Re: Series[log[x], {x, 0, 3}]
- To: mathgroup at smc.vnet.net
- Subject: [mg119269] Re: Series[log[x], {x, 0, 3}]
- From: Helen Read <readhpr at gmail.com>
- Date: Sat, 28 May 2011 07:18:46 -0400 (EDT)
- References: <irntgd$soc$1@smc.vnet.net>
This is getting way off topic, but I don't generally have occasion to write such things, and I didn't say that I never use the circle notation, rather, *almost* never. HPR On 5/27/2011 6:13 AM, Murray Eisenberg wrote: > Then how would you state in symbols the fact, say, that the standard > matrix of the composite of two linear transformations is their matrix > product? Or that the derivative of the composite f@g is (f'@g)*g' ? > Do you always write such things either in words or symbolically but with > explicit arguments? > > On 5/25/2011 7:31 PM, Helen Read wrote: >> It's definitely a matter of taste. I almost never use the circle >> notation for function composition, and I dislike the @ notation for >> similar reasons. >> >> HPR >> >> On 5/25/2011 5:55 AM, Murray Eisenberg wrote: >>> I agree that in many instances, using something of the form f@x may seem >>> at odds with traditional mathematical notation. (Although it's still >>> useful in avoiding the eye-nuisance of nested brackets in a construction >>> such as g[f[x]].) >>> >>> But something of the form g@f[x] is very natural from the viewpoint of >>> traditional mathematical notation: the "@" is reminiscent of the circle >>> operator denoting functional composition. >>> >>> Usually, using @ seems to be a matter of either stressing a particular >>> meaning or else making an expression easier to read. (Making an >>> expression easier to type is hardly ever the reason I, at least, would >>> use @.) >>> >>> On 5/24/2011 5:59 AM, Helen Read wrote: >>>> On 5/23/2011 6:24 AM, Bill Rowe wrote: >>>>> On 5/22/11 at 6:55 AM, hszhao.cn at gmail.com (Hongsheng Zhao) wrote: >>>>> >>>>> While I cannot speak for DrMajorBob, my reason for using the >>>>> notation f@x rather than f[x] is primarily readability. Constrast >>>>> >>>>> Sqrt[Abs[Sin[x]]] >>>>> >>>>> with Sqrt[Abs@Sin@x] >>>>> >>>>> Both do the same, but for me, it is easier to see what the >>>>> second form does than the first. Deeply nested brackets are more >>>>> difficult for me to read. And there is the additional factor of >>>>> less typing required for the second form. >>>> >>>> Each to his/her own. Personally I far prefer the nested brackets, which >>>> to me is more readable -- it's closer to familiar written mathematical >>>> notation, and it's clear where each function ends. >>>> >>>> And I don't see how the @ sign results in any less typing. >>>> >>>> @ requires pressing two keys simultaneously, Shift+2 >>>> >>>> [ ] requires two keys (one at a time), the [ and ] >>>> or two keys simultaneously Alt+] to get matched brackets >>>> >>>> >>> >> >> >> >> >