[R] The "**" exponentiation operator.

Sat Aug 30 20:32:35 CEST 2025

You may be kidding, Spencer, but there already is a multiplication extension using a single asterisk to signify matrix multiplication using %*% as the multiplication operator is not overloaded to do something when both operands are of type matrix.

But for real clarity, you are allowed text so rather than %**% it might make sense to make a longer but self-documenting %exponentiate_by% as in

`%exponentiate_by%` <- function(base, power) base^power

Now here is code showing the use:

e <- 2.718281828
i <- complex(real = 0, imaginary= -1)
# pi is already built-in to R

minus_one  <- e %exponentiate_by% (pi * i)

On my machine, the result is close enough to minus one:

> e %exponentiate_by% (pi * i)
[1] -1-5.305313e-10i

But, of course, once you play some games, you can skip making inline operations and just use a normal function version.
-----Original Message-----
From: Spencer Graves <spencer.graves using effectivedefense.org> 
Sent: Saturday, August 30, 2025 9:38 AM
To: avi.e.gross using gmail.com; 'Richard O'Keefe' <raoknz using gmail.com>; 'Leo Mada' <leo.mada using syonic.eu>
Cc: 'Leo Mada via R-help' <r-help using r-project.org>
Subject: Re: [R] The "**" exponentiation operator.

How about:

"%**%" <- function(x, y)x^y

2%**%3

spencer graves ;-)

On 8/30/25 08:23, avi.e.gross using gmail.com wrote:
> Richard,
> 
> As noted, we have had a history of computer languages using a very small number of symbols to do too many things. A few languages like APL sort of created new symbols by overwriting. Some simply used functions rather than symbols. And, I note languages like C used asterisk to mean very different things like following a pointer in concise but not trivial code as in how to copy a null terminated character string:
> 
> while (*p++ = *q++)
> 
> If you had a pointer to a pointer to a pointer to a pointer, you could see code with many stars and often many parentheses.
> 
> As for your suggestion, I think you need to consider the people who have to create a compiler or interpreter to handle the requirements. I am sure it is doable in some ways but I suggest care. Many languages accept octal or hexadecimal notation and thus a number like 2A is allowed but since this can lead to ambiguous situations, often a x must be prepended as a sort of special case. In such a language, you might not want to use x or X OR you may insist on whitespace around it as compared to other operators that need nonw. And, need I say that x is a very common variable name.
> 
> Back to R, it is what it is and if someone designs yet another new language in x decades, who knows what they will come up with that may be hodgepodge of features and ways from R and python and ... and will have so many features and ways that no one person or group knows it all as it will include use of thousands of symbols from something like UNICODE.
> 
> For now, if we use R, we have what we have and we will make mistakes. Anyone here think there can be problems if someone creates read_csv() as their version of read.csv() and some people use the wrong one, ...?
> 
> 
> 
> 
> -----Original Message-----
> From: R-help <r-help-bounces using r-project.org> On Behalf Of Richard O'Keefe
> Sent: Saturday, August 30, 2025 3:09 AM
> To: Leo Mada <leo.mada using syonic.eu>
> Cc: Leo Mada via R-help <r-help using r-project.org>
> Subject: Re: [R] The "**" exponentiation operator.
> 
> I did mathematics up to University level and finally petered out at
> Category Theory, which I never got the hang of.
> Here's the fun: I *never* saw the asterisk used for multiplication in
> my mathematics or physics courses.
> And I never saw any operator at all used for exponentiation.
> Asterisk was a superscript operator for conjugation or duals.  Had
> nothing to do with products.
> 
> Fortran COBOL, and PL/I used. and still use, * for multiplication and
> ** for exponentiation.
> APL used × for multiplication and * for exponentiation.
> 
> Could I recommend that R allow × as a synonym for * ?  It has been the
> mathematical sign for
> multiplication for >400 years, when a sign is used, and it's been
> available on computers for decades.
> 
> On Sat, 30 Aug 2025 at 03:05, Leo Mada via R-help <r-help using r-project.org> wrote:
>>
>> Dear Rolf,
>>
>> I join this discussion a little bit late.
>>
>> Indeed, the '**' operator is a very poor choice for exponentiation. I can give some examples to justify my claim. Notice that '**' and '*' would almost always get mixed in real mathematics.
>>
>> Fortunately, I am used to "^"; otherwise, I would have had a very hard time to  debug the *monster*:
>> https://github.com/discoleo/R/blob/master/Math/Poly.System.S5.Ht.Formulas.Derivation.Coeffs.R
>>
>> Those are the coefficients of a polynomial of order 7 (see below for further information). And I have plenty of examples.
>>
>> Unfortunately, some "programming" languages mix '*' and '**'; which makes any work with polynomials a nightmare!
>>
>> I "found" something on this topic - hope everyone gets a little bit amused:
>> https://github.com/discoleo/R/blob/master/Math.NewTerminology.wiki
>>
>> Sincerely,
>>
>> Leonard
>>
>> ===========
>> Regarding the *Monster*:
>>
>> It enables to solve a particular system with 5 variables with cyclic symmetry:
>> x1+x2+x3+x4+x5 = R1
>> # Note: this is NOT the full E2
>> x1*x2+x2*x3+x3*x4+x4*x5+x5*x1 = R2
>> E3 = R3
>> E4 = R4
>> E5 (= x1*x2*x3*x4*x5) = R5;
>>
>> This system can be transformed into a system that can be solved using a polynomial of lower order than the original system.
>>
>> Unfortunately, I do not have a methemtical theory yet for the Ht5 System. I worked it out the hard way; it is almost finished, but I did not have any more time during the last 2 years.
>>
>> For some (very) basic details, see:
>> https://github.com/discoleo/R/blob/master/Math/Poly.System.md
>>
>> Again, I did not have time to write anything more thoroughly.
>>
>>
>>          [[alternative HTML version deleted]]
>>
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> 
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
> ______________________________________________
> R-help using r-project.org mailing list -- To UNSUBSCRIBE and more, see
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide https://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.