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I need help with these two questions. anything is helpful

I'm trying to define some multilinear forms to study differential geometry. What I need is only symbolic. My intention is symplify computations involving multilinear forms.

For example, to create an symbolic inner product "g" I used the command "define" like in this post:

http://www.mapleprimes.com/questions/203480-Define-And-Use-Abstract-Linear-Operator

 

So I tipped:

define(g, orderless, multilinear);

 

My doubt is: how can I declare that g(x,y) is always scalar?

With it I would simplify things like g(g(z,w)*x,y) = g(z,w)*g(x,y)

 

In my case, specifically, I type:

v:=(X,Y,Z)->g(Y,Z)*X-g(X,Z)*Y;

r:=(X,Y,Z,W)->g(v(X,Y,Z),W)-g(Y,T)*g(v(X,T,Z),W)+g(X,T)*g(v(Y,T,Z),W);

expand(r(X,Y,Z,W));

and the result is:

g(W,g(Y,Z)*X)-g(W,g(X,Z)*Y)-g(T,Y)*g(W,g(T,Z)*X)+g(T,Y)*g(W,g(X,Z)*T)+g(T,X)*g(W,g(T,Z)*Y)-g(T,X)*g(W,g(Y,Z)*T)

But I would enjoy that it were:

g(Y,Z)*g(W,X)-g(X,Z)*g(W,Y)-g(T,Z)*g(T,Y)*g(W,X)+g(X,Z)*g(T,Y)*g(W,T)+g(T,Z)*g(T,X)*g(W,Y)-g(Y,Z)*g(T,X)*g(W,T)

 

Is there a way to declare that g(x,y) is always scalar?

Thanks.

 

 

hi,

i'am beginers in  the maple programmation, i want to solve the einstien equation in the spherical coordinate,

 

 

Hi

How Maple knows free and dummy index?

 

How to plot magnetic field of maxwell equations like vector field

I attempt to understand is it possible whether to calculate the next expression by means of mathematica:

where

{,}- anti-communicator;

 a=0,1,2,3;

\tau^{0}-unity matrix; \tau^{i} - Pauli matrix;

and:
 

 

 


 
finally - Levi-Civita symbol; -Hermitian conjugation.

 

Thank you for your kind replies .

I would like to set a metric in its contravariant form before its covariant form but Maple does not do this operation.

Thanks!

I need hepl.  I work with the physics paсkage and I set:

with(Physics);
with(StandardModel);
Setup(mathematicalnotation = true)

Coordinates(X)

Define(p)

Setup(su2)

CompactDisplay(p(X))

U := 1+i*(1/f)*p[a](X)*Psigma[a]

H := v*U

DD[mu] := (d_[mu]+2*i*nu_5*KroneckerDelta[mu, 0])*Psigma[0]

And next:

Trace(DD[mu]*H*DD[mu]*H) or simplify(DD[mu]*H*DD[mu]*H)

Maple speaks:

Error, (in Physics:-Trace) invalid input: `union` received Physics:-d_[mu] = F1, which is not valid for its 1st argument

What I am doing wrong? (f, v, nu_5 is constans; a=1,2,3 and mu=0,1,2,3, Psigma[0] is unit matrix 2x2)

 

And if I write:

simplify(Trace(Psigma[a]*Psigma[a]))

Maple doesn't understand that it equals six. 

 

I need yours hepl.  I work with the physics paсkage and I set:

with(Physics)

Setup(mathematicalnotation = true)

 Coordinates(X)

Setup(Dgammarepresentation = standard)

Setup(spaceindices = uppercaselatin)

Define(m, m5, y, p, mm, pp)

I try to square the next value: 

W := Dgamma[mu]*d_[mu]+M+Psigma[A]*aa[A]-mm*Dgamma[0]-m5*Dgamma[0]*Dgamma[5]+I*Dgamma[5]*Psigma[B]*pp[B]+I*Dgamma[5]*y

("*" is multiplication)

W*W

And after that I want to simplify it:

Simplify(W*W)

I guess that matter is owing to d_[`~mu`]. If I remove this term:

E:=Psigma[A]*aa[A]-mm*Dgamma[0]-m5*Dgamma[0]*Dgamma[5]+I*Dgamma[5]*Psigma[B]*pp[B]+I*Dgamma[5]*y

And if i do:

E*E

Then next error emerges:

What is it?

 

I have to prove the following:

So I do not need the explicit derivative of the function Psi(r,t) . The metric is:

ds^2=(1-rg/r)*dt^2-(1-rg/r)^(-1)*dr^2

I am in the case of a collapsing star that emit radiation during the collapsing.  And I do not need to have a rotating black hole so that the reason I dont have dt*dr term in the metric, and I fix theta and phi.  So if you look in the Maple file attach to this post, I don't manage to obtain what I need to prove the equality between the two aspect of the same calculation.

Plese, take into account that I am sort of novice with the Physcis package and that the question is not part of an exam.

Thank you in advance for your help. 

Mario Lemelin

dAlembertian.mw

 

 

Hello! 

For the last couple of days I've been trying really hard to solve the linear PDE 

dR/dt = -dRdH/dqdp + dRdH/(dpdq) . Where R is a function R(t,q(t),p(t)) and H is the hamiltonian H=  p^2/2 +q^2 +2*q .

(dH/dp= p and dH/dq= -2q-2), q and p depends on the time t, and I'm supposed to solve the PDE and then plot the gaussian distribution (2D). 

I tried doing this:

pde := diff(R(t, q1(t), p1(t)), t) = -(diff(R(t, q(t), p(t)), q(t)))*p(t)+(diff(R(t, q(t), p(t)), p(t)))*(-2*q(t)-2)

But pdsolve(pde) gives me:  "Error, (in pdsolve/info) the name of the indeterminate function must be given". 

When I change q(t) to q and p(t) to p I get:

R(t, q, p) = _F1(p^2-2*q^2-4*q, -(1/2)*ln(sqrt(2)*q+p+sqrt(2))*sqrt(2)+t)

And then I'm lost. How do I solve this PDE in maple? 

Thankful for any help 

 

 

I need yours hepl.  I work with the physics paсkage and I set:

with(Physics)

Setup(mathematicalnotation = true)

 Coordinates(X)

Setup(Dgammarepresentation = standard)

Setup(spaceindices = uppercaselatin)

Define(M, aa, mu, mu5, Pi, eta)

M_[mu, mu5] := Dgamma[mu]*d_[mu]+M+Psigma[A]*aa[A]-mu*Dgamma[0]-mu5*Dgamma[0]*Dgamma[5]+i*Dgamma[5]*Psigma[B]*Pi[B]+i*Dgamma[5]*eta

And next:

Dagger(M_[mu, mu5])

How is Maple explained that  

Dagger(d_[mu])=d_[mu]

conjugate(M)=M

conjugate(aa[A])=aa[A]

conjugate(i)=i

and so on?

Dear Friends, I work with physics paсkage. I have a quation. I don't understend how one works with metrics. For example, let:

Nice!
Very good!

1) It doesn't work. Why? (I want exactly gamma_[A,B], rather than g_[A,B], because as i guess gamma_[A,B] has a signature [1,1,1] but g_[A,B] has a signature [-1,-1,-1])

 2) And how may I see what is matrices g_[A, B], gamma_[A, B] explicitly? That is I know how to see what is g_[mu, nu], for this one needs write "g_[];".  But how may I see g_[A, B] and gamma_[A, B] in explicitly forms?

3) Why command Trace(g_[mu, nu]))  does not work?"

Dear Friends, I work with physics paсkage. And I don't know how to simplify the next expression: Dgamma[mu]*a[mu]*Dgamma[nu]*a[nu]

(I want to obtain  the well-known result a2 )

The command "Simplify" doesn't work in this case.

Dear Friends, I work with physics paсkage. One allows to calculate in four dimensional space-time. But in addition, I need to calculate in three dimensional space. For example, I need t0 use the next scalar products: xAy and zawa  where A=0,1,2,3 and a=1,2,3. How may I do it?

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