sub multi_cmp_old{ ####.............########### # }

# this does not seem to be in use, so I'm commenting it out. Mike Gage 6/27/05

# sub mult_cmp{ ####.............########### # }

1;