I am working with the Physics package in Maple 2018. I have a spacetime with a metric g and the vector field l is the tangent to a null curve. I have two problems:

(1) I want to check in maple that indeed g(l,l)=0. For this I wrote:

SumOverRepeatedIndices(g_[mu,nu]l[~mu]l[~nu])

Firstly, when I try to execute this command, the program keeps on evaluating for a long time. So, I have to `interrupt the current operation', undo this command, save and reopen the file, execute the entire worksheet again and then somehow it works. However, as you can see in step(13) of the attached worksheet, Maple returns an expression for this command but doesn't cancel out terms and show that it is indeed zero. How can I do this?

(2) I wish to find $(\nabla_l l)^\nu$. Is there a way to directly do this? Or should I do something like:

Define(L[mu,~nu]=D_mu l[~nu])

SumOverRepeatedIndices(l[~mu]L[mu,~nu])

Thanks a lot.

Edit: I actually carried out these steps too. First, I defined $L_\mu^\nu$ in step (14). Then, when I ask for the non-zero components of L, I find that the L_\mu,\nu components are given. How can I get the non-zero L_\mu^\nu components? Also, in step (16), I did the `SumOverRepeatedindices' but it returned only a symbolic result without evaluationg.

try2.mw

Hi I have encounted this error:

Error, (in diffalg/DAparse_polynomial) unknown indeterminate or coefficient outside base field, -Cp+Cf/(1+Kw*(-sigma*`ΔPi`+`ΔP`)*(1-(1/2)*Fp/Ff)/Ks)

The text highlighted in bold is an equation that I typed in.

Can I know what it means?

I was trying to verify some solution to pde in textbook using Maple. The book gives the Cauchy data for this first order PDE in the form that Maple does not like when I used it as input. Here is an example

When I typed

pde:=u(x,y)*(x+y)*diff(u(x,y),x)+u(x,y)*(x-y)*diff(u(x,y),y)=x^2+y^2;
ic:=u(x,2*x)=0;
pdsolve([pde,ic],u(x,y))

Maple complained

Error, (in PDEtools:-Library:-NormalizeBoundaryConditions) unexpected 
occurrence of the variables {x} in the 2nd operand of u(x, 2*x) in the given initial conditions

In Mathematica it accepts such form of Cauchy data:

pde=u[x,y]*(x+y)*D[u[x,y],x]+u[x,y]*(x-y)*D[u[x,y],y]==x^2+y^2;
ic=u[x,2*x]==0;
DSolve[{pde,ic},u[x,y],{x,y}]

(I have not verified the above answer is correct or not).

Am I doing something wrong in Maple?

Or is there a trick or option or method to allow Maple to accepts such initial conditions? The book I am looking at has many problems where Cauch data is given on such form (i.e. u=0 on specific curve or in 3D on some specific surface). Here is another example

Which I'd like write its initial conditions as u(x,1/x)=0 but can not.

I could ofcourse solve the pde without these initial conditions, and then post process the answer to find the constants of integration from the Cauchy data given. But it will be nice if Maple would accept the IC as is.

@chandrashekhar 

There are no efficient algorithms for this.
How would you simplify by hand the expression

512*b^9 + (2303*a + 2304)*b^8 + (4616*a^2 + 9216*a + 4608)*b^7 + (5348*a^3 + 16128*a^2 + 16128*a + 5376)*b^6
 + (4088*a^4 + 16128*a^3 + 24192*a^2 + 16128*a + 4032)*b^5 + (1946*a^5 + 10080*a^4 + 20160*a^3 + 20160*a^2 
+ 10080*a + 2016)*b^4 + (728*a^6 + 4032*a^5 + 10080*a^4 + 13440*a^3 + 10080*a^2 + 4032*a + 672)*b^3 
+ (116*a^7 + 1008*a^6 + 3024*a^5 + 5040*a^4 + 5040*a^3 + 3024*a^2 + 1008*a + 144)*b^2 
+ (26*a^8 + 144*a^7 + 504*a^6 + 1008*a^5 + 1260*a^4 + 1008*a^3 + 504*a^2 + 144*a + 18)*b + 9*a^8 
+ 36*a^7 + 84*a^6 + 126*a^5 + 126*a^4 + 84*a^3 + 36*a^2 + 9*a + 1

to  (a+2*b+1)^9 - a*(a-b)^8   ?

sdf.pdf,sdf.mw

1,1,2,2,2,3,3,2,2,1,2,2,2,3,3,1,1

i would like to research the ordering mechanism of this kind of series Before sorting.

How I can simplify result? For factor or using rule.

Thanks

Dear there, 

Is there a possibility for tracking changes like Microsoft Office in the saved a Maple worksheet after some editings?

I think that we all encounter the same case. I mean we don't remember generally all changes after editing our codes. 

If there is no possibility for tracking changes,  what are your solutions or suggestions in order to prevent to forget? 

Hi

how can i find x in terms of y(x)

y(x)=

Is it considered a bug when pdetest does not give zero for a solution given by pdsolve? 

restart;
pde := x*diff(w(x,y,z),x)+  a*z*diff(w(x,y,z),y)+b*y*diff(w(x,y,z),z)=c:
sol:=pdsolve(pde,w(x,y,z));
pdetest(sol,pde)

Gives

which is not zero.

This is the first time I've seen this happen. 

Maple 2019.1 using Physics version 362

If we have following expression

4*beta*c*lambda^2*mu^2+2*beta*c*lambda*mu^3+2*beta*c*lambda*mu^2*nu+beta*c*mu^3*nu-4*c*lambda^2*mu^2*sigma-2*c*lambda*mu^3*sigma-2*c*lambda*mu^2*nu*sigma-c*mu^3*nu*sigma+4*beta*lambda^3*sigma+4*beta*lambda^2*mu*sigma+2*beta*lambda^2*nu*sigma+2*beta*lambda*mu^2*sigma+2*beta*lambda*mu*nu*sigma+beta*mu^3*sigma+beta*mu^2*nu*sigma+4*lambda^2*mu^2*sigma+2*lambda*mu^3*sigma+2*lambda*mu^2*nu*sigma+mu^3*nu*sigma

If I use the command simplify(---,size), it gives

((2*c-2)*lambda-beta+nu*(-1+c))*mu^3+(2*(lambda*(-1+c)-(1/2)*beta))*(2*lambda+nu)*mu^2-2*beta*lambda*(2*lambda+nu)*mu-2*lambda^2*beta*(2*lambda+nu)

which can also be written if i did manually as

beta*mu^3+(2*lambda+nu)*(beta*mu^2+2*beta*lambda*mu+2*beta*lambda^2+(1-c)*(2*lambda+mu)*mu^2)

My question with all learned people is: in Maple, how i can get most simplified and short expression automaticall?

Please help me to understand the Maple.

Thanking you in anticipation.

I need to use gamma as a "free" symbol in pde that I pass to pdsolve, so that the latex comes out as \gamma OK in the solution.

in other words, the pde itself uses the symbol gamma (as it is written in the textbook and I want to keep it the same). This gamma is not the known constant gamma. Something similar to using alpha and beta or x and y. 

But gamma in a known constant in Maple and I am worried this will affect some computation inside pdsolve if I use gamma  as known number in the PDE (even though I think it should not change the result of pdsolve as there are no other numbers in the PDE input, I just wanted to be safe).

I am not able to clear gamma

unassign(gamma)  gives error since it is protected.

Is  there a way around this? Should I use wrap the name with 'gamma'  or `gamma` for example? 

Here is an example

pde := a*diff(w(x,y,z),x)+ b*diff(w(x,y,z),y)+c*diff(w(x,y,z),z)= alpha*x+beta*y+gamma*z+delta;

It is the gamma above I am worried about using in the input. What is the correct way to do this?  

Hello,

I am trying to work with the Physics package to calculate Christoffel symbols. I have just started using Maple today and am coming up against a few hurdles.

I want to change the signature of the metric from (+---) to (-+++). I am typing the following in math mode:

Setup( signature = '-+++')

However, this is returning the following error:

"Error, invalid sum/difference" with my command rewritten within a red box together with the last '+" within another red box. Can you please help me out with this?

Thank you.

I am completely new to maple and am stuck in the very beginning trying to use the Physics package to calculate Christoffel symbols. Suppose I have coordinates (t, x, sigma, theta). The metric g_ has coefficients that are functions of (t,x,sigma) i.e. the metric is like

g_ = a(t,x,sigma) dt^2 + b(t,x,sigma)dt dx + dx^2 + dsigma^2 + sigma^2 dtheta^2.

(Should I write dsigma^2 or (d sigma)^2?)

How do I tell maple to treat a, b as functions of (t,x,sigma)?

Thank you.

HI, 

Yesterday I replied  denitsastaicova's question while providing an attached file. 

Surprisingly, I wasn't able to save the worksheet after having executed it. The only way I found to save it was to copy-paste it's content in a new worksheet and save this latter without any execution.
Here is the file
events.mw

For info I'm working with  Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895
on Mac OS Mojave 10.14.3
If I open this file and execute it (and even if I execute only the commands from the initial restart to the three dsolve), I get this pop-up error message when trying to save it:

Does my worksheet contain some undesired character or is it a bug ?