Bug #44829 for Math-Polynomial: verbose stringize with leading -1 coeff

Thanks for your report. Stringification issues like this one are addressed in the upcoming release of Math::Polynomial. The old code for this has been replaced completely. You'll get nicer results and more control, too. Stay tuned. -Martin

"Martin Becker via RT" <bug-Math-Polynomial@rt.cpan.org> writes: Show quoted text
One form I wanted was something to cut and paste as code with nesting instead of powering, like ((($x + 1)*$x + 2)*$x) + 3 for x^3+x^2+2x+3. I got to the slightly nasty few lines below. I know there's advanced strategies for reducing operations in such an expression to eval though. Something geared towards perl could be cute. Maybe it would mean += and *= if they save a couple of cycles by being "in-place". do { my $result=$x; $result+=1; $result*=$x; ...; $result } sub to_string_for_eval { my ($poly) = @_; my $i = $poly->degree; if ($i < 0) { return '0'; } # build in @ret to avoid O(N^2) string copying from a ".=" append my @ret = (undef); my $need_parens = 0; my $open_parens = 0; my $times = ''; my $xpow = 0; { my $coeff = $poly->coeff($i); if ($coeff == 1 && $i > 0) { # just "$X" to start } elsif ($coeff == -1 && $i > 0) { my $minus = $CONFIG{MINUS}; $minus =~ tr/ //d; # no spaces on leading '-$X' push @ret, $minus; } else { push @ret, "$coeff"; # stringize $times = $CONFIG{TIMES}; } } for (;;) { $i--; my $coeff; if ($i >= 0) { $xpow++; $coeff = $poly->coeff($i); if ($coeff == 0) { next; } } if ($xpow != 0) { if ($need_parens) { $open_parens++; push @ret, ')'; } push @ret, "$times$CONFIG{VARIABLE}"; $times = $CONFIG{TIMES}; if ($xpow > 1) { push @ret, "$CONFIG{POWER}$xpow"; } $xpow = 0; } if ($i < 0) { last; } push @ret, ($coeff > 0 ? $CONFIG{PLUS}.$coeff : $CONFIG{MINUS}.-$coeff); $need_parens = 1; } $ret[0] = '(' x $open_parens; return join('', @ret); }

"Martin Becker via RT" <bug-Math-Polynomial@rt.cpan.org> writes: Show quoted text
Yes, and I'd be open to other eval strategies too. Show quoted text
Maybe a sub-module could do some things with eval strategies, either to run within the program, or to print the approach chosen as an expression or program code. I suppose for a start it might find the roots and see if there's some squared or higher terms to take out. Though that might be a bit like hard work, or might only work properly at all if coefficients are exact (integers or BigRats or whatnot). Show quoted text
I had a bit of code with a poly in a single function, and thought not to depend on a math module at runtime when I could cut and paste reasonably easily. For interest the worst one is a kind of nested job, a poly with terms which are polys themselves. sub laguerre_omitted { my ($f, $k) = @_; return $f ** ($k-2) * ((1/36*$k**2 + -1/36)*$k + ($f # f^($k-1) * ((1/4*$k + 1/4)*$k + ($f # f^$k * ((((-1/12*$k + -1/6)*$k + 3/4)*$k + 5/6) ... I calculate the terms like "(1/36*$k**2 + -1/36)*$k" in a separate slow program and it prints the slightly diabolical result to paste. The outer eval in $f is an explicit print, I was only looking at the terms in $k for Math::Polynomial to do.

On Wed May 27 19:58:22 2009, user42@zip.com.au wrote: Show quoted text
I see, but I think stuff like this should best be covered by a symbolic math package or in any case something more generic than Math::Polynomial. You'd use very similar algorithms for rational functions, for example. Show quoted text
Thanks for the background. Now I can see where a different kind of formatting would have come in handy for you. But I stand by my decision not to make this core functionality. It will be in Math::Polynomial::PrettyPrint when I get around to it. I close this ticket again, as it was mainly about a bug which has been fixed. Cheers, -Martin

"Martin Becker via RT" <bug-Math-Polynomial@rt.cpan.org> writes: Show quoted text
Some horner form printing could go in a submodule like Math::Polynomial::Horner. A separate module would keep it out of normal operations, but be more accessible than an example program. It could obey existing stringize options, plus perhaps some extras like emitting perl code with "*=" etc if that looks like being a speedup, or clearer. I might work up something like that, if you don't get to it first.