See the help-page ?Task,EquationOfLineBetweenTwo2DPoints Or, run the command, Student[Precalculus][LineTutor](); acer

How many times do we have to see submitters' getting caught up with the less-than symbol, before the mapleprimes maintainers switch the default Input format to plaintext? Most submitters are not using marked-up input. It's the new submitters who pay most here. The old hands would know better, if by default they had to toggle on Filtered HTML as the Input format. acer

While it may require an extra step to use, mint may also assist with locating syntax errors. On the one hand it may take an extra step to invoke, be that as a separate shell command or as use of a vi/emacs macro. But I mention mint because it can do so much more, to help author large maple sources, and because not every user out there will have heard of it. I have always supposed that its name is a joke on `lint` (for C). On Unix at least, mint is a program than sits in the bin.ZZZ directory alongside the `maple` and `xmaple` scripts. It has a help-page accessible within maple itself. It also comes with a man-page on Unix. It can do a lot more than simple syntax checking, including reporting on undeclared locals, globals, dead code sections, and lots of other good stuff. The level of reporting can be fine-tuned, via options. I find that mint is especially good for finding some sorts of coding mistakes that, while not syntax errors per se, can still come back and bite in unexpected ways. While I'm showing my preference for the commandline Maple interface for managing larger programming jobs, I can also point out the very nice $include and $define directives. I have seen $include used both for module source layout (each local procedure gets its own $include in the module source defn file) and for injecting common code fragments. acer

Let's try to create a customized refinement of the Atomic system of units, in which energy is simplified and displayed by default to keV, length to cm, area to cm^2, and volume to cm^3. Units:-AddSystem(customAtomic,Units:-GetSystem(Atomic),cm,cm^2,cm^3,keV); Units:-UseSystem(customAtomic); Now to try and test that, simplify(3.0*Unit(g)*Unit(mm)^2/Unit(s^2)); with(Units[Standard]): T:=3.0*Unit(g)*Unit(mm)^2/Unit(s^2); T/(1.1*3.0*Unit(g)*Unit(mm)/Unit(s^2)); T/(1.1*3.0*Unit(g)/Unit(s^2)); T/(1.1*3.0*Unit(g)*Unit(mm^(-1))/Unit(s^2)); acer

You're calling int() with the wrong syntax. It should be, int((4*x-3)^3, x); and not, int((4*x-3)^3, dx); Using the correct syntax, you should get the right answer straight away. If you'd like to try the change of variables anyway, just for fun, it can be done as follows. First, step by step, P:=Int((4*x-3)^3, x); Pu:=student[changevar](u=4*x-3,P,u); pu:=value(Pu); eval(pu,u=4*x-3); Or, in one single line, eval(value(student[changevar](4*x-3=u,Int((4*x-3)^3, x),u)),u=4*x-3); acer

This raises several interesting questions. How can one create a variable which gets dislayed with a long overbar as 2D Math input but which does not have any of the mathematical meaning of conjugation? It should be clear that sometimes one will want both foo and \overbar{foo} without a relationship between them of conjugation. One approach is to convert the input object, which underneath the hood is actually conjugate(foo), into a unique variable with no relationship or mathematical connection to variable foo. This can be done inplace on the input using the context-menu choice 2-D Math -> Convert To -> Atomic Identifier. Does the conversion to atomic identifier (unique variable name, independent of name foo) need to be done each time the variable is entered as input? Apparently it usually does. Copy & paste of overbar output wipes out the atomic identifier aspect, getting back to conjugate(). Programmatically, one can also enter something like `#mover(mi("foo"),mi("_"))` to get a unique name, independent of name foo, which gets displayed as output with an overbar. This is not as nice as LaTeX syntax. Also, how can one use this to get an atomic identifier which gets actually typeset as foo overbar for input? Notice the two Layout palette entries whose hover-over bubble help are "over" and "over2". The first produces a conjugate() object. The second entry, "over2" can sometimes produce an atomic identifier, it seems. So, I tried using the "over2" entry. For the upper part, entering a minus sign, ie. - , produced something with an unfortunately short bar. After selecting palette entry over2 I also tried the keystrokes, foo\_ but this just produced an object which was conjugate(foo) in nature and also showing with the short overbar as input. Wouldn't it be more appropriate if the "over" entry instead had bubble help stating "conjugate", and if the "over2" entry instead had bubble help something like "overliteral". I couldn't find a way to get a long bar for the 2D Math input, as there can be for the 2D output of the same object. Is there a way? How can one discern whether a 2D typeset object (input and output) is an atomic identifier or an instance of conjugate()? Is there something easier than lprint? Maple 11.00, Linux. acer

It should be possible to "fix up" the pie chart after the fact, using Maple itself. The pie chart gets created as just another PLOT structure, and hence should be subject to programmatic manipulation. For example, restart: with(Statistics): p:=PieChart([Wales = 40, Unknown = 56, GB = 341, E = 237, RUS = 31, D = 93, F = 91, IRL = 39, S = 35, Other = 244], color = orange .. green): newp:=subsindets(p,specfunc({list,identical("Wales")},TEXT),f->subsop([1][1]=[op(1,f)[1]+0.5,op(1,f)[2]],f)): plots[display](newp); It should be possible to construct a maple procedure that moves all the captions away from the centre and outside the unit circle. One could likely make such a procedure reusable, for other pie charts. acer

What do you mean by good quality random numbers? Do you mean that they have to pass some statistical tests? For example, something like the diehard tests? Or perhaps you intend to use these numbers in some sort of simulation, perhaps as entry values for some Monte Carlo computation. Maybe a strict battery of tests isn't what would serve you best? Perhaps all that you actually need is that the numbers, entered into some simulation, provide an unbiased estimator for the result of your particular computational goal? acer

I suggest asking your lattermost questions, about fast complex numerical computations, on the usenet newsgroup sci.math.num-analysis . acer

See the help-page ?type,series for an explanation of the series datastructure. That datastructure is quite different from the explicit sum of terms in your s. See ?convert,polynom for examples of converting a series object to a polynomial (SUM). acer

Yes. If you are on Linux/UNIX, the bin/maple script acts like this: maple -x <- Std Java GUI maple -cw <- Classic GUI maple <- TTY interface On Windows, the TTY interface is named cmaple.exe , I think. It can be started from a DOS shell, or from a cygwin bash. Also, you spoke before of computations that take longer according to some bracketing. I assume that means that you are using the Std GUI. If so, try it in "worksheet" mode with 1D maple notation input instead of Document mode with 2D Math input. You can select the mode, Document or Worksheet, from the File drop-down menu. And in the Options menu you can configure which you want as default (mode, and entry style, etc). acer

Is this the sort of thing that you're after? sys := {diff(y(x), x) = x, y(0) = 1}: sol0 := dsolve(sys, numeric, output = listprocedure): s := subs(sol0, y(x)): s(1); SS := proc(t) global s; if type(t,numeric) then s(t) else 'procname'(t); end if; end proc; sys2 := {diff(U(x), x) = SS(x), U(0) = 1}: sol1 := dsolve(sys2, numeric, output = listprocedure, known=[SS]): s2 := subs(sol1, U(x)): s2(1); It seemed that this also worked, sys2 := {diff(U(x), x) = 's'(x), U(0) = 1}: sol1 := dsolve(sys2, numeric, output = listprocedure, known=[s]): acer

If you set infolevel[LinearAlgebra]:=2 then you will see that external compiled routines are already in use. The names appear to be NAG function names, each equivalent to some BLAS name, according to NAG online docs. Experience with performance testing shows that these must be linked to fast 3rd party BLAS, ie. ATLAS. Consider this internal routine: kernelopts(opaquemodules=false); showstat(LinearAlgebra:-LA_Main:-`MatrixExponential/complexfloat`); It is all Matrix functions to do multiplications, norms, and additions, in NAG/BLAS calls. I have some edits to the original posting, which cut out some copying and maple library function call overhead. But after a certain extent, further optimization is difficult. For example, one could take that internal routine and squeeze it. By calling it directly, a few more function calls could be avoided. Also, look at how it uses temp1 and temp2. It only ever Copies data into them, and so keeps maple from creating any unnecessary Matrix garbage. It might be possible to make its temp1 and temp2 global instead of local, so that they get re-used for each exponential computation. Using private workspace is an extreme optimization step (acknowledging that maple's rtable memory management can be bettered in special cases). One could also do it in C, and link to it. But the objective to work entirely at the maple library level is appealing. Let me cut n' paste my code edits, in a followup. I found this problem instructive. acer

Are the Matrix entries exact quantities (integers, rationals, symbolic quantities with exact coefficients, etc) or approximate floating-point values (7.3, etc) ? It makes a difference, as to what is a good way to compute the rank. If the entries are floats, then a singular value decomposition would do. If not, then row reduction and counting the non-zero rows could do. It might depend on whether you are, say, taking a class in numerical analysis or basic linear algebra. I'd first guess that it's the latter. But I thought that I'd check. acer

Could you upload the Matrix example? It's more difficult to discern what's happening without it. acer