Thanks for this nice formulated answer :-) Hm, in this special case I am looking for public infos, which would make it a bit difficult here ... More or less I am aware of the links, it is the specific, exceptional case I am looking for.

Alec, Thanks (so my earlier crimes where against commutative algebra in some of its geometric appearances ...)

while i would not mind the example with the absolute function
i would be interested in the others, they are periodic functions
and live on the circle S^1, so there is a natural factorization
IR^1 -> S^1 -> IR. Does that mean, that the antiderivative lives
on S^1 as well and one is seeking a lift to IR^1 ?

  restart; st:=time():
  Int(sin(x)^n,x): IntegrationTools[Change](%, sin(x) = t, t): %%=value(%); 
  `seconds needed` = time()-st;
  
    /
   |        n
   |  sin(x)  dx =
   |
  /

             (1 + n)                                           2
            t        hypergeom([1/2, 1/2 + n/2], [3/2 + n/2], t )
        1/2 -----------------------------------------------------
                                  1/2 + n/2


                        seconds needed = 0.079

... and look up, how fcts are defined ... you now owe us a nice cartoon for your homework plot([(x+2)^3/(x^2)-1,x+6], x=-20..20,y=-15..20,color=wheat, thickness=2);

My English is not good enough for details and I am not used to US/CAN legal aspects (besides that I am not a lawyer ...), but is should be comparable to EC or Germany: As an author (which covers SW code) you have all rights as a natural person and those can not be given away. You only can *allow usage* and that's what is in that text. Otherwise the usage would be illegal and somebody may owe you money (there are exceptions, say employment contracts or others). The point is: the one who wants to 'use' them can not rely on a loose statement (yeah_its_ok) if (s)he wants to sure - (s)he needs all the dedicated cases (otherwise legally it would be useless - this is to protect authors). This is why such texts sound so strange ... Note however they do not demand that you assure that you do not violate other copyrights in submitting and you do not accept to heal possible (commercial) consequences if it would be the case. So (at least in EC) it is a bit worthless under commercial aspects in my opinion. If you want to knock it out there are certain ways - but I do not want to tease this community. If you are really afraid submit your code under GPL, which is the simpliest way. A usual contract for software authors would cover several pages to exclude most troubles. Whatever: if you publish a short proof for Riemann's conjecture here it still will be yours and I guess Maple will send you at least a six-pack with an appropriate letter acknowledging your copyrights :-)

.... Download 102_(Fay)ZakiansAlgorithm.mws ... and now I have some beer instead of tea :-)

hm ... i would have no problem to add new contribs until all my typos are gone and the formating incl HTML issues vanish :-) a common solution i know from other boards is: a user can edit his contribs - especially can delete his content - but never can delete an existing contribution or ever a thread (s.th. like the old CRUD (create read update delete) paradigma in classical data processing

Will answered to the thread, i deleted it (some warning appears "Are you sure you want to delete i will try to delete this post after a reply? This action cannot be undone.") Schwuppdiwuppwegisser ... It also disappeared from my own tracking list ... this observation should be worth 3.14 points for Alec

will see what happens with: http://www.mapleprimes.com/forum/i-will-try-to-delete-this-post-after-a-reply PS: thx for your other answer, it helps

if i enter "axel" i get 2 pages of results ~ 20 hits, but did ~ 150 contributions or lets say i remember a discussion with jakubi concerning numerical integration: how do i find it (guessing it was 1st half of 2006)?

I second Alec, a better search functionality would improve the
side's value for users.

I am not subscribed to many sites, but usually one can search
for several keywords in contributions, for authors (user names)
and periods (and if structured by categories even for that).
It never makes a difference whether a site was restructured or
relaunched.

May be you can find a way for the special board SW?

:-) ... not needed and of course it is a good idea to keep your corrected typo as secret :-) > restart; > c := 2.998*10^(8); h := 6.626*10^(-34); k := 1.38*10^(-23); > # in case of trouble one way might be to use symbolic integration > # in that case do not assign to much numerical values, note that > # standard is 10 Digits and evalf will use hardware floats, but > # those constants are quite small and this will give unprecise > # results > > A[d] := 30*10^(-6); tau[d] := 10*10^(-3); T[300] := 300; > # Maple sometimes has problems with this notation of indexed variables > # or constants, try to use A_d or tau_d or similar > > `f/#` := 4; > # legal with that quotes, but pun intended ... try to use f_hash or so > > K(theta) := (cos(theta))^4; > # the notation for functions is K := theta -> (cos(theta))^4 or similar > > L[b1] := (2*h*(c^2)/(lambda^5))*(1/(exp(h*c/lambda*k*T[300])-1)); > # ditto - what should it mean? > > `I[b1]` := Pi/((4*(`f/#`^2))+1)*L[b1]; > # even worse: this notation defines a variable ... > > N[b1] = 'A[d]'*'tau[d]'*Int((lambda/('h'*'c'))* I[b](lambda), lambda = 3*10^(-6)..5*10^(-6)); > N[b1]:= evalf(Int(A[d]*tau[d]*lambda/(h*c)*`I[b1]`, lambda = 3*10^(-6)..5*10^(-6))); > # one can guess from printing what can be meant ... but what is meant? > # in case of trouble for integration try to plot the integrand and using > # Int(blabla); plot( op(%) ); will take the situation into acount ... > # here Maple gives up - it can not plot > # Try to evaluate in the boundaries and in the midth to see if integrand > # can be evaluated and if there are singularities, put constants outside > # the integral > # you have "numerical singularities": .8224005672e-45/lambda ~ 1e-39, so > # exp gives ~ 1 and exp - 1 is almost 0, ditto lambda^5 ~ 1e-28 so your > # denominator is almost 0 ... a scaling problem and higher precision may > # help (might be expensive in computational time) > # hence try to use symbolics to find a solution and insert values later > # or use convert(..., rational) to have better numerics, solve symbolically > # and use evalf later > # or translate to the unit interval by change of variables or ... > restart; > > # essentially you seem to want: > lambda^5*exp(const/lambda-1): 1/%: Int(%, lambda); value(%); > > # this has no singularities for positive boundaries (Maple can > # not know that in advance and numerical it may be a trap ... > # so use "fundamental theorem": evaluate anti-derivative > > eval(%, lambda=5*10^(-6)) - eval(%, lambda=3*10^(-6));

:-) ... not needed and of course it is a good idea to keep your corrected typo as secret :-) > restart; > c := 2.998*10^(8); h := 6.626*10^(-34); k := 1.38*10^(-23); > # in case of trouble one way might be to use symbolic integration > # in that case do not assign to much numerical values, note that > # standard is 10 Digits and evalf will use hardware floats, but > # those constants are quite small and this will give unprecise > # results > > A[d] := 30*10^(-6); tau[d] := 10*10^(-3); T[300] := 300; > # Maple sometimes has problems with this notation of indexed variables > # or constants, try to use A_d or tau_d or similar > > `f/#` := 4; > # legal with that quotes, but pun intended ... try to use f_hash or so > > K(theta) := (cos(theta))^4; > # the notation for functions is K := theta -> (cos(theta))^4 or similar > > L[b1] := (2*h*(c^2)/(lambda^5))*(1/(exp(h*c/lambda*k*T[300])-1)); > # ditto - what should it mean? > > `I[b1]` := Pi/((4*(`f/#`^2))+1)*L[b1]; > # even worse: this notation defines a variable ... > > N[b1] = 'A[d]'*'tau[d]'*Int((lambda/('h'*'c'))* I[b](lambda), lambda = 3*10^(-6)..5*10^(-6)); > N[b1]:= evalf(Int(A[d]*tau[d]*lambda/(h*c)*`I[b1]`, lambda = 3*10^(-6)..5*10^(-6))); > # one can guess from printing what can be meant ... but what is meant? > # in case of trouble for integration try to plot the integrand and using > # Int(blabla); plot( op(%) ); will take the situation into acount ... > # here Maple gives up - it can not plot > # Try to evaluate in the boundaries and in the midth to see if integrand > # can be evaluated and if there are singularities, put constants outside > # the integral > # you have "numerical singularities": .8224005672e-45/lambda ~ 1e-39, so > # exp gives ~ 1 and exp - 1 is almost 0, ditto lambda^5 ~ 1e-28 so your > # denominator is almost 0 ... a scaling problem and higher precision may > # help (might be expensive in computational time) > # hence try to use symbolics to find a solution and insert values later > # or use convert(..., rational) to have better numerics, solve symbolically > # and use evalf later > # or translate to the unit interval by change of variables or ... > restart; > > # essentially you seem to want: > lambda^5*exp(const/lambda-1): 1/%: Int(%, lambda); value(%); > > # this has no singularities for positive boundaries (Maple can > # not know that in advance and numerical it may be a trap ... > # so use "fundamental theorem": evaluate anti-derivative > > eval(%, lambda=5*10^(-6)) - eval(%, lambda=3*10^(-6));

Thx for finding out, it works now (on IE [old bookmark] and with Firefox [where i changed nothing])!