Replace and ReplaceAll -- simple application
in [Mathematica]
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From: AES on 31 Dec 2009 03:14 In article <hhf5kg$go6$1(a)smc.vnet.net>, Murray Eisenberg <murray(a)math.umass.edu> wrote: [Re the I -> -I problem in particular:] > On the other hand, not every possible issue can be addressed immediately > at the top of documentation just because this or that user happened to > experience some difficulty with it. > > Only gathering usage statistics, or having a focus group of users trying > stuff, might suffice to escalate some issues to the point of requiring > more prominent warnings. > > I wonder how many users in fact experience this issue. I'll give you one sizable group. Engineering and science students and practitioners, at all levels down to at least college sophomores and even advanced high school students, are taught to solve systems of coupled linear differential equations (e.g., the loop or node equations for linear electrical networks with current and/or voltage sources, or forcing functions) using the phasor approach. The first step in doing this is of course to replace d^n /dt^n by (I w)^n (w as shorthand for omega), thereby converting these to coupled algebraic equations. The next step is then to solve these equations to obtain a matrix-valued transfer function or scattering matrix, whose elements contain only *real-valued* parameters (R's, L's and C's in the electrical circuit case) and I -- elements that look like R + I w L. In practice, the instructor and the students do a few problems of this type by hand, with just one or two variables; define and examine the poles and zeros of the transfer function; learn about concepts like resonance and impedance and admittance, and scattering matrices and input and output ports; and so on. But the instant one goes to anything more realistic and interesting, with three or more variables, the algebra and the numerical calculations just become too tedious. But, hey, Mathematica is just beautiful for this task. The Solve[ ] function is perfect for doing the algebra to find the transfer function -- simple, easy to understand, obvious; and all the elementary Plot functions (David Park's "set pieces") will give you all the plots you could ask for. And since the output variables are phasors, e.g. voltages and currents, vc(t) and ic(t) (generally indexed and often written with superimposed tildes to indicate that they are complex variables), you can get numerical results for power flows and energy densities using notations like p([t_] = Re[vc(t)] Re[ic(t)]. But at some point you may want to get analytical formulas as well, e.g. the modulus and argument of the transfer function from an input to an output port. And, maybe move on to the ideas of "lossless", that is, unitary, and Hermitian scattering matrices. At which point, the idea of the transfer function, call it tFunc, and its complex conjugate, tFunctStar, become significant. EE students say "v" and "vStar" and "i" and "iStar" all the time! And at that point, if you're focusing on the system properties and not specific numerical calculations it's very tempting to note that these tFunc's contain nothing but purely real circuit elements (R's. L's and C's, or masses and spring constants, or whatever), and I. And a quick test confirms that the rule {a->-a} does what it's supposed to (whether or not a has a minus sign in front of it). Or, a quick test confirms that I->-I properly converts R + I w L into R - I w L. Why shouldn't it??? It just does what you'd expect a global find and replace to do, or what you'd do "by hand" -- right? Take a look at the Mathworld entries for "phasor" and "transfer function" and see how far down you'd have to dig to get an explicit warning that the previous paragraph is misleading. (And note that the entry for "Phasor" does not contain a "SEE ALSO:" for the term "Complex Conjugation", and the link to that term within the text does not -- so far as I can see -- give any hint the the rule I->-I will fail for an expression containing -I.)
From: Murray Eisenberg on 31 Dec 2009 03:16 If you search for "atom" in the Documentation Center, the first thing you'll find is AtomQ. The term "atom", with a lower-case "a", appears in examples there. But you'll find no entry for "Atom" as a built-in symbol. AES wrote: > In article <hhc79g$2np$1(a)smc.vnet.net>, > DrMajorBob <btreat1(a)austin.rr.com> wrote: > >> -1. is a Real, hence an Atom, so it has no subordinate parts. >> >> Bobby >> > > Thanks -- except, after digging out and reading the Basic Objects > tutorial (which was useful), I think you mean "hence an atomic object"? > > Is "Atom" a defined term in Mathematica? The tutorial doesn't seem to > use it. > > [And as an aside, is the shaded table of atomic objects in this tutorial > supposed to be a *complete* list of *all* the atomic objects in > Mathematica? I'm never clear whether these shaded lists are supposed to > contain all, or just some, of the objects they illustrate.]. > -- Murray Eisenberg murray(a)math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
From: Andrzej Kozlowski on 31 Dec 2009 03:18 On 31 Dec 2009, at 02:18, Richard Fateman wrote: > Andrzej Kozlowski wrote: >> What I find kind of impressive is that there are people who find it amusing to keep posting essentially the same posts for about two decades and this despite the fact that they are being completely ignored by the developers (and there is no reason to think that anything will ever change in this respect). Masochism? > > No, I think it is not masochism. > It is an attempt to provide a useful to answer questions that come up from time to time from people who would otherwise dismiss a CAS as useless and stupid bedause they find unexplainable (to them) behavior. Useful? Funny you should mention that. "Dismiss as useless and stupid"? Its only you that keeps doing that. A remarkable example of the purest hypocrisy. Do you really think you have ever posted anything that would be useful to anyone on this forum it its entire history? Everything you have posted over the years can be quite fairly summarised as the following advice to new and naive users : Mathematica is full of "bugs", and other evil and perverse things, and worse, was created by a guy whose guts I hate, so give it up and use instead my own favourite CAS, which years ago I helped to make. Oh, and don't mind that it is practically defunct and useless nowadays. > > >> I try to move with the times so what concerns me is that my Front End is crashing too often. > > Maybe you should tie your shoelaces? > Well, this comment just shows typical shallowness of thinking and lack of knowledge and well as manners. Has it ever occurred to you that here (in Japan) people generally do not use shoelaces? Andrzej Kozlowski
From: DrMajorBob on 31 Dec 2009 03:18 [I doubt Steve is interested in all this, and he certainly won't post it... but here goes.] I think Andrzej's post (rant?) is overstated... but largely in style, not substance. I complain (rant?) quite a bit myself, but I also answer a lot of questions. I give VERY substantial offline assistance at times (sometimes without an initial post to the group), and I try to contribute positives, in general, in terms of coding style and responsiveness to beginning users. I help people understand Mathematica, whenever I can. I fully admit that Mathematica is better documented than most or all software I've worked with, despite my sometimes harsh assessment of Help deficiencies. I get annoyed at having to figure things out the hard way, and if that's what it is, that's what I call it. I sound more critical than I really am, but I have no patience for hints hidden somewhere in the docs. I want solid information, easily found. Andrzej contributes far more to the group than I do, in some ways at least, and he rarely critiques anything but outright "bugs", both of which speak well of him. I agree with Andrzej that some complainers don't contribute much to balance their criticism, but I don't believe I'm in that group. I fit, I hope, well into the middle ground between Andrzej and RJF. I also agree that most of my gripes (and many of the gripes of others) have little to do with getting things done; Andrzej ignores problems that don't matter in practice, as well he should. I frequently have to remind myself to do the same, and when I forget... there's always Andrzej! Bobby On Wed, 30 Dec 2009 17:06:30 -0600, Andrzej Kozlowski <akoz(a)mimuw.edu.pl> wrote: > > On 31 Dec 2009, at 02:18, Richard Fateman wrote: > >> Andrzej Kozlowski wrote: >>> What I find kind of impressive is that there are people who find it >>> amusing to keep posting essentially the same posts for about two >>> decades and this despite the fact that they are being completely >>> ignored by the developers (and there is no reason to think that >>> anything will ever change in this respect). Masochism? >> >> No, I think it is not masochism. >> It is an attempt to provide a useful to answer questions that come up >> from time to time from people who would otherwise dismiss a CAS as >> useless and stupid bedause they find unexplainable (to them) behavior. > > Useful? Funny you should mention that. "Dismiss as useless and stupid"? > Its only you that keeps doing that. A remarkable example of the purest > hypocrisy. > > Do you really think you have ever posted anything that would be useful > to anyone on this forum it its entire history? Everything you have > posted over the years can be quite fairly summarised as the following > advice to new and naive users : Mathematica is full of "bugs", and > other evil and perverse things, and worse, was created by a guy whose > guts I hate, so give it up and use instead my own favourite CAS, which > years ago I helped to make. Oh, and don't mind that it is practically > defunct and useless nowadays. >> >> >>> I try to move with the times so what concerns me is that my Front End >>> is crashing too often. >> >> Maybe you should tie your shoelaces? >> > > Well, this comment just shows typical shallowness of thinking and lack > of knowledge and well as manners. > Has it ever occurred to you that here (in Japan) people generally do not > use shoelaces? > > Andrzej Kozlowski -- DrMajorBob(a)yahoo.com
From: Andrzej Kozlowski on 31 Dec 2009 03:19
On 31 Dec 2009, at 09:42, DrMajorBob wrote: > I agree with Andrzej that some complainers don't contribute much to balance their criticism, but I don't believe I'm in that group. I fit, I hope, well into the middle ground between Andrzej and RJF. Actually I never mean to associate you in any way with RJF. I only replied to your post because I always feel a little sick when replying to him directly. Andrzej= |