Christopher2222

MaplePrimes Activity


These are replies submitted by Christopher2222

@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

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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.

Try Settings in Typesetting

for example

with(Typesetting):
Settings(prime=r,typesetprime=true,typesetdot=true)

diff(v(t),t)+diff(v(r),r)

                              

(**edit ** sorry it may not work with a function of 2 variables)

I'll rephrase that.  How would you do it? 

adding the argument (1/cot=tan) does not work.

What would be the best way to write that so that when simplify is called on 1/cot is converted to tan

@Thiago_Rangel7 since ecterrab mentioned that in the past Maple's preferred form was in sin and cos.  Then maybe we should first convert trigonometric expressions to sincos and then simplify.

We could add a command in the initialization file in a similar way that simplification to sec and csc could be "turned off" done here https://www.mapleprimes.com/questions/236026-Can-Simplification-To-Sec-And-Csc-Be-Turned-Of

 

It looks like a combination of using Windows10 with Windows XP in a virutal machine will provide the best coverage for all versions of Maple. 

@charlie_fcl What version of Linux are you using?  I'm not too familiar with Linux but I recall most software through wine works best with Ubuntu. 

Alternatively you could always use Oracle VM virtualbox and use that virtual environment inside linux to install windows and from there can use Maple that way if you want. The difference is, it chews up more hard drive space (because you're installing another full operating system) and resources are shared with the host machine - but it's guaranteed to work.  WineHQ is not so much guaranteed like you've shown it doesn't appear to work but WineHQ is a much smaller footprint.  Personally I've never had much luck with Wine, I've always resorted to virtualbox.  With windows I use virtualbox to intstall older versions of windows for older software - works for my purposes.

@charlie_fcl It might run on the wine application in linux. 

There is some comparisons you might find here https://12000.org/ some old and some up to date.  It might offer some insight.

What is the purpose if knowing that Maple 16 might be faster than 2019?  Did you want to revert to an older version of Maple if that were the case?  And why would you do that if there have been significant improvements otherwise, since then?

@Carl Love Thanks for that.  In my opinion I think the default should be 100%. 

Regarding the error I'm getting above, I'm still getting the error using Import.  I tried adding the tag ,TrustServerCertificate=true but that didn't work.  I've enabled it through my firewall so it doesn't appear that is the reason.  But strange it's occurring on all versions 2019, 2018 on my windows 7 machine.  That being the case, it seems possibly a setting has changed (but I don't know if it ever worked before). 

I can access the file through firefox which leads me to believe it's an issue with Maple.  I'm using Maple 2020.1, so if someone else using that version could verify, I could narrow my issue further.

**edit add**  Confirmed that it seems to be localized to my computer.  I should maybe uninstall and re-install and take it from there but if it occurs on the earlier versions of maple then a re-install probably won't solve my issue. 

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