Re: FindRoots?

To Andrzej Kozlowski and MathGroup, Yes, I was too harsh in using the word "snobbery". But I feel that it is not good to let the best (the Semenov method?) be an enemy of the good (RootSearch), when the Semenov method not yet is fully implemented. You have argued for the capabilities of Reduce to find zeroes, so I wonder of course if a routine based on the Semenov method would fail in a similar way. So much better if it does not. Maybe we should ask MathGroup, if there is anyone willing to implement your demonstrations as a more general package? The code does not look too difficult, ev

Re: FindRoots?

On 9 Sep 2010, at 09:50, Ingolf Dahl wrote: > To Andrzej Kozlowski and MathGroup, > > However, in order to implement the Semenov method and to obtain provable > results, you state that there are "certain mild conditions" that must be > fulfilled. These conditions seem to be that the program needs to obtain > explicit and valid upper bounds for the first and second derivatives. The > task to find these bounds cannot be automated in a provable way in the > general case, so one problem has effectively been replaced by another. One > could put the responsibility to solve this second p

System of linear equation

Hi community, I have a system of linear equation 8x8. So I use LinearSolve but I obtain LinearSolve::matrix: Argument (<<1>>) at position 1 is not a nonempty rectangular matrix. I don't know why doesn't work this program. Please help.

Help with Solve

Hello! A newb question I'm sure... :-) Here's a couple of equations: eq1 = n*Sin[x] == (m*v^2)/r; eq2 = n*Cos[x] == m*g; The goal is to solve for 'x'. I can do this in a roundabout way via: Solve[eq1 /. Solve[eq2, n], x] I.e. solve eq2 for 'n', substitute this into eq1, and solve the result for 'x'. But this approach seems too "manual". Is there a more straightforward way to carry out the problem? I tried this: Solve[{eq1, eq2}, x] but it doesn't seem to work. What's a good way to go about this? Thanks! Ed

Re: Please help

On 7 Sep 2010, at 08:02, olfa wrote: > On 5 sep, 11:28, Andrzej Kozlowski <a...@mimuw.edu.pl> wrote: >> On 4 Sep 2010, at 10:00, olfa wrote: >> >>> Hi Mathematica Community, >> >>> Is Mathematica able to detect(recognize) implication between equations? >> >>> Thank you. >> >> Your question is not clear enough to answer with much confidence but at least Mathematica can do things like these: >> >> Assuming[x^2 + y^2 ======== 1, Refine[x^4 + 2 x^2 y^2 + y^4 ====== > ==== 1]] >> >> True >> >> or >> >> Assuming[x^2 + y^2 ======== 1, Refine[x ======== 0 || x^2 + y^2 == > ====

Re: SelectionMove[nb,Next,?Group?]

Jeremy, >From the tenor of your three questions it seems clear that you are interested in using Mathematica to both develop technical material and present it in a semi-classical style, while taking advantage of the active dynamics of Mathematica. The normal Mathematica working paradigm is Input/Output cells in a Mathematica notebook. However, this is not the paradigm for classical technical papers. Quite often the "input" part will be "boiler plate" specification that you may not be interested in showing to the reader, especially if it involves custom graphics, tables or dynamics.

Generating table of contents

Hi all, Thought I could solve this myself easily, but alas, I don't seem to be able to find the method to generate the table of contents of a Mathematica document I'm working on. Anyone knows this feauture's hideout? Cheers -- Sjoerd

Re: How to delay action of ...[[i]] (Part[...,i])

On Tue, Sep 7, 2010 at 9:59 AM, Greylander <greylander@gmail.com> wrote: > I have answered my own question! And understand a bit more how to > 'think' in Mathematica... > > The problem is that Part[[]] acts on any expression. What I have > finally figured out is that I need a version of part (or a version of > [[...]]) that acts *only* on lists (i.e. expressions with "List" > head), and searching and exploring the documentation, I eventually > learned how to do that. This will have exactly the desired result. > > Here is what I did: > > VPart[expr_List,k_] :=Part[expr,k]

Re: Sorting a list of names

Use SortBy: In[2]:= SortBy[names, Last[StringSplit[#1, " "]] & ] Out[2]= {"Mackenzie Christensen", "Cole Dockter", "Rebecca Eastham", "Cecilia Ford", "David Gartzke", "Tyler Hullett", "Matthew \ Lundberg", "Grant Patterson"} Adriano Pascoletti On 20100907, at 08.02, Jon Joseph wrote: > All: I have a list of names read in as strings with first names first. > Can anyone suggest a mechanism to sort the list by the last names with > the final output being the entire name? > > Starting array: > > names = {"Cole Dockter", "Mackenzie Christensen", "Rebecca Eastham"

Re: FindRoots?

On 7 Sep 2010, at 06:03, Mark McClure wrote: > On Mon, Sep 6, 2010 at 4:13 AM, Andrzej Kozlowski <akozlowski@gmail.com> wrote: > >> The point of my original post was not that Mathematica should not have >> a functionality to produce complete solutions of numerical equations but >> that leasing packages from users is not the right approach for Wolfram. >> ... >> I know of only one exception that WRI has made to this rule: the >> Combinatorica package, co-authored by Steven Skiena > > Actually, Mathematica contains quite a lot of code authored by users. > The palettes introduced i

Changing from Utopia font to arial

I like using arial 10 pt as my base font. It is more compact and I find it easier to read. I have checked previous posts which tend to talk about font substitutions and the like and relate to earlier versions. How do I change the default font (if there is such a thing) for all notebooks at a global level or by inserting a little code at the beginning of each notebook in an initialisation cell. Jeremy Duncan

notebooks default context

Firstly a problem, my packages (.m) keep having their context reset to global every time I open them to edit rather than "unique to each cell" to which I have previously set them to. THIS IS THE QUESTION (rest waffle) I would like to set a notebooks default context to "Unique to each cell" in a notebook initialisation cell. Usually I use "Unique to this notebook" from the menu (which is fine and persists), however on occasion I would like to tighten things up. ------------ WAFFLE ------------ I think I don't clearly understand the use of the Package` context instructions. My

What is the problem? There are no images and no wrong reports for this small program.

Hello Mathematica community, I really need some help.... I realized there are some mistakes in this program, but I can't find out what it is, I keep trying for weeks, still there are some problem, I never used Mathematica before a==Exp[(-2r^2)/3]; b==BesselJ[0,(r*Sqrt[x^2+y^2])/0.8]; c==r^2; d==5a; Plot[Abs[Integrate[r*b*a*Exp[-I(c+d)]dr,{r,0,=E2=88=9E}]]^2,{x,-0.01,0.01}, {y,-0.01,0.01}] =EF=BC=88I is Complex i=EF=BC=89

Sorting a list of names

All: I have a list of names read in as strings with first names first. Can anyone suggest a mechanism to sort the list by the last names with the final output being the entire name? Starting array: names = {"Cole Dockter", "Mackenzie Christensen", "Rebecca Eastham", "David Gartzke", \ "Matthew Lundberg", "Tyler Hullett", "Cecilia Ford", "Grant Patterson"} Ending array: names_sorted = {"Mackenzie Christensen", "Cole Dockter", "Rebecca Eastham", "Cecilia Ford", "David Gartzke", "Tyler Hullett", "Matthew Lundberg", "Grant Patterson"} As a note Sort[StringSplit[names][[Al

Re: Finite Groups...infinite disappoinment

On 9/6/2010 3:15 AM, David Bailey wrote: [snip] > My feeling is that you hit the nail on the head - the idea of curated > data over such a broad range is basically not possible. Another such > area is chemical information, thus you are rewarded by: > > ChemicalData["Caffeine"] > > however > > ChemicalData["Copper Sulphate"] > > or > > ChemicalData["Copper Sulfate"] > You need to use a standard camelcased name: In[30]:= ChemicalData["CopperSulfate"] Out[30]= {"CopperIISulfate", "CopperIISulfatePentahydrate", "CopperIISulfateHydrate"} You can also use a chemi

Re: Holding arguments of a family of functions

Write as a Function, and checkout the last note on the Function Help page. f[1,3]:= Function[y, ..., {HoldFirst}] David Park djmpark@comcast.net http://home.comcast.net/~djmpark/ From: magma [mailto:maderri2@gmail.com] I am building a family of functions, parametrized by 2 variables. These functions take one argument, so i have these definitions: f[1,3][y_]:=.... f[1,2][y_]:=.... f[1,3][y_]:=... f[2,1][y_]:=.... etc. As you see it's a case of subvalues being defined. The problem is that I also require that the y argument should be held. That is the function

Re: FindRoots?

I do not find any reference to or instance of FindRoot in the RootSearch code. David Park djmpark@comcast.net http://home.comcast.net/~djmpark/ From: Andrzej Kozlowski [mailto:akozlowski@gmail.com] This is, of course, not an argument against having in Mathematica the sort of capabilities that Gianluca wrote about. Rather, I don't think the existing RootSearch actually offers them, since I think it relies on the built in FindRoot function. Although FindRoot is indeed intended for solving numerical equations I do not think it can be reliably used with InterpolatingFuncti

Re: FindRoots?

It has been a long time since I looked at the source code of the RootSearchpackage (Ted sent it to me several years ago). I forgot the details of it and when writing this simply assumed it used FindRoot or an essentially equivalent method. In fact it implements Brent's method, which is of course one of the values of the Method option in FindRoot. I don't know exactly why Ted did wanted to implement this independently, but in any case it is not relevant to my comments. Everything "mathematical" that I wrote applies just as much to RootSearch as to FindRoot. The point of my original post was

Help with differential equation

Dear experts, I tried solving the following differential equation using DSolve: y' ' [x]+a( y' [x] ) = b( cos[y] ) But I got error message which asked me to provide proper arguments for cos.. So I changed cos[y] to cos[kx] and obtained solution... However, I have to solve the equation by keeping cos[y] in order to obtain a solution of relevance to my work. Please help. praveen

Finite Groups...infinite disappoinment

I have just checked some basic info using FiniteGroupData. I was looking for some MultiplicationTable for some groups. Indeed you can get the MultiplicationTable for the Quaternion group without a problem FiniteGroupData["Quaternion", "MultiplicationTable"] but no such luck with many/most other groups. For example: FiniteGroupData["C2", "MultiplicationTable"] and also FiniteGroupData["D4", "MultiplicationTable"] both return Missing[NotAvailable] Consulting the wonderful wizard of W.Alfa you get.... well exactly the same. No MultiplicationTable for either group.

Re: Time Series Data in Quarters

Jroge: Try In[1]:= data = {{{"2007, Q1"}, 10},{{"2007, Q2"}, 20},{{"2007, Q3"}, 30},{{"2007, Q4"}, 40}} Out[1]= {{{2007, Q1},10},{{2007, Q2},20},{{2007, Q3},30},{{2007, Q4},40}} In[2]:= DateListPlot[data, DateFunction :> (DateList[ToString[StringReplace[#,{"Q1" -> "03, 01", "Q2" -> "06, 01","Q3" -> "09, 01","Q4" -> "12, 01"}]]] &), DateTicksFormat->{"Year", " ", "QuarterNameShort"}] "Quarter", "QuarterName", and "QuarterNameShort" are geared towards output regrettably not for datetime parsing to Date. You may wish to choose different Month and Day for the replacement rules

Re: FindRoots?

Hola: In each re-posting of the original messages, cf. below, the Equal signs appear to increase in number according to two to the power n, n positive integer. Here == I wrote one equal sign. Just ONE. Best regards, MATTHIAS BODE COCHABAMBA/BOLIVIA > Date: Sat, 4 Sep 2010 03:58:24 -0400 > From: akozlowski@gmail.com > Subject: Re: FindRoots? > To: mathgroup@smc.vnet.net > > > On 3 Sep 2010, at 12:10, Gianluca Gorni wrote: > > > > > In my opinion Reduce can replace RootSearch in some > > cases but not in others. > > > > First of all, Reduce has bugs. Here is an a

Re: Question about ArrayFlatten

In[59]:= genindex = Range[2]; m1 = ConstantArray[0, {2*Length[genindex], 2*Length[genindex]}]; m2 = ConstantArray[0, {Length[genindex], 2*Length[genindex]}]; m3 = ConstantArray[0, {Length[genindex], Length[genindex]}]; m4 = IdentityMatrix[Length[genindex]]; Au1 = ArrayFlatten[{{m1}, {m2}, {ArrayFlatten[{{m3, m4}}]}}] Out[64]= {{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}} Adriano Pascoletti 2010/9/4 lightnation <lightnation@naver.com> > The coding below is not working. I don't know what is wrong. > Please

Re: NDSolve -- n-body indexing ([[]]) problem

The problem is that your differential equations are stochastic. I asked wolfram about it (see email below) using the following as a minimal example (which doesn't work): Remove@g1 g1[t_?NumberQ] := (RandomReal[] - 0.5)*t; sln = NDSolve[{ y'[t] == g1[t], y[0] == 0 }, {y}, {t, 0, 1}] Plot[Evaluate[y /. sln[[1]]][t], {t, 0, 1}, PlotRange -> All, AxesOrigin -> {0, 0}] Wolfram's answer is basically that you cannot do this NDSolve. Tech support suggested to use RecurrenceTable: Remove@g1 ; Clear [a, pp]; g1[t_?NumberQ] := (RandomReal[] - 0.5)*t; dt = 0.0001; pp = Recur

Re: Please help

On 4 Sep 2010, at 10:00, olfa wrote: > Hi Mathematica Community, > > Is Mathematica able to detect(recognize) implication between equations? > > Thank you. > Your question is not clear enough to answer with much confidence but at least Mathematica can do things like these: Assuming[x^2 + y^2 ==== 1, Refine[x^4 + 2 x^2 y^2 + y^4 ==== 1]] True or Assuming[x^2 + y^2 ==== 1, Refine[x ==== 0 || x^2 + y^2 ==== 1]] True etc. Andrzej Kozlowski