How can I work around this TikZ bug: (\x)^2 and \x^2 produce different results in TikZ plot?

Question

I have some files with TikZ graphics that have suddenly changed appearance since I upgraded to PGF-2.10. Here is a minimal example:

\documentclass{minimal}
\usepackage{tikz}
\begin{document}
\pgfversion\par
\begin{tikzpicture}
\draw[blue] plot[domain=-1:1] (\x,{\x^2 + \x^3});
\draw[xshift=4cm,blue] plot[domain=-1:1] (\x,{(\x)^2 + (\x)^3});
\end{tikzpicture}
\end{document}

In PGF 2.00 I had this:

while in 2.10 I have this:

The one on the left in PGF 2.10 looks like the graph of y=x^3 but could also be y=x^3 + x|x|. This has been reported on sourceforge and discussed on the pgf-users mailing list. Although I haven't checked myself yet, the bug remains open and some of the commenters below report that problems still exist in the CVS version.

Geoffrey Jones notes the bug is in the 2.00 CVS version:

Hi Matthew, not an answer, just an FYI that's too large for the comment box. My compile of your code through pgf v2.00 produces the result you see with v2.10, above:

I.e., the difference you observe seems to pre-date v2.10.

There is a workaround by inserting parentheses. But since I have so many old lecture files I'd rather find a solution that doesn't involve rewriting my TikZ code. And I'm squeamish about using the CVS bleeding edge code even if it were fixed, since I don't want to introduce other problems. Ideally I'd like a simple patch that I can stick at the preamble, or just fix one file in the PGF distro.

Answer 1

The bug ticket has been rejected on 2013-07-12, with the following comment from Till Tantau:

This is not a bug. TeX does a pure textual replacement, so {\x^2} for \x being -2 gets replaced by {-2^2}, which correctly evaluates to -4 because, indeed, the power operator takes precedence over unary negation (as it should).

What you are looking for is {(\x)^2}, which works as expected.

Answer 2

OK, here's a new improved patch for the bug (now tested in more cases):

\documentclass{minimal}
\usepackage{tikz}
\makeatletter
\def\tikz@scan@no@calculator#1(#2){%
    \patch@tikz(#2)%
    \expandafter\tikz@@scan@@no@calculator\expandafter#1\tikz@temp
    }
\def\patch@tikz(#1,#2){%
    {\expandafter\let\expandafter\save@tikz@plot@var\tikz@plot@var
     \expandafter\def\tikz@plot@var{(\save@tikz@plot@var)}%
     \xdef\tikz@temp@i{#1}%
     \xdef\tikz@temp@ii{#2}%
     }%
    \edef\tikz@temp{({\tikz@temp@i},{\tikz@temp@ii})}%
    }
\makeatother
\begin{document}
\pgfversion\par
\begin{tikzpicture}
\draw[blue,variable=\t] plot[domain=-1:1] (\t,{\t^2 + \t^3});
\draw[xshift=4cm,blue] plot[domain=-1:1] (\x,{(\x)^2 + (\x)^3});
\draw[xshift=8cm,scale=0.5,domain=-3.141:3.141,smooth,variable=\t]
plot ({\t*sin(\t r)},{\t*cos(\t r)});
\end{tikzpicture}
\end{document}

In \patch@tikz, parentheses are put around the \x (or the \t, whichever the plot variable is).

Here's part of my initial answer:

The following short code reveals the problem.

\documentclass{minimal}
\usepackage{pgf}
\begin{document}
\pgfversion\par
\pgfmathparse{-1^2}\pgfmathresult
\end{document}

In v 2.00 the result is 1.0 (which yields the correct graph!), in v 2.10 it is -1.0 (which is mathematically correct, but apparently incompatible with other pgf/TikZ components). Indeed, in the pgf-users list I linked to in a comment to the question, I find

The problem arose in an earlier version because the precedence of the prefix negation was incorrect.

So, the mathematical bug -1.0^2 = 1.0 was corrected, but the correction (naturally) lead to another bug.

Beware! Some things written in the posts at the above link are misleading. It says, e.g.,

The CVS version gives -0.008 for both -0.2^3 and (-0.2)^3

Well, of course it does. The problem only arises for even powers.

(Yet another) Edit:

The mathematical bug in PGF 2.00 also has consequences for drawing graphs: If you want -\x^2, then that's not so easy.

\draw plot[domain=-1:1] (\x,-\x^2);

and

\draw plot[domain=-1:1] (\x,{-(\x)^2});

both yield the graph of y=x^2 (for the second version this is still a miracle to me), and

\draw plot[domain=-1:1] (\x,{-\x^2});

throws an error (which I also don't understand). The workaround is to use

\draw plot[domain=-1:1] (\x,0-\x^2);

(In PGF 2.10 all 4 versions compile, but only the second version yields the correct result; with my patch all 4 versions are OK.)

Answer 3

The proposed patch in solution 1 did not work for me. It seems the problem is fixed in the CVS. The alternative patch https://tex.stackexchange.com/a/31791/14564 worked for me, I would suggest it as an alternative to the patch in solution 1.