Andrew Carmichael

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14 years, 195 days

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These are answers submitted by Andrew Carmichael

Suppose I wanted to kill all powers of mu and omega greater than 2? Andrew
Dear All, That's all working now, thanks. The next thing I want to do is make maple spit out a table with the numerical value of the integral and that of the series and most importantly the difference between the two for different values of m to see how good the series is. I tried something like this: NUMINTP:=(m)->evalf(Int(P1(x, m), x = 0 .. infinity), 25); NUMASERIES:=(n)->evalf(eval(ASeries,m=n), 25); DIFFERENCE:=(p)->abs(evalf(NUMINTP(p)-NUMASERIES(p),25)); for p by 10 to 100 do {DIFFERENCE(p), NUMASERIES(p), NUMINTP(p)} end do This seems to work, but is it the best way forward? It produces a list, which is OK. Can I make it produce a nice table which I can export? And can I make it restrict the sig figs evaluated by the difference function? Thanks, Andrew
Thanks Robert. You're a genius. That's the same result we've seen with Mathematica, using numerics. Much appreciated. I'll mention you in the acknowledgements. Andrew
Thanks everybody. That seems to all be working. I have another problem with a related system, but I think it's different enough to warrent starting a new thread. Regards, Drew
It seems that all is well now. One last thing, though. I've calculated the values of (alpha,beta,Omega) from one equation using plot. I then used plottransform to change these into (Omega,delta,alpha) in the one case and (Omega,delta,beta) in the other case as you suggested. plotB=implicitplot3d(f4(alpha,beta,Omega)=0,alpha=0..1,beta=0..1,Omega=0..5,grid=[50,50,50],labels=[alpha,beta,Omega]): plotBTrans:=transform((alpha,beta,Omega)->[Omega,2*(-beta*Omega/sqrt(2))+Omega/sqrt(2)*(alpha^2+(3*(abs(beta*Omega))^(3/2)*(IntegralA(1,0,infinity))/(4*2^(3/4))))*(1/beta),alpha])(plotB); plotBTrans1 := (transform(proc (alpha, beta, Omega) options operator, arrow; [Omega, -2*beta*Omega/sqrt(2)+Omega*(alpha^2+(3/8)*abs(beta*Omega)^(3/2)*IntegralA(1, 0, infinity)*2^(1/4))/(sqrt(2)*beta), beta] end proc))(plotB) This seems to be all working fine, but I wonder if it would be more efficient to take the initial values of (alpha,beta,Omega) and use plottransform only once to get a bigger array of (Omega,delta,alpha,beta) and then tell it to plot, in the one case columns 1,2 & 3 and in the other case columns 1,2 & 4. This means that all the values of delta would only be calculated once rather than twice. Is this possible? Thanks again, everybody, Andrew
Dear all, There's another possibility that might work. One of the variables (delta) can be simply written in terms of the other three. I'd like to be able to give maple the equation g(alpha,beta,Omega)=0 but have it plot on three axes Omega, beta and delta (given by the other equation. In other words, is it possible to give an implicit finction of three variables, and have it plot two of the variables on two axes and some function of the third variable on the third axis. For the simple sphere case, imagine giving the equation x^2+y^2+z^2-1=0 and asking it to plot not (x,y,z) but rather (x,y,f(z)) where f is some function of z you specify. Does anybody know how to do this? By the way folks, thanks for your help on this. I appreciate it. Drew
I'll try that. Thanks. It is a shame, though, that one can't tell it to plot all the points which satisfy two equations rather than just one. Is it possible, for example, to tell it to solve the two equations and find all points which satisfy both equations and spit out a table of numbers for each of the four variables, which could then be plotted as data points? For example, leaving my monster equations aside or a moment and looking to something simpler, suppose I wanted to tell it to give me all the points which satisfy both f1(x,y,z)=x^2+y^2+z^2-1=0 and f2(z)=z=0, and have it give (in this case) all the points in that circle? This doesn't sound like something which should be difficult. I know that in this simple example it's trivial to combine the functions symbolically anyway but that won't work for my real equations. Drew
Dear Comrades, Sorry I've been offline for a while. The equations I'm looking at aren't really integral equations in the standard sense. They involve integrals, but the integrals can be done (as opposed to standard integral equations where the mystery function is under one of the integrals). So, I have two equations involving four quantities; alpha, beta, Omega and delta, and I want to plot the surface of beta as a function of Omega and delta (eliminating alpha leaves one equation in three variables, which defines a surface). Without having to eliminate alpha myself by hand, I want to give maple both equations and have it plot those points which satisfy both equations. My equations are complicated, so I tried a simpler example to get the syntax right. I tried to plot the circle where a cylinder cuts through a sphere. Unfortunately, using plot(eq1, eq2) command it plots both surfaces (cylinder and sphere), not just the intersection. So, do any of you know a way to give maple two equations and have it plot the points which satisfy both equations?
F:=(beta,Omega,delta)->6*Omega^2*beta^2+sqrt(2)*delta*abs(Omega*beta)+2^(5/4)*4*Omega^2*(abs(Omega*beta))^(3/2)-2*Omega^2; h:=(beta,Omega)->1-beta^2-2^(1/4)*abs(abs(Omega*beta)^(3/2));
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