MaplePrimes Questions

alternatingseries.mw
I have a double about this alternating series.
According to maple this series converges:

evalf(sum((-1)^(n+1)*(ln(n)/n+1),n=1..infinity))
                          0.3401310963

However limit ln(n)/n + 1 does not equal to zero, it equals 1. Therefore the series should diverge.

Also while I am on the subject of series and limits, why is limit (-1)^n  as n goes to infinity a range between -1-I and 1 + I.

limit((-1)^(n), n=infinity)
                        -1 - I .. 1 + I

 

 

Hello, I am having a bit of difficulty simplifying some calculations in Maple 2019. In short, in order to verify that the tensors that I am trying to use are indeed inverses of each other, I am simply trying to multiply component wise, for example the tensor component e[2,~2] with the tensor component f[~2,2], since they are essentially inverses of each other, i.e. the matrix defining f is actually the inverse of the matrix e, i.e. f=e^(-1), should give back 1 as an answer. Nonetheless, when I attempt to take this simple multiplication Maple does not reduce it, but rather just gives multiplies the terms with no simplification. Is there anything I can do so that Maple may simplify its calculations? I have already tried the "eval" calling sequence but that didn't do the trick, and I fear that when escalating the calculations I will get a bunch of long expressions rather than concise solutions. Thank you for your help in advance,
 

Christoffel_symbols_of_de_Sitter_metric_research.mw

Lets say you have this simple list here 

L := [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];

 

Which command would you use to partion into intervals? 

L_g := [1..2,3..4,5..6,7..8,9..10]

Hello

Although I am (remotely) running the following piece of code in a linux machine with 256 GB of ram, the error msg "Execution stopped: Stack limit reached" comes out 

 

kernelopts(stacklimit);
NestList:= proc(f, x, n::nonnegint)
local R:= rtable(0..n, [x]), k;
   for k to n do R[k]:= simplify(f(R[k-1])) od:
   [seq(R)]
end proc:
n:=34;
yreal:=NestList(y-> 4*y*(1-y),1/8,n):

I have tried to increase stacklimit issuing the command "kernelopts(stacklimit=256000)" but to no avail.  Is there anything else I can do?  A similar code run successfully in a mac with Mathematica. 

Many thanks 

Ed

 

PS. The default kernelopts(stacklimit) shows 8192 on the linux machine and  but 32736 on the mac pro.  I was expecting a higher number on the linux machine.  

 

restart;
with(LinearAlgebra);
G := Matrix([[beta1^2, 0, -beta2^2, 0], [0, beta1*(b^2 - beta1^2), 0, beta2*(b^2 + beta2^2)], [beta1^2*cosh(beta1*l), beta1^2*sinh(beta1*l), -beta2^2*cos(beta2*l), -beta2^2*sin(beta2*l)], [beta1*sinh(beta1*l)*(b^2 - beta1^2), beta1*cosh(beta1*l)*(b^2 - beta1^2), -beta2*sin(beta2*l)*(b^2 - beta2^2), beta2*cos(beta2*l)*(b^2 + beta2^2)]]);
NULL;
NULL;
S := Determinant(G);
S := simplify(S);
S1 := S/(beta1^2*beta2^2);
F := Pi*d^2/4;
Q := F*d^2/8;
u := E/(2*(1 + v));
lambda := sqrt(w^2/c^2);
j := v*d*lambda/sqrt(8);
y1 := 1 - j^2 + sqrt((j^2 - 1)^2 + 4*j^2*u/(c^2*p))/(2*j^2*u/(c^2*lambda^2*p));
y2 := 1 - j^2 - sqrt((j^2 - 1)^2 + 4*j^2*u/(c^2*p))/(2*j^2*u/(c^2*lambda^2*p));
b := 2*(1 + v)*(8/(v^2*d^2) - w^2/c^2);
beta1 := sqrt(y1);
beta2 := sqrt(-y2);
S;
d := 24.8;
c := 5100;
v := 0.34;
l := 2000;
E := 2.1*10^5;
p := 7700;
S;
plot(S, w = 0*2*Pi .. 100000*2*Pi);

# Here I get an error

Error, (in plot) incorrect first argument (-HFloat(2.757556062608314e294)-HFloat(2.757556062608314e294)*I)*(HFloat(2.757556062608314e294)-HFloat(2.757556062608314e294)*I+(HFloat(2.918216722364015e-174)+HFloat(7.045198389075166e-174)*I)*(HFloat(1.2899139595562734e220)+HFloat(1.2899139595562734e220)*I+(HFloat(2.345679734289597e162)+HFloat(9.71612358926469e161)*I)*(.3015529528-0.1030372934e-6*w^2)^2)+(HFloat(2.739493386336394e-116)+HFloat(2.739493386336394e-116)*I)*(HFloat(1.5009648027561687e-231)-HFloat(2.757556062608314e294)*I+(-HFloat(5.478986772672788e-116)+HFloat(5.478986772672788e-116)*I)*(.3015529528-0.103 ... HFloat(2.739493386336394e-116)*I)*(.3015529528-0.1030372934e-6*w^2)^4)

w1 := fsolve(S, w = 0*2*Pi .. 100000*2*Pi);

# Here I get an error 

Error, (in fsolve) Digits cannot exceed 38654705646
 

I want to substitute the solution back into the original equation.  I get caught up in RootOf and have to manually do the substitutions.

F := [x^2+y+z-1, y^2+x+z-1, z^2+x+y-1];

soln1 := solve(F);

for s in soln1 do

subs(s,F)

end do;

The 4th soln has RootOf.

soln2 := solve(_Z^2 + 2*_Z - 1);

for s in soln2 do

evala(subs({x=s,y=s,z=s},F))

end do;

How do I do this all in one step?


I was starting to set up a curved axisymmetric metric using the Physics package and came across an error message that I could not resolve. I was actually writing the metric in the form given after output line (5) in the code attcahed below. This returned the error message:

Error, (in Physics:-Setup) invalid subscript selector

Then I started fiddling and discovered that somehow braces and order of coefficients are making a difference in the metric. I have written the flat space metric in three different ways after output line (2). The difference is only in the coefficient of the last $d\phi^2$ term. For some reason, $r^2 (sin(\theta))^2$ is shown as $r (sin(\theta))^4$ in output line (3). Removing the brackets around $sin(theta)$ or writing $r^2$ after it is resolving the problem. Is this in someway related to the whole square operation? Can you please help me understand why this is happening?

The original error message I was getting went away after I similarly changed the order of coefficients in the second term of the curved metric to get output (6). Here again, there was a whole square operation!

Thank you!

 

restart

with(Physics)

[`*`, `.`, Annihilation, AntiCommutator, Antisymmetrize, Assume, Bra, Bracket, Cactus, Check, Christoffel, Coefficients, Commutator, CompactDisplay, Coordinates, Creation, D_, Dagger, Decompose, Define, Dgamma, Einstein, EnergyMomentum, Expand, ExteriorDerivative, Factor, FeynmanDiagrams, Fundiff, Geodesics, GrassmannParity, Gtaylor, Intc, Inverse, Ket, KillingVectors, KroneckerDelta, LeviCivita, Library, LieBracket, LieDerivative, Normal, Parameters, PerformOnAnticommutativeSystem, Projector, Psigma, Redefine, Ricci, Riemann, Setup, Simplify, SpaceTimeVector, StandardModel, SubstituteTensor, SubstituteTensorIndices, SumOverRepeatedIndices, Symmetrize, TensorArray, Tetrads, ThreePlusOne, ToFieldComponents, ToSuperfields, Trace, TransformCoordinates, Vectors, Weyl, `^`, dAlembertian, d_, diff, g_, gamma_]

(1)

Setup(signature = `-+++`, coordinates = (X = [t, r, theta, phi]))

`* Partial match of  'coordinates' against keyword 'coordinatesystems'`

 

`Default differentiation variables for d_, D_ and dAlembertian are: `*{X = (t, r, theta, phi)}

 

`Systems of spacetime Coordinates are: `*{X = (t, r, theta, phi)}

 

[coordinatesystems = {X}, signature = `- + + +`]

(2)

Setup(g_ = -dt^2+dr^2+r^2*dtheta^2+r(sin(theta))^4*dphi^2)

[metric = {(1, 1) = -1, (2, 2) = 1, (3, 3) = r^2, (4, 4) = r(sin(theta))^4}]

(3)

Setup(g_ = -dt^2+dr^2+r^2*dtheta^2+sin(theta)^2*r^2*dphi^2)

[metric = {(1, 1) = -1, (2, 2) = 1, (3, 3) = r^2, (4, 4) = sin(theta)^2*r^2}]

(4)

Setup(g_ = -dt^2+dr^2+r^2*dtheta^2+sin(theta)^2*r^2*dphi^2)

[metric = {(1, 1) = -1, (2, 2) = 1, (3, 3) = r^2, (4, 4) = sin(theta)^2*r^2}]

(5)

Setup(g_ = -exp(2*nu(r, theta))*dt^2+(exp(2*psi(r, theta)))(dphi-omega(r, theta)*dt)^2+(exp(2*mu(r, theta)))(dtheta)^2+exp(2*lambda(r, theta))*dr^2)

Error, (in Physics:-Setup) invalid subscript selector

 

Setup(g_ = -exp(2*nu(r, theta))*dt^2+(dphi-omega(r, theta)*dt)^2*exp(2*psi(r, theta))+exp(2*mu(r, theta))*dtheta^2+exp(2*lambda(r, theta))*dr^2)

[metric = {(1, 1) = -exp(2*nu(r, theta))+omega(r, theta)^2*exp(2*psi(r, theta)), (1, 4) = -omega(r, theta)*exp(2*psi(r, theta)), (2, 2) = exp(2*lambda(r, theta)), (3, 3) = exp(2*mu(r, theta)), (4, 4) = exp(2*psi(r, theta))}]

(6)

``


 

Download qstn.mw

For some reason machine thinks that I am trying to add a matrix to an equal sign.

Is it italic when copied and pasted?  Is it bold when copied from maple 8?  I just ahve not been able to work it out.

The only way that I can think of doing it is by multiplying by a tetrad.  Even then it does not work well see my worksheet:  The Dirac Equation in Robertson-Walker spacetime.

Factorise

   

into your Maple worksheet and copy and paste the Maple output into the answer box below.

I have a recursive function that spits out recursive formulates "evaluated inertly" so bascially it produces a formula simply like a symbolic formula(doesn't reduce the addition of values though).

 

What I would like is to color code each recursive step

e.g.,

F := proc(n)
    local i,k:
    if n <= 0 then return 1; end if:
    F(n-2) %+ F(n-1):
end proc:

F(5);

value(F(5));
 

so I would like to cover each part of the recursion differently so it is easier to see, maybe even use the previous colors so one can visualize the nestings of the recursion. (e.g., F(n-2) takes the previous formals color and tweaks it towards the red and and F(n-1) takes the porevious formulas color and tweaks it towards green)
(this would then pass an RGB value that(default, say blue) to the functions above).

 

Any way to accomplish this?

 

 

 

 

Enter the value of cos^-1(0.62) to 15 significant figures in the box below.

by cos^-1(0.62) I mean arccos(0.62) or inverse of cos(0.62)

 

For the following system, the parameters D_1,D_2,D_3,D_4,D_5,D_6,S are all positive, How can I get all the  equilibrium  and their stability.

diff(x1,t)=fS;diff(x2,t)=fV;diff(x3,t)=fC;diff(x4,t)=fR;

fS := -D2*x1*x2-D1*x1-x1*x3+S; fV := D2*x1*x2-D4*x2+x1*x3; fC := -D6*x3*x4-D5*x3+x2; fR := D6*x3*x4-x4

I want to set up an RSS or IFTTT so that I get a notification on my phone whenever there's something new in the Active Conversations stack. My phone uses Google Android. I'd prefer to not need to rely on email/gmail for the notification; something more endogenous to Android would be preferable. I've never used RSS or IFTTT, so detailed instructions are preferable.

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