In my above posting one should use RootOf(f(x)-t=0,x, label=1): g:=unapply(%,t); Then it works for all reals, try it with plot(g(tau),tau=-10..10, color=blue). Adding to the other answers: you might google for Geddes "What is a closed form?" which gives additional insight for the 'philosophy' in Maple using RootsOf. Also http://front.math.ucdavis.edu/math.NT/9805045 might interest you: "What is a closed-form number ?" And a posting of Robert Israel in the Maple NG now comes to mind (last year? can not find it again ...): root-finding for elementary function is undecidable, so no hope for a general algorithm (he gave a proper citation) ...

It is not meaningless (even if the notation for RootOf is really ugly for my taste, since one can not see the according variable). As acer said: operational Maple handles it as a solution in most cases, just as if it would call the function "i_know_it_but_can_not_show_in_usual_terms". Let's try it, in your case it is the inverse w.r.t. composition: restart; Digits:=14; 5.*x*sqrt(1.+4.*x^2)+2.500000000*arcsinh(2.*x): convert(%,rational): f:=unapply(%,x); plot(f(x),x=-6..60); t = f(x); solve(%,x); g:=unapply(%,t); plot(g(t),t=0..35000, color=blue); fsolve( g(t) = 30, t=0..infinity); evalf(f(30)); or fsolve( f(z) = 1000, z); evalf(g(1000)); The solution is known to Maple, even for plotting, showing the inverse as reflection at the diagonal (does not work for t < -4, may be a bug or may be a problem with branch cuts?). Also t-f(g(t)); plot(%, t=0..1); and z-g(f(z)); plot(%,z=0..1); shows what I would expect: graphics gittering around 0 (well, it does not evaluate to 0 symbolically). It even would know the taylor series (but it would be better to use a different function which is not so time consuming, take 'erf' or so). And Maple behaves so for most cases: one can not expect that (locally) inverting a function can be given in known terms - that is already not the case for polynomials.

Thank you for both the answers! The reason for the question was how to terminate summing a series with reasonable fast decaying summands, I felt unsure for that.

use double backslash (escape character) or single slash like libname:= "C:\\Programme\\Maple11\\lib": #, libname: myLib:="C:/Programme/Maple11/_Packages/mylib/": then i would never use international characters (like an "ä") across different systems and would avoid blanks in file names and possibly would always use lower case characters Additionally be aware: exporting from German Excel depends on local language settings for decimal character (you may check your data for "." and ","), Maple uses its own.

why is it exp(1)/24 ?

Yes, eval is safer (just hate to type " [ " on German keyboards, sorry), but here one can do it. unapply: wanted to show how to plot 2 functions as 1 graphic and think it is better for a 'newbie' to show simple, single steps (and I prefer 'unapply' instead of the arrow notation).

There are various ways, here is one: restart; # good practice Digits:=14; # better than the 10 as standard n*C^2/(C*(C+n*e*h)); subs(C=100, e=1, h=2.8, %); f:=unapply(%,n); 4*n*C^2/(2*C+n*e*h)^2; subs(C=100, e=1, h=2.8, %); g:=unapply(%,n); P1:=plot(f(n), n=0..20, color=magenta): P2:=plot(g(n), n=0..20, color=blue): plots[display]([P1,P2]); For the commands used try to look up the help (and the manuals) and also look at the links given at the bootom of the help pages pointing to related stuff. PS: it is easier if you post your equations either as text (or as file, if they are longer): saves typing for others and makes it more likely they answer ...

one idea would be to look in the manual ... another to press the F1 key ... if you want to solve I would search for something like solve ... in old times one used the index of a book ... in modern times there are input fields to search ... and in current times it seems best not to do anything else but posting ...

hi you first posting do not sbeak pidsching englisch gut but can say: hope you can learn to write in english quite soon and will also be able to solve your homeworks achmed, the invisble

I always write explicite loops for i from 1 to 331 and be sure that you did not interchange rows and columns, check Demand[1, 2] and Demand[2, 1] in Maple against your data

Tried to look at your data, 4416_All_Math dep FORUM.mw however does not work for me. But I could play with viewing. Though I have no idea what it stands for, here is what I think to observe and that says: your fitting function can not be correct I take the first plot in the mentioned sheet. Setting theta=0, phi=90 i look transverse. First I ignore the last data cloud, it is different from texture ("unripe", incomplete, chaotic?). Then roughly the first mountains increase linear in size while the valleys only mildly increase (even constant ... outliers?) Comparing peaks and lows the periodics is not constant - they increase. For the shapes it seems that (compared to the extrema in each period) the values increase quite fast (not able to judge whether like root functions, but certainly not like sin/cos) and break down (like sawtooth) while for lower values this is quite smooth. With that view the last data cloud is just incomplete, your data stream seems to increase 'over time' (choose theta=0=phi). Using a 'contour plot' theta=0=phi (i.e. viewing from above) also gives the idea to clean up the data: May be you can try to adjust them in lines (hope it is clear what I mean), if the values are only different by small amounts: in this way you can make them discrete into data series or 'strips' and will be able finally to plot the beast as curves in 3 space (which has the advantage to view the curves separatly before fitting to a surface ... not sure whether I would do that in Maple only). Is there no model available in your field, which tries to describe the data? That sawtooth only for relatively high values and smooth below will be ugly to model, you need a kind of 'saturation' given by the overall hull (= a line?) Not very scientific, but my 2 cents after 2 beers :-) NB: you call yourself not an expert - but the sheet seems not that bad at all, very good visible graphic (can you try to make all walls in black?).

just guessing: a memory problem? At least such messages may appear if the DLL was killed. But one can not look closer, there are no sources ... I would ask the author, his email is in the docu

Thanks for confirming ... now I will have some ice cream :-)

thanks, i tried that (needs some guessing what-is-what), but can not get rid of the italics

my fault ... I should have read the help more carefully :-) The global array is what I did in Maple (with an hfarray), but wanted to have it local for the procedure. Anyway I am not happy with that limitation: say you have a list for a numerical proc it is not fine to declare each value ... The reason for my question was: I put Ooura's C code for BesselK into Maple and was wandering, how one could use it with Compile (so without explicitly making a DLL).