inverse hyperbolic function
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Re: inverse hyperbolic function
 
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2011/4/22 Ken G. Brown <[hidden email]>:
> At 12:58 AM +0200 4/22/11, Nicolas Cellier apparently wrote: >>2011/4/22 Ken G. Brown <[hidden email]>: >><snip> >> >>>> >>>>>> "H" is much better than "h". >>>>>> >>>>>> - Bert - >> >>>> >>>>> >>>>> -1 >>>>> Not according to Wolfram. They suggest lower case 'h'. >>>>> >>>>> Ken, >>>>> from my iPhone >>>> >>>> So what? Wolfram's use of "arc" for the hyperbolic inverse is wrong too, as Nicolas pointed out. >>>> >>>> - Bert - >>>> >>> >>> So let's pretend Wolfram knows something about mathematical notation. >>> >>> Ken >>> >>> >> >>Thinking of Wolfram as a God is Religion and there is nothing to >>debate in this case. >>But thinking of Wolfram as a human creation helps exercizing rational >>skeptical inquiry. >> >>Until someone exhibits a good rationale for employing arcus, it will be area. >> >>Nicolas > > No one is saying Wolfram is a God, I am just saying that he is an authority on mathematical programming. > Mathematica is very successful, and based on sound mathematical principles. > If you do not want to accept Wolfram as an authority, that's up to you I suppose. > If I can't disagree with an authority then it must be God. Maybe it will sound anarchist, but I recognize Mathematica as a reference, not as an authority. > I also see Maple uses arcsinh etc. > Oh yes, even Axiom, I'm very disappointed ! > Mathematica and Maple are two of the main mathematical programs out there. > I see no real useful purpose in going against their standards. > And I think you will be hard pressed to find 'H' in the notation for inverse hyperbolic functions in math textbooks. > > Ken > Certainly, neither postfixed notation, x cosH, so at the end I'm not sure it matters that much. Look, Mathematica and Axiom don't agree on casing ArcSinh vs arcsinh, why would we have to ? Nicolas |
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At 1:48 AM +0200 4/22/11, Nicolas Cellier apparently wrote:
>2011/4/22 Ken G. Brown <[hidden email]>: >> At 12:58 AM +0200 4/22/11, Nicolas Cellier apparently wrote: >>>2011/4/22 Ken G. Brown <[hidden email]>: >>><snip> >>> >>>> >>>>>>> "H" is much better than "h". >>>>>>> >>>>>>> - Bert - >>> >>>> >>>>>> >>>>>> -1 >>>>>> Not according to Wolfram. They suggest lower case 'h'. >>>>>> >>>>>> Ken, >>>>>> from my iPhone >>>>> >>>>> So what? Wolfram's use of "arc" for the hyperbolic inverse is wrong too, as Nicolas pointed out. >>>>> >>>>> - Bert - >>>>> >>>> >>>> So let's pretend Wolfram knows something about mathematical notation. >>>> >>>> Ken >>>> >>>> >>> >>>Thinking of Wolfram as a God is Religion and there is nothing to >>>debate in this case. >>>But thinking of Wolfram as a human creation helps exercizing rational >>>skeptical inquiry. >>> >>>Until someone exhibits a good rationale for employing arcus, it will be area. >>> >>>Nicolas >> >> No one is saying Wolfram is a God, I am just saying that he is an authority on mathematical programming. >> Mathematica is very successful, and based on sound mathematical principles. >> If you do not want to accept Wolfram as an authority, that's up to you I suppose. >> > >If I can't disagree with an authority then it must be God. >Maybe it will sound anarchist, but I recognize Mathematica as a >reference, not as an authority. > >> I also see Maple uses arcsinh etc. >> > >Oh yes, even Axiom, I'm very disappointed ! > >> Mathematica and Maple are two of the main mathematical programs out there. >> I see no real useful purpose in going against their standards. >> And I think you will be hard pressed to find 'H' in the notation for inverse hyperbolic functions in math textbooks. >> >> Ken >> > >Certainly, neither postfixed notation, x cosH, so at the end I'm not >sure it matters that much. >Look, Mathematica and Axiom don't agree on casing ArcSinh vs arcsinh, >why would we have to ? > >Nicolas My point of view is to try to make your mathematical functions look the way they are most commonly used in math. I used Mathematica and Maple as two examples of mathematical programming systems. Sure, you can symbolize them any way you want, but why not the way they are most commonly? Ken |
[OT] Re: [squeak-dev] inverse hyperbolic function
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In reply to this post by Levente Uzonyi-2
At 1:43 AM +0200 4/22/11, Levente Uzonyi apparently wrote:
>On Thu, 21 Apr 2011, Ken G. Brown wrote: > >>No one is saying Wolfram is a God, I am just saying that he is an authority on mathematical programming. >>Mathematica is very successful, and based on sound mathematical principles. >>If you do not want to accept Wolfram as an authority, that's up to you I suppose. >> >>I also see Maple uses arcsinh etc. >> >>Mathematica and Maple are two of the main mathematical programs out there. >>I see no real useful purpose in going against their standards. >>And I think you will be hard pressed to find 'H' in the notation for inverse hyperbolic functions in math textbooks. > >Should we do everything like VW or Gemstone, just because those are the successful commercial smalltalk implementations nowadays? No. So why should we follow the conventions of the two successful commercial computer algebra systems? And what about Matlab? That's also a "main mathematical program", isn't it? I'm basically saying go with the most commonly used conventions of mathematics. I think Mathematica has tried to do that and has documented it well. If the function in mathematics is commonly arcsinh, then I'm thinking it should be arcsinh in Squeak, and not redefined in some other somewhat arbitrary way with camelcase. Ken > >Levente > >> >>Ken |
Re: [OT] Re: [squeak-dev] inverse hyperbolic function
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On 22.04.2011, at 02:18, Ken G. Brown wrote: > At 1:43 AM +0200 4/22/11, Levente Uzonyi apparently wrote: >> On Thu, 21 Apr 2011, Ken G. Brown wrote: >> >>> No one is saying Wolfram is a God, I am just saying that he is an authority on mathematical programming. >>> Mathematica is very successful, and based on sound mathematical principles. >>> If you do not want to accept Wolfram as an authority, that's up to you I suppose. >>> >>> I also see Maple uses arcsinh etc. >>> >>> Mathematica and Maple are two of the main mathematical programs out there. >>> I see no real useful purpose in going against their standards. >>> And I think you will be hard pressed to find 'H' in the notation for inverse hyperbolic functions in math textbooks. >> >> Should we do everything like VW or Gemstone, just because those are the successful commercial smalltalk implementations nowadays? No. So why should we follow the conventions of the two successful commercial computer algebra systems? And what about Matlab? That's also a "main mathematical program", isn't it? > > I'm basically saying go with the most commonly used conventions of mathematics. I think Mathematica has tried to do that and has documented it well. > If the function in mathematics is commonly arcsinh, then I'm thinking it should be arcsinh in Squeak, and not redefined in some other somewhat arbitrary way with camelcase. > > Ken As previously pointed out, Mathematica actually uses CamelCase. If Mathematica can use two capital letters, we are allowed to, too, yes? ;) I think Nicolas should decide. He has done the most for math support in Squeak over the last years. He probably is implementing it right now anyway ... - Bert - |
Re: inverse hyperbolic function
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In reply to this post by Levente Uzonyi-2
On Fri, Apr 22, 2011 at 12:00:33AM +0200, Levente Uzonyi wrote:
> On Thu, 21 Apr 2011, Ken G. Brown wrote: > > >On 2011-04-21, at 15:16, Bert Freudenberg <[hidden email]> wrote: > > > >> > >>On 21.04.2011, at 23:01, Levente Uzonyi wrote: > >> > >>>On Thu, 21 Apr 2011, Frank Shearar wrote: > >>> > >>>>On 2011/04/21 21:18, Bert Freudenberg wrote: > >>>>>On 21.04.2011, at 21:24, Nicolas Cellier wrote: > >>>>>>Just a question of language: how to name them in English ? > >>>>>>Using asinh acosh atanh like any other programming language do would > >>>>>>be that simple... > >>>>>>But Smalltalk did not follow that path and didn't implement asin acos > >>>>>>atan... > >>>>>>In French, inverse hyperbolic functions are named like this > >>>>>>argument sinus hyperbolique (argsh ou argsinh) > >>>>>>http://fr.wikipedia.org/wiki/Fonction_hyperbolique#Argument_tangente_hyperbolique > >>>>>>So I decided to use argSinh argCosh argTanh quite naturally (like we > >>>>>>have arcSin arcCos arcTan). > >>>>>>However I'm not sure English has same conventions. Can someone > >>>>>>enlighten me? > >>>>>>Nicolas > >>>>>How about hypSin, hypArcSin, etc.? Alternatively, sinHyp, arcSinHyp. > >>>>>This would fit the existing theme better, since we use arcSin where > >>>>>others use asin, etc. Just appending an "h" looks odd. > >>>> > >>>>Heh, I think appending an "h" looks exactly right :) > >>>> > >>>>http://mathworld.wolfram.com/InverseHyperbolicCosine.html for instance > >>>>uses "arccosh". > >>> > >>>+1 :) > >>> > >>>Actually searching my image with the message names browser for > >>>'arcSinH', I found the following: > >>>arcSinH > >>>testArcSinH > >>>testArcSinHStd > >> > >>"H" is much better than "h". > >> > >>- Bert - > >> > > > >-1 > >Not according to Wolfram. They suggest lower case 'h'. > > Since arccosh is an abbreviation of arcus cosinus hyperbolicus, the > camelcase version should be arcCosH. Just as a data point: As a native speaker of American English with a typically weak education in mathematics, "arcCosH" seems good to me. If I were to look for this in a method finder, I would probably be looking for "cos" and "arccos" (not acos). I would not know or remember the actual meaning of the function, and I definitely would not be aware of the origins of the name. But I would be very pleased if I were able to find it in a method finder and then see a method comment that explained the "arcus cosinus hyperbolicus" derivation along with a brief description of the function. Wolfram as a reference makes sense to me, although I do like the upper case "H" to indicate that the name is derived from three words. Before writing this reply, I did a "man arccos" on my unix box, expecting to see a man page. Actually it is "acos", but I did not know that. So for whatever reason, my intuitive expectation was that I would find a function named "arccos" and this is probably the same thing I would have searched for in a Squeak method finder. I am not advocating anything (I would prefer to have it named by someone with a real mathematical background, not me), so this is just feedback as to what "sounds good" to one American English speaker. Dave |
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In reply to this post by Levente Uzonyi-2
Since arccosh is an abbreviation of arcus cosinus hyperbolicus, the camelcase version should be arcCosH.+2 asinh - most "not incorrect" for all options +1 arsinh - most correct mathematically -1 any camelcase A newcomer looking in... (*1) camelCase is for the concatenation of individual words. However the short form of these mathematical functions have gained an identity of their own in common usage. From Smalltalk's perspective, arccosh is an individual word that does not need camelcase. Camelcase would seem appropriate only if it was to be called by its full name arcusCosinusHyperbolicus. The prinicipal of least surprise for newcomers would be to not use camelcase in this instance. Old timers would know already better know where to look, or ask. That aside, the discussion at wikipedia[1] is enlightning... (assumedly by people who care about such things)
google results (top contenders are a near thing.) arcsinh 110,000 asinh 106,000 arsinh 28,000 argsinh 2,570 hope that helps [1] http://en.wikipedia.org/wiki/Talk:Hyperbolic_function#Names_of_inverses (*1) If, as I hope to get move involved (time permitting) rather than just lurking, it will be interesting to track how long I feel the need for such disclaimers. *grin* |
Re: inverse hyperbolic function
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In reply to this post by Ken G. Brown
On 2011/04/22 00:19, Ken G. Brown wrote:
> At 12:58 AM +0200 4/22/11, Nicolas Cellier apparently wrote: >> 2011/4/22 Ken G. Brown<[hidden email]>: >> <snip> >>>>>> >>>>>> "H" is much better than "h". >>>>>> >>>>>> - Bert - >>>>>> >>>>> >>>>> -1 >>>>> Not according to Wolfram. They suggest lower case 'h'. >>>>> >>>>> Ken, >>>>> from my iPhone >>>> >>>> So what? Wolfram's use of "arc" for the hyperbolic inverse is wrong too, as Nicolas pointed out. >>>> >>>> - Bert - >>>> >>> >>> So let's pretend Wolfram knows something about mathematical notation. >>> >>> Ken >>> >>> >> >> Thinking of Wolfram as a God is Religion and there is nothing to >> debate in this case. >> But thinking of Wolfram as a human creation helps exercizing rational >> skeptical inquiry. >> >> Until someone exhibits a good rationale for employing arcus, it will be area. >> >> Nicolas > > No one is saying Wolfram is a God, I am just saying that he is an authority on mathematical programming. > Mathematica is very successful, and based on sound mathematical principles. > If you do not want to accept Wolfram as an authority, that's up to you I suppose. Well. It's actually Eric Weisstein; Wolfram the _company_ merely hosts the site and employs Weisstein. Furthermore, mathworld doesn't invent this stuff; it makes enormous numbers of references to mathematical literature, and points out when notations are confused (as they often are, in mathematics). We should use the most commonly used terminology, and mimic in our code what actual mathematicians use, because otherwise we are, for no good reason, making life difficult for the users of our code. Making up names is just annoying. This whole thread's turned into a bikeshed. Nicolas, you know better than anyone else here what the names should be, given your training. frank > I also see Maple uses arcsinh etc. > > Mathematica and Maple are two of the main mathematical programs out there. > I see no real useful purpose in going against their standards. > And I think you will be hard pressed to find 'H' in the notation for inverse hyperbolic functions in math textbooks. > > Ken > > > |
Re[2]: [squeak-dev] inverse hyperbolic function
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In reply to this post by Nicolas Cellier
Hi Nicolas,
NC> Yes I saw that, thanks, it's just that it sounds incorrect to French ears... NC> It should also sound incorrect to English ones because the inverse NC> function does not measure an arc of hyperbole, but rather the area of NC> a sector of hyperbole. fwiw, that's how i learned at (a German) school: arcsin and arsinh cheers, Herbert |
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In reply to this post by Nicolas Cellier
With respect to the camelcase question only, I think we can look at it from
two directions. A Smalltalk programmer looking to do some math work would expect to find the functions implemented in methods with camelcase names. A math person, new to Smalltalk would expect to find the functions implemented in methods with names commonly used for math. Can we have both (I know that might be a lot of work). Implement with what ever naming convention you prefer and in a loadable package implement with the other naming convention as extensions that call the methods named in the main package. I apologize in advance for possibly adding to anyone's work load. Lou ----------------------------------------------------------- Louis LaBrunda Keystone Software Corp. SkypeMe callto://PhotonDemon mailto:[hidden email] http://www.Keystone-Software.com |
Re: inverse hyperbolic function
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Thanks everybody for your answers.
I abandon argSh because mostly French and don't translate well in English. I abandon sh because there is no reason to abbreviate that much (again mostly a French usage). Basically there are two choices to make - arcus (arc) vs area (ar) or just a (stdlib, matlab etc...) - lowercase or camelCase I abandon arcus because not correct, though it seems widely used, even by computer algebra references (hey, I think they copy each other). My point is that Smalltalk goal is primarily to educate. By homogeneity with arcSin I abandon asinh... We don't have asin, no reason to abbreviate that much. By homogeneity with already existing arcSin I will also choose camelCase. Between arSinh and areaSinh I choose arSinh because a bit more standard (recommended by an ISO 31-11) Also, if sine and hyperbolic are abbreviated, why wouldn't area? Now, the question of the final H or h remains sinH cosH tanH arSinH arCosH arTanH Or: sinh cosh tanh arSinh arCosh arTanh Though H would be more correct since clearly belonging to another word, I personnally find it unaesthetic (maybe just because I'm not used to it ?) Also it would make Smalltalk choice different from any other language for a minor reason. Using sinHyp and arSinHyp as Bert suggested would equilibrate the camelCasing, but would put us a bit further off the standards. So my preference is for keeping sinh (but sinH would not hurt me that much...) Nicolas 2011/4/22 Louis LaBrunda <[hidden email]>: > With respect to the camelcase question only, I think we can look at it from > two directions. A Smalltalk programmer looking to do some math work would > expect to find the functions implemented in methods with camelcase names. A > math person, new to Smalltalk would expect to find the functions > implemented in methods with names commonly used for math. > > Can we have both (I know that might be a lot of work). Implement with what > ever naming convention you prefer and in a loadable package implement with > the other naming convention as extensions that call the methods named in > the main package. > > I apologize in advance for possibly adding to anyone's work load. > > Lou > ----------------------------------------------------------- > Louis LaBrunda > Keystone Software Corp. > SkypeMe callto://PhotonDemon > mailto:[hidden email] http://www.Keystone-Software.com > > > |
Re: inverse hyperbolic function
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On 2011/04/22 22:05, Nicolas Cellier wrote:
> Thanks everybody for your answers. > > I abandon argSh because mostly French and don't translate well in English. > I abandon sh because there is no reason to abbreviate that much (again > mostly a French usage). > > Basically there are two choices to make > - arcus (arc) vs area (ar) or just a (stdlib, matlab etc...) > - lowercase or camelCase > > I abandon arcus because not correct, though it seems widely used, even > by computer algebra references (hey, I think they copy each other). > My point is that Smalltalk goal is primarily to educate. > > By homogeneity with arcSin I abandon asinh... We don't have asin, no > reason to abbreviate that much. > By homogeneity with already existing arcSin I will also choose camelCase. > > Between arSinh and areaSinh I choose arSinh because a bit more > standard (recommended by an ISO 31-11) > Also, if sine and hyperbolic are abbreviated, why wouldn't area? > > Now, the question of the final H or h remains > > sinH cosH tanH > arSinH arCosH arTanH > > Or: > > sinh cosh tanh > arSinh arCosh arTanh > > Though H would be more correct since clearly belonging to another word, > I personnally find it unaesthetic (maybe just because I'm not used to it ?) > Also it would make Smalltalk choice different from any other language > for a minor reason. > > Using sinHyp and arSinHyp as Bert suggested would equilibrate the > camelCasing, but would put us a bit further off the standards. > So my preference is for keeping sinh (but sinH would not hurt me that much...) > > Nicolas I certainly appreciate the depth of thought you've put into naming things, Nicolas! Of the two options I'd vote for sinh / arSinh, mainly because that's closer to what I've seen in my maths textbooks. frank > 2011/4/22 Louis LaBrunda<[hidden email]>: >> With respect to the camelcase question only, I think we can look at it from >> two directions. A Smalltalk programmer looking to do some math work would >> expect to find the functions implemented in methods with camelcase names. A >> math person, new to Smalltalk would expect to find the functions >> implemented in methods with names commonly used for math. >> >> Can we have both (I know that might be a lot of work). Implement with what >> ever naming convention you prefer and in a loadable package implement with >> the other naming convention as extensions that call the methods named in >> the main package. >> >> I apologize in advance for possibly adding to anyone's work load. >> >> Lou >> ----------------------------------------------------------- >> Louis LaBrunda >> Keystone Software Corp. >> SkypeMe callto://PhotonDemon >> mailto:[hidden email] http://www.Keystone-Software.com >> >> >> > > > |
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