Raymond Hettinger wrote: > Frequency of usage: Math provides ∑ and ∏ because they are common. It > doesn't provide a special operator for sqrt(c**2 - b**2) because the latter > is less fundamental and less common.
Here's some more information. Below is an example of an area, where sqrt(c**2 - b**2) is both fundamental and common. And that it might be helpful for Python to provide a (named) function for this operation. Whether or not, or how, a symbolic expression should be provided is another question. This one example by itself does not refute Raymond's argument. I certainly think caution is required, in promoting the needs of one group of users at the expense of another. Best avoided, if possible. GORY DETAILS Don Knuth, in METAFONT, implemented special '++' and '+-+' operators, that he called Pythagorean addition and subtraction. The latter is precisely Raymond's sqrt(c**2 - b**2), but calculated more efficiently and accurately. This is described on page 66 of Don Knuth's METAFONT Book. https://ctan.org/tex-archive/systems/knuth/dist/mf/mfbook.tex The `^|++|' operation is called {\sl^{Pythagorean addition}\/}; $a\pyth+b$ is the same thing as $\sqrt{\stt a^2+b^2}$. Most of the ^{square root} operations in computer programs could probably be avoided if $++$ were more widely available, because people seem to want square roots primarily when they are computing distances. Notice that $a\pyth+b\pyth+c= \sqrt{\stt a^2+b^2+c^2}$; we have the identity $(a\pyth+b)\pyth+c=a\pyth+( b\pyth+c)$ as well as $a\pyth+b=b\pyth+a$. It is better to use Pythagorean addition than to calculate $\sqrt{\stt a^2+b^2}$, because the computation of $a^2$ and $b^2$ might produce numbers that are too large even when $a\pyth+b$ is rather small. There's also an inverse operation, ^{Pythagorean subtraction}, which is denoted by `^|+-+|'; the quantity $a\mathbin{+{-}+}b$ is equal to $\sqrt{\stt a^2-b^2}$. ASIDE - wikipedia In https://en.wikipedia.org/wiki/Pythagorean_addition, wikipedia using the symbol \oplus for Pythagorean addition, and does not mention Pythagorean subtraction. ASIDE- \pyth and Python Don Knuth uses \pyth as a macro (shorthand) for Pythagorean. It's got nothing to do with Python. The METAFONT book goes back to 1986, which predates Pyth-on by about 5 years. That said, Pythagoras was the founder of a new way of life, and Python is a new way of programming. -- Jonathan _______________________________________________ Python-ideas mailing list Python-ideas@python.org https://mail.python.org/mailman/listinfo/python-ideas Code of Conduct: http://python.org/psf/codeofconduct/
