##########################################################
#
#  Example of the non-standard precedences as a possible alternative
#  that makes it possible to write "sin 2x" and get "sin(2x)"
#

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
  "PGbasicmacros.pl",
  "PGanswermacros.pl",
  "Parser.pl",
  "parserTables.pl",
);

TEXT(beginproblem());

##########################################################
#
#  Use standard precedences for multiplication
#

Context()->usePrecedence("Standard");

$standard = ParserTable(
   'Formula("sin 2xy/3")',
   'Formula("sin 2x y/3")',
   'Formula("sin 2x y / 3")',
   'Formula("sin 2x+5")',
   'Formula("sin x(x+1)")',
   'Formula("sin x (x+1)")',
   'Formula("1/2xy")',
   'Formula("1/2 xy")',
   'Formula("1/2x y")',
   'Formula("sin^2 x")',
   'Formula("sin^(-1) x")',
   'Formula("x^2x")',
);

Context()->usePrecedence("Non-Standard");

$nonstandard = ParserTable(
   'Formula("sin 2xy/3")',
   'Formula("sin 2x y/3")',
   'Formula("sin 2x y / 3")',
   'Formula("sin 2x+5")',
   'Formula("sin x(x+1)")',
   'Formula("sin x (x+1)")',
   'Formula("1/2xy")',
   'Formula("1/2 xy")',
   'Formula("1/2x y")',
   'Formula("sin^2 x")',
   'Formula("sin^(-1) x")',
   'Formula("x^2x")',
);



###########################################################
#
#  The problem text
#
BEGIN_TEXT
$BEGIN_ONE_COLUMN

In this problem, we compare the standard and non-standard precedences for
multiplication.
$PAR

\{Title("The Non-Standard precedences:")\}
$PAR
$nonstandard
$PAR$BR

\{Title("The Standard precedences:")\}
$PAR
$standard

$END_ONE_COLUMN
END_TEXT

###########################################################

ENDDOCUMENT();        # This should be the last executable line in the problem.