Properly add parentheses to Fraction::Value objects based on precedence.

[dpvc]

Currently, Fraction MathObjects may lose necessary parentheses when stringified or texified. For example Compute("x^(2/7)")->string; will produce x^2/7. This means that

$f = Compute("x^(2/7)");
$g = Compute("$f");

would produce $g equivalent to Compute("(x^2)/7") rather than equivalent to $f. (See this Forum post for more details.)

This PR resolves the issue by overriding the string() and TeX() methods to properly insert parentheses when needed. These are added when the operator precedences require it, or (in string()) when the original had them (since the TeX version is a vertical fraction, they are are only added when precedence requires it).

To test, use

loadMacros("PGML.pl", "contextFraction.pl");

sub LaTeX {
  my $f = shift;
  return PGML::LaTeX('\(' . $f->TeX . '\)');
};

Context("Fraction");

$f1 = Compute("x^(2/7)");
$f2 = Compute("(2/7)*x");
$f3 = Compute("2/7 x");

TEXT($f1, " has parens", $BR);
TEXT(Compute("$f1"), " has parens", $BR);
TEXT($f2, " has parens", $BR);
TEXT(Compute("$f2"), " has parens", $BR);
TEXT($f3, " has no parens", $BR);
TEXT(Compute("$f3"), " has no parens", $BR);
TEXT($HR);

$x = Formula("x");
$f = Fraction(2,7);

$f4 = $x ** $f;
$f5 = $f * $x;

TEXT($f4, " has parens", $BR);
TEXT(Compute("$f4"), " has parens", $BR);
TEXT($f5, " has no parens", $BR);
TEXT(Compute("$f5"), " has no parens", $BR);

TEXT($HR, "No parens:", $BR);
TEXT(LaTeX($f1), $BR);
TEXT(LaTeX(Compute("$f1")), $BR);
TEXT(LaTeX($f2), $BR);
TEXT(LaTeX(Compute("$f2")), $BR);
TEXT(LaTeX($f3), $BR);
TEXT(LaTeX(Compute("$f3")), $BR);

TEXT($HR, "No parens:", $BR);
TEXT(LaTeX($f4), $BR);
TEXT(LaTeX(Compute("$f4")), $BR);
TEXT(LaTeX($f5), $BR);
TEXT(LaTeX(Compute("$f5")), $BR);

[drgrice1]

Thanks for fixing this. Looks good.

[Alex-Jordan]

I tested as well, and it works as expected.

[drdrew42]

I didn't have time to deep-dive, but look at the differences between:

• Fraction(1,2) -- no Function wrapper
• Formula(Fraction(1,2)) vs Formula("1/2")
• what changes with Context('Fraction')->flags->set(reduceConstants=>0)

[Alex-Jordan]

• Making a Fraction object (Fraction(1,2) or Fraction("1/2") or Fraction(1/2)), there are no extra parens. It's only happening with Formula objects.
• Any way I make a Formula object in the Fraction context, I get extra parens. Both of these Formula(Fraction(1,2)) and Formula("1/2") end up displaying extra parens.
• You hit on something: using Context('Fraction')->flags->set(reduceConstants=>0) does leave off the excess parens. It's not a solution but that's an interesting clue.
• I tried setting the flag showExtraParens=>0, but that is not helping.

[drdrew42]

After further testing, when seeing double-parens, the outer parens are from this commit. (So in this example, $neg with reduceConstants=>1)

The parens that appear for $pos (and the inner-parens on $neg) are due to the changes in this commit: 77c45ea from #569 (stemming from issue #567)

Also note: Formula("1/2") and Formula(Fraction(1,2)) do render differently when reduceConstants=>0. (Parens appearing here are also due to that other commit...)

[drdrew42]

Furthermore, the other PR only corrects the use of input parameters to the TeX subroutine -- so presumably precedence is now actually being handled properly.

Also, look at the difference in behavior for the non-TeX strings $pos and $neg = Formula("-$pos")

MathObject $pos	reduceConstants	$pos string parens	$pos TeX parens	$neg string parens	$neg TeX parens
Formula("1/2")	Y	2	1	2	2
Formula("1/2")	N	0	0	1	0
Formula(Fraction(1,2))	Y	1	1	2	2
Formula(Fraction(1,2))	N	1	1	1	0