it would be bad to learn that using Maple ... and if you have that as exercise you should have heard how to do it ... anyway: isolate e from the 2nd equation and insert it into the 1st this is now an equation in 1 variable, solve it for f now take that f, put it in the 2nd equation and solve for e

let say it this way: the system wants to work with a normalized form, but a human would like to see a different, but equivalent presentation. if you really want it: put a minus sign in front and one for the numerator after decomposing

Hm ... searching for only 'e' shows some hits and results look strange to me, seems it was produced with some not so common options :-( Now opened as ps file and converted to pdf ... blows up while the Into Guide became quite small ... Would be nice, if a searchable document would be available

Just a thought for the shift by 1: If you export your data from Excel not from a Excel sheet by storing as CSV but through VBA code by writing matrix entries to a file, it may be an indexing issue in Excel. By default in Excel arrays are 0-based (like in C), while in Maple they are 1-based. One can change that by 'Option Base 1' in VBA. I remark this since your first pair is (-.498e-1,0), while the other y-values are *not* integers. This typically occurs if the array is not explicitely given a data type 'float' (or is not declared by a 'dim' statement at all). This may indicate a neccessary index shift for y as well. In that case you need to take care for the fitting equation. May be you check for the first and last pair and the number of data in both Excel and Maple.

there should be special software available, for example http://curveexpert.webhop.biz/ edited: viewing at the data it looks like a sum of densities, however for the maxima I can not recognize a pattern

are you sure for your task, not a minus sign within the exp terms? do not have a solution, but the terms are diff( f, b) where f = the exp terms so it is something like integrating D(f1)(b)*D(f2)(b) after expanding which may be good for partial integration and re-collecting if a minus is missing ... where does the question arise?

naming your expression 'theRatio' the following might do:

  restart; interface(version);
  Digits:=30;
  read "D:\\_Work\\Maple_Work\\ratio.txt": # read from file
  length(theRatio): evalf[2](%/80/60);     # 19 pages
  indets(theRatio,atomic): indets(%);      # check: actual depends on f0 only
  fnormal(theRatio,14);                    # check: nonsense with low precision, needs at leat 16
  
  
  
  convert(theRatio, rational):
  eval(%, f0=g0/Pi):
  eval(%, g0=a^2):
  R:=%:
  ``;
  R1:=simplify(R,size): 
  #length(%): evalf[2](%/80/60);
  
  Digits:=16;
  evalf[16](R1): evalc(Re(%)):
  codegen[makeproc](%,a):
  p:=codegen[optimize] (%,tryhard):
  
  length(p(a)): evalf[2](%/80/60);
  
  
  #q:=proc(f0) p(sqrt(Pi*f0)); subs(pow=`^`,%); evalhf( % ) end proc;
  q:=proc(f0) subs( pow(1/(a^2),1/2) = 1/a,p(a)); subs(a=sqrt(Pi*f0),%); subs(pow=`^`,%); evalf( % ) end proc;
  q(5.0e9);
  
  
  #plots[semilogplot]('q'(f0),f0=5e9..1e12);
  plots[semilogplot]('q'(f0),f0=5e9..1e12,color=magenta,numpoints=1000,axis[1] =
  [tickmarks=[4,subticks=8]],axis[2] = [tickmarks=[4,subticks=5]],
  view=[1.0e9..1.0e12,0.40..1.00]);

you can read it from the following plot x=(1/5)*exp(y/2); plot(rhs(%), y=-infinity .. infinity); either directly or remembering that the (compositional) inverse is the reflection at the diagonal (for that use paper and pencil)

Your expression is about 20 pages long and you seem to use 10 Digits of precision. It sounds like brute force and it is very likely you are killed by rounding errors. Additionally it contains complex values, what should be plotted? Try to plot x + I*1e-10 to see ... Being not sure whether 'ratio' is a reserved word I call it the Ratio. Now fnormal(theRatio) returns Float(undefined)*Pi*f0^2. This indicates numerical division by 0 or a singularity with 'jumps'. BTW: your variable seems to be actually Pi*f0. If you want a reasonable answer you may want to upload a sheet or text file showing the steps and not only the final result, so may get hints how to proceed better. PS: you also should edit your post (if possible) and delete your expression, otherwise the replies may not be readable.

Well, there are various answers.

The first: RTFM.

Now some more polite ones :-)

If you dont use Maple in your course: try it without Maple.
Be sure you will not survive your studies else ...

If you use Maple in the course: read your notes (if you did
attend, otherwise the copies ...). Most likely excercises
are around the subject, try to identify.

If you want to cheat and provide an answer, here it is:

1) 4*sin(x)^2 + 2*cos(x)^2 = 3: solve(%,x);

2) solve(sin(u)=3/5, u); solve(%,u);
   [sin(u/2), cos(u/2), tan(u/2)]; 
   eval(%,u=%%); convert(%,exp); simplify(%);

Now be aware you will be asked to explain it and are assumed
to answer whether these are all solutions.


So the actual answer: if you cheat to often you will not
finish your studies - that's the true answer.

Cheers

Would say: impossible in that general setting, even without all the non-analytic ingrediences you have in your function. First get rid of Heaviside, it is 'undefined' in 0, write it as max and may be write all 'max' through piecewise (for which you may have to decide for the conditions). Second you can try to restrict to each of that cases and solve there. F1(x,y) = F2(x,y) is a curve, yes ... but an implicitely defined one. Looking at your graphics alpha = fct(delta) may be true, so you may try to solve for that - there is no reason an analytic or symbolic solution should exist. One way also might be to approximate your functions to come into a polynomial situation and use Groebner package (no, I never used it seriously, but others may give hints). For this there are variuos ways: series developments terminated early or may be some transforms of variables or ... More or less: you have to be creative, just writing down something like RootOf(F1(x,y) - F2(x,y), y) is unlikely to give a meaningfull result: that (in general) would not even work in intersecting 2 curves to get all their common points And: have in mind Maple looks for solutions over the Complex as well. For estimating for *some* parameters you may try the RootOf + evalf + fitting, but have to suggest models (which may be contrary to some analytic solutions)

reminds me to Sokrates and Menon ... hope that remark is not offending ...

using Chebyshev polynomials to fit against data - is it that, what is meant? i think it is in the Statistics package, Statistics[Fit], provide a polynomial and follow the examples

Besides the given solution [x,b] = [exp(1), exp(exp(-1))] the other is [exp(-1), exp(-exp(1))].

One solves p(x) = q(x) for b, simplifies for positive x and then uses the given 'contact equation'

sorry for being too short ... it is a command to get info about a variable, type in ?about _Z is a shorthand notation (used by the system) to stand for an arbitrary integer if you see it in solutions it stands for multiple solutions, like for solving sin(Pi*x) = 0: any integer x would do hope it's clearer now, first times it is a bit confusing