Re: InverseFunction[]
- To: mathgroup at smc.vnet.net
- Subject: [mg42006] Re: InverseFunction[]
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Mon, 16 Jun 2003 03:57:34 -0400 (EDT)
- Organization: The University of Western Australia
- References: <bbt23g$nj3$1@smc.vnet.net> <bc1jh1$bjp$1@smc.vnet.net> <200306110749.DAA02507@smc.vnet.net> <bc7pet$6f0$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bc7pet$6f0$1 at smc.vnet.net>, Murray Eisenberg <murray at math.umass.edu> wrote: > What does "knows about" mean in your answer? Evidently Mathematica > knows a NAME (ProductLog) for the inverse function and can evaluate it > numerically. And it knows (some) algebraic properties of ProductLog. For example, it knows how to differentiate and integrate it. > But what is the definition of the function as Mathematica knows it? I do not understand your question. What is the definition of _any_ function in Mathematica? E.g., can you tell me what is the definition of Sin (in Mathematica)? Further, InverseFunction[Sin] yields ArcSin and Mathematica "knows about" ArcSin in the sense that it can evaluate it numerically _and_ algebraically. > Reply to "REPLY TO" address and NOT to the "FROM" address!! > Otherwise I will never see your reply!!!!!!!!!!!!!!!!!!!!!! I don't understand this: According to the message headers I get, your "REPLY TO" and "FROM" addresses are identical? Cheers, Paul > Paul Abbott wrote: > > In article <bc1jh1$bjp$1 at smc.vnet.net>, > > wself at msubillings.edu (Will Self) wrote: > > > > > >>You can easily write down a function which has an inverse, but the > >>inverse cannot be expressed in closed form, or in symbols that anyone > >>has invented. For example, f[x_]= x*E^x. This function is increasing > >>on (for example) the interval [1,3], therefore an inverse exists, at > >>least for 1 <= x <= 3. But (as far as I know) this inverse function > >>has no name. > > > > > > Your point is valid. However, try Solve[x*E^x == y, x] and you'll see > > Mathematica knows about the inverse function for your example. > > > > Cheers, > > Paul > > > > -- > > Murray Eisenberg murray at 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 -- Paul Abbott Phone: +61 8 9380 2734 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul
- References:
- Re: InverseFunction[]
- From: Paul Abbott <paul@physics.uwa.edu.au>
- Re: InverseFunction[]