Christopher2222

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15 years, 333 days

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These are replies submitted by Christopher2222

@acer You've obviously pointed out my method is ridiculous and terrible.  Someone else can come up with a more concrete way of my intentions, I quit. 

I'll start it off.  I've made one run here but we should make 5 runs and take the average for the result
Here's a sample test problem run with Maple 2022.0 on a Win7 64bit, 8Gb RAM, Toshiba Tecra S10, Intel Core2 Duo, P8700 @2.53GHz

restart;
UseHardwareFloats := true;
n := 3500;
t0 := time();
M := LinearAlgebra:-RandomMatrix(n, n, generator = 0. .. 1, outputoptions = [datatype = float[8]]);
randTime := time() - t0;
LinearAlgebra:-LA_Main:-Rank(M);
rankTime := time() + (-t0 - randTime);
total := rankTime + randTime;

There are performace comparisons across the different versions of Maple and competing products, but no real comparisons across various platform setups (which would be befificial in your case - but would also be interesting to others)

I wonder if we could set up a section or table somewhere (in a post) with specific test calculations and time them with various system steups by users in the community.  As a side post I will start it. 

@Carl Love I can confirm that works in MapleFlow.

As well the select command will be more compact

 

@Thomas Richard Thanks.  Was that by design? 

Programming in Mapleflow is a slightly different ballgame. 

@SiggiN You're right .flow files can not be uploaded.  You can always zip any file.  Here's the complete list of files that can be uploaded.  Mapleprimes will have to update so that .flow files can  be uploaded.

Maple

@C_R works fine in 2022.0

I suspect when generating the sigma_t equation something was accidentally typed.

The only way to be sure is if SiggiN can upload his Mapleflow sheet. 

Not sure how you're going to get numbers from an equation that doesn't have any values assigned to the variables. 

You have nothing assigned to sigma_p nor is anything assigned to sigma_uts_t. 

@MapleUser2017 Now that you mention it.  That has happened to me a couple of times.  The command just doesn't execute.  Now I can't recall if it was version 2022 or 2023 - I'll keep an eye out for it next time it happens. 

Executing the code (Enter) just returns to the next line with nothing done, like it was in text mode or something.  I'll definitely watch for that occurrence.

@Carl Love ToInert is to prevent unintential evaluation, it's to move an active form to an inactive form.  It did what it was supposed to.  During my "experimentation" it may have been grouped as a left over.  There were some un-intentional side effects when I was playing around with alias so ToInert was needed at the time.  However, thanks for making that discovery.

@ecterrab Nice work!

Is it possible to have mixed derivatives as prime and dot?

**edit add**  Actually, now that I think of it since dot and prime appear in specific orders above the function being operated on it would be difficult to discern between diff(f(x,t),x,t) and diff(f(x,t),t,x) .  A new convention would have to be adopted to - maybe moving the prime from a trailing postion to a forward postion ?? 

I'm not sure given the way they work if that would be an easy thing to do, but for an example case to show explicitly what I mean :
we could show diff(f(x),x,t) as 

and also show diff(f(x),t,x) as   

**extra added**  That would of course depend on what variables you've assigned dot and prime as to the order they would appear above the function.  The standard form as having dot associated with time. 

@lemelinm I thought you wanted a dot and prime notation.  Nonetheless you achieved the goal of removing the partial derivative symbols and making the form more compact.

Adding this

Results in a compact form.  I added at the end and recalulated the scalar.


 

NULL

General metric

Lecture 5 in Math Prediction

NULL

NULL

restart

with(Physics); Setup(mathematicalnotation = true); Setup(signature = `+---`)

[signature = `+ - - -`]

(1)

ds2 := exp(v(r, t))*c^2*dt^2-exp(lambda(r, t))*dr^2-r^2*(da^2+sin(a)^2*dp^2)

exp(v(r, t))*c^2*dt^2-exp(lambda(r, t))*dr^2-r^2*(da^2+sin(a)^2*dp^2)

(2)

Setup(coordinatesystems = (Z = [t, r, a, p]), metric = ds2)

[coordinatesystems = {Z}, metric = {(1, 1) = exp(v(r, t))*c^2, (2, 2) = -exp(lambda(r, t)), (3, 3) = -r^2, (4, 4) = -r^2*sin(a)^2}, spaceindices = lowercaselatin_is]

(3)

g_[]

Physics:-g_[mu, nu] = Matrix(%id = 36893488148105121172)

(4)

Christoffel[`~alpha`, mu, nu, nonzero]

Physics:-Christoffel[`~alpha`, mu, nu] = {(1, 1, 1) = (1/2)*(diff(v(r, t), t)), (1, 1, 2) = (1/2)*(diff(v(r, t), r)), (1, 2, 1) = (1/2)*(diff(v(r, t), r)), (1, 2, 2) = (1/2)*exp(-v(r, t)+lambda(r, t))*(diff(lambda(r, t), t))/c^2, (2, 1, 1) = (1/2)*c^2*exp(v(r, t)-lambda(r, t))*(diff(v(r, t), r)), (2, 1, 2) = (1/2)*(diff(lambda(r, t), t)), (2, 2, 1) = (1/2)*(diff(lambda(r, t), t)), (2, 2, 2) = (1/2)*(diff(lambda(r, t), r)), (2, 3, 3) = -exp(-lambda(r, t))*r, (2, 4, 4) = -exp(-lambda(r, t))*r*sin(a)^2, (3, 2, 3) = 1/r, (3, 3, 2) = 1/r, (3, 4, 4) = -sin(a)*cos(a), (4, 2, 4) = 1/r, (4, 3, 4) = cot(a), (4, 4, 2) = 1/r, (4, 4, 3) = cot(a)}

(5)

Ricci[nonzero]

Physics:-Ricci[mu, nu] = {(1, 1) = (1/4)*(2*c^2*((diff(diff(v(r, t), r), r))*r+(1/2)*(diff(v(r, t), r))*((diff(v(r, t), r))*r-(diff(lambda(r, t), r))*r+4))*exp(v(r, t)-lambda(r, t))-2*(diff(diff(lambda(r, t), t), t)-(1/2)*(diff(lambda(r, t), t))*(diff(v(r, t), t)-(diff(lambda(r, t), t))))*r)/r, (1, 2) = (diff(lambda(r, t), t))/r, (2, 1) = (diff(lambda(r, t), t))/r, (2, 2) = (1/4)*(2*(diff(diff(lambda(r, t), t), t)-(1/2)*(diff(lambda(r, t), t))*(diff(v(r, t), t)-(diff(lambda(r, t), t))))*r*exp(-v(r, t)+lambda(r, t))-2*c^2*((1/2)*r*(diff(v(r, t), r))^2-(1/2)*r*(diff(v(r, t), r))*(diff(lambda(r, t), r))+(diff(diff(v(r, t), r), r))*r-2*(diff(lambda(r, t), r))))/(c^2*r), (3, 3) = 1+(1/2)*(-(diff(v(r, t), r))*r+(diff(lambda(r, t), r))*r-2)*exp(-lambda(r, t)), (4, 4) = -(1/2)*(-2+((diff(v(r, t), r))*r-(diff(lambda(r, t), r))*r+2)*exp(-lambda(r, t)))*sin(a)^2}

(6)

Ricci[scalar]

(1/2)*(-exp(v(r, t))*(diff(lambda(r, t), r))*(diff(v(r, t), r))*exp(-v(r, t)-lambda(r, t))*c^2*r^2+exp(v(r, t))*(diff(v(r, t), r))^2*exp(-v(r, t)-lambda(r, t))*c^2*r^2+2*exp(v(r, t))*(diff(diff(v(r, t), r), r))*exp(-v(r, t)-lambda(r, t))*c^2*r^2-2*exp(v(r, t))*(diff(lambda(r, t), r))*exp(-v(r, t)-lambda(r, t))*c^2*r+2*exp(v(r, t))*(diff(v(r, t), r))*exp(-v(r, t)-lambda(r, t))*c^2*r+exp(lambda(r, t))*(diff(v(r, t), t))*(diff(lambda(r, t), t))*exp(-v(r, t)-lambda(r, t))*r^2-exp(lambda(r, t))*(diff(lambda(r, t), t))^2*exp(-v(r, t)-lambda(r, t))*r^2-2*exp(lambda(r, t))*(diff(diff(lambda(r, t), t), t))*exp(-v(r, t)-lambda(r, t))*r^2-2*(diff(lambda(r, t), r))*exp(-lambda(r, t))*c^2*r+2*exp(-lambda(r, t))*(diff(v(r, t), r))*c^2*r+4*exp(-lambda(r, t))*c^2-4*c^2)/(c^2*r^2)

(7)

NULL

ToInert(v(r, t))

alias(diff(v(t), t) = diff(v(r, t), t))

alias(diff(v(t), t, t) = diff(v(r, t), t, t))

alias(diff(v(x), x) = diff(v(r, t), r))

alias(diff(v(x), x, x) = diff(v(r, t), r, r))

ToInert(lambda(r, t))

alias(diff(lambda(t), t) = diff(lambda(r, t), t))

alias(diff(lambda(x), x) = diff(lambda(r, t), r))

alias(diff(lambda(x), x, x) = diff(lambda(r, t), r, r))

alias(diff(lambda(t), t, t) = diff(lambda(r, t), t, t))

NULL

Ricci[scalar]

(1/2)*(-exp(v(r, t))*`λ'`*`v'`*exp(-v(r, t)-lambda(r, t))*c^2*r^2+exp(v(r, t))*`v'`^2*exp(-v(r, t)-lambda(r, t))*c^2*r^2+2*exp(v(r, t))*(diff(`v'`, r))*exp(-v(r, t)-lambda(r, t))*c^2*r^2-2*exp(v(r, t))*`λ'`*exp(-v(r, t)-lambda(r, t))*c^2*r+2*exp(v(r, t))*`v'`*exp(-v(r, t)-lambda(r, t))*c^2*r+exp(lambda(r, t))*(diff(v(t), t))*(diff(lambda(t), t))*exp(-v(r, t)-lambda(r, t))*r^2-exp(lambda(r, t))*(diff(lambda(t), t))^2*exp(-v(r, t)-lambda(r, t))*r^2-2*exp(lambda(r, t))*(diff(diff(lambda(t), t), t))*exp(-v(r, t)-lambda(r, t))*r^2-2*`λ'`*exp(-lambda(r, t))*c^2*r+2*exp(-lambda(r, t))*`v'`*c^2*r+4*exp(-lambda(r, t))*c^2-4*c^2)/(c^2*r^2)

(8)

NULL


 

Download General_metric-2.mw

So to clarify a little you want diff(v(r,t),t) displayed as or just

and the diff(v(r,t),r) displayed as or

I think using ToInert or something might be a work around. 

I'm surprised ecterrab hasn't chimed in, he might even be working on an update to his Physics package to handle this sort of thing.  We could suggest it as a Physics package improvement?

@lemelinm

Perhaps you can make "alias" work in this case somehow.

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