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Michael_Watson

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These are questions asked by Michael_Watson

Not evaluating theta in volume integral...

Michael_Watson 125 Maple 2021
integration
September 09 2021
1 1

Not_evaluating_theta.mw

 

When I tried to explain to a student how to set it up, it stopped working.  I tried changing the order, but got the same result. I tried using "t" instead of theta, but got the same result. Please help.

Dirac delta function...

Michael_Watson 125 Maple 2021
physics dirac incomplete-question
August 30 2021
0 0

Can you use the Dirac function in different coordinate systems?

factoring a variable...

Michael_Watson 125 Maple
simplification
August 17 2021
3 6

I need to express a function after factoring out a variable. How do I do this?

L/(z*sqrt(z^2 + L^2)

Need to write in terms of L/z or z/L.

 

how do I solve an algebra problem with a...

Michael_Watson 125 Maple 2016
solve syntax 2dmath
August 01 2016
1 0

I have a simple algebraic problem, but Maple can't eliminate the exp(3P) in each term. Please help.

I get the following error:

Error, (in solve) cannot solve for an unknown function with other operations in its arguments


restart

R13eqn := -2*H*Ybar3*Zbar-H*Z1-H1*Z+H1*Zbar+H4*Ybar3-H41 = 0

-2*H*Ybar3*Zbar-H*Z1-H1*Z+H1*Zbar+H4*Ybar3-H41 = 0

 (1)

H := exp(3*P)*(Z+Zbar)

exp(3*P)*(Z+Zbar)

 (2)

H1 := 3*P1*exp(3*P)*(Z+Zbar)+exp(3*P)*(Z1+Zbar1)

3*P1*exp(3*P)*(Z+Zbar)+exp(3*P)*(Z1+Zbar1)

 (3)

H4 := H*(Z4+Zbar4)/(Z+Zbar)

exp(3*P)*(Z4+Zbar4)

 (4)

H41 := ((H1*(Z4+Zbar4)+H*(Z41+Zbar41))(Z+Zbar)-H*(Z4+Zbar4)(Z1+Zbar1))/(Z+Zbar)^2

((3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*(Z(Z+Zbar)+Zbar(Z+Zbar))+(exp(3*P))(Z+Zbar)*(Z1(Z+Zbar)+Zbar1(Z+Zbar)))*(Z4(Z+Zbar)+Zbar4(Z+Zbar))+(exp(3*P))(Z+Zbar)*(Z(Z+Zbar)+Zbar(Z+Zbar))*(Z41(Z+Zbar)+Zbar41(Z+Zbar))-exp(3*P)*(Z+Zbar)*(Z4(Z1+Zbar1)+Zbar4(Z1+Zbar1)))/(Z+Zbar)^2

 (5)

simplify(R13eqn)

(((-3*Z(Z+Zbar)*P1(Z+Zbar)-3*P1(Z+Zbar)*Zbar(Z+Zbar)-Z1(Z+Zbar)-Zbar1(Z+Zbar))*Zbar4(Z+Zbar)+(-3*P1(Z+Zbar)*Z4(Z+Zbar)-Z41(Z+Zbar)-Zbar41(Z+Zbar))*Zbar(Z+Zbar)-3*P1(Z+Zbar)*Z(Z+Zbar)*Z4(Z+Zbar)+(-Z1(Z+Zbar)-Zbar1(Z+Zbar))*Z4(Z+Zbar)-Z(Z+Zbar)*(Z41(Z+Zbar)+Zbar41(Z+Zbar)))*(exp(3*P))(Z+Zbar)+exp(3*P)*(Z+Zbar)*(Zbar4(Z1+Zbar1)+Z4(Z1+Zbar1)+(3*P1-2*Ybar3)*Zbar^3+((3*P1-4*Ybar3)*Z+Zbar1)*Zbar^2+((-3*P1-2*Ybar3)*Z^2-2*Z1*Z+(Z4+Zbar4)*Ybar3)*Zbar-3*P1*Z^3+(-2*Z1-Zbar1)*Z^2+(Z4+Zbar4)*Ybar3*Z))/(Z+Zbar)^2 = 0

 (6)

Zbar41 := -2*Zbar*Zbar1

-2*Zbar*Zbar1

 (7)

Z41 := -2*Z1*Z

-2*Z1*Z``

 (8)

Z4 := -Z^2

-Z^2

 (9)

Zbar4 := -Zbar^2

-Zbar^2

 (10)

simplify(R13eqn)

((3*P1(Z+Zbar)*Zbar(Z+Zbar)^3+(3*Z(Z+Zbar)*P1(Z+Zbar)+Z1(Z+Zbar)+3*Zbar1(Z+Zbar))*Zbar(Z+Zbar)^2+3*(Z(Z+Zbar)*P1(Z+Zbar)+(2/3)*Z1(Z+Zbar)+(2/3)*Zbar1(Z+Zbar))*Z(Z+Zbar)*Zbar(Z+Zbar)+3*(Z(Z+Zbar)*P1(Z+Zbar)+Z1(Z+Zbar)+(1/3)*Zbar1(Z+Zbar))*Z(Z+Zbar)^2)*(exp(3*P))(Z+Zbar)-exp(3*P)*(Z+Zbar)*(Zbar(Z1+Zbar1)^2+Z(Z1+Zbar1)^2+3*(Z+Zbar)*((P1+(1/3)*Ybar3)*Z^2+((2/3)*Zbar*Ybar3+(2/3)*Z1+(1/3)*Zbar1)*Z-Zbar*((P1-Ybar3)*Zbar+(1/3)*Zbar1))))/(Z+Zbar)^2 = 0

 (11)

expand(((3*P1(Z+Zbar)*Zbar(Z+Zbar)^3+(3*Z(Z+Zbar)*P1(Z+Zbar)+Z1(Z+Zbar)+3*Zbar1(Z+Zbar))*Zbar(Z+Zbar)^2+3*(Z(Z+Zbar)*P1(Z+Zbar)+(2/3)*Z1(Z+Zbar)+(2/3)*Zbar1(Z+Zbar))*Z(Z+Zbar)*Zbar(Z+Zbar)+3*(Z(Z+Zbar)*P1(Z+Zbar)+Z1(Z+Zbar)+(1/3)*Zbar1(Z+Zbar))*Z(Z+Zbar)^2)*(exp(3*P))(Z+Zbar)-exp(3*P)*(Z+Zbar)*(Zbar(Z1+Zbar1)^2+Z(Z1+Zbar1)^2+3*(Z+Zbar)*((P1+(1/3)*Ybar3)*Z^2+((2/3)*Zbar*Ybar3+(2/3)*Z1+(1/3)*Zbar1)*Z-Zbar*((P1-Ybar3)*Zbar+(1/3)*Zbar1))))/(Z+Zbar)^2 = 0)

-3*(exp(P))^3*Ybar3*Zbar^4/(Z+Zbar)^2-2*(exp(P))^3*Z^3*Z1/(Z+Zbar)^2-3*(exp(P))^3*P1*Z^4/(Z+Zbar)^2-(exp(P))^3*Z^3*Zbar1/(Z+Zbar)^2+3*(exp(P))^3*P1*Zbar^4/(Z+Zbar)^2+(exp(P))^3*Zbar^3*Zbar1/(Z+Zbar)^2-(exp(P))^3*Z*Zbar(Z1+Zbar1)^2/(Z+Zbar)^2-(exp(P))^3*Z*Z(Z1+Zbar1)^2/(Z+Zbar)^2-(exp(P))^3*Z^4*Ybar3/(Z+Zbar)^2-(exp(P))^3*Zbar*Zbar(Z1+Zbar1)^2/(Z+Zbar)^2-(exp(P))^3*Zbar*Z(Z1+Zbar1)^2/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^3/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Zbar(Z+Zbar)^3/(Z+Zbar)^2+3*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^2*Z1(Z+Zbar)/(Z+Zbar)^2+(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^2*Zbar1(Z+Zbar)/(Z+Zbar)^2+(exp(3*P))(Z+Zbar)*Zbar(Z+Zbar)^2*Z1(Z+Zbar)/(Z+Zbar)^2+3*(exp(3*P))(Z+Zbar)*Zbar(Z+Zbar)^2*Zbar1(Z+Zbar)/(Z+Zbar)^2-4*(exp(P))^3*Ybar3*Z^3*Zbar/(Z+Zbar)^2-8*(exp(P))^3*Ybar3*Z^2*Zbar^2/(Z+Zbar)^2-8*(exp(P))^3*Ybar3*Z*Zbar^3/(Z+Zbar)^2-4*(exp(P))^3*Z^2*Z1*Zbar/(Z+Zbar)^2-2*(exp(P))^3*Z*Z1*Zbar^2/(Z+Zbar)^2-6*(exp(P))^3*P1*Z^3*Zbar/(Z+Zbar)^2+6*(exp(P))^3*P1*Z*Zbar^3/(Z+Zbar)^2-(exp(P))^3*Z^2*Zbar*Zbar1/(Z+Zbar)^2+(exp(P))^3*Z*Zbar^2*Zbar1/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^2*Zbar(Z+Zbar)/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)*Zbar(Z+Zbar)^2/(Z+Zbar)^2+2*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)*Zbar(Z+Zbar)*Z1(Z+Zbar)/(Z+Zbar)^2+2*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)*Zbar(Z+Zbar)*Zbar1(Z+Zbar)/(Z+Zbar)^2 = 0

 (12)

solve(-(exp(P))^3*Z^2*Zbar*Zbar1/(Z+Zbar)^2+(exp(P))^3*Z*Zbar^2*Zbar1/(Z+Zbar)^2-4*(exp(P))^3*Ybar3*Z^3*Zbar/(Z+Zbar)^2-8*(exp(P))^3*Ybar3*Z^2*Zbar^2/(Z+Zbar)^2-8*(exp(P))^3*Ybar3*Z*Zbar^3/(Z+Zbar)^2-4*(exp(P))^3*Z^2*Z1*Zbar/(Z+Zbar)^2-2*(exp(P))^3*Z*Z1*Zbar^2/(Z+Zbar)^2-6*(exp(P))^3*P1*Z^3*Zbar/(Z+Zbar)^2+6*(exp(P))^3*P1*Z*Zbar^3/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^2*Zbar(Z+Zbar)/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)*Zbar(Z+Zbar)^2/(Z+Zbar)^2+2*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)*Zbar(Z+Zbar)*Z1(Z+Zbar)/(Z+Zbar)^2+2*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)*Zbar(Z+Zbar)*Zbar1(Z+Zbar)/(Z+Zbar)^2-(exp(P))^3*Z^3*Zbar1/(Z+Zbar)^2+(exp(P))^3*Zbar^3*Zbar1/(Z+Zbar)^2-(exp(P))^3*Z*Zbar(Z1+Zbar1)^2/(Z+Zbar)^2-(exp(P))^3*Z*Z(Z1+Zbar1)^2/(Z+Zbar)^2-(exp(P))^3*Z^4*Ybar3/(Z+Zbar)^2-(exp(P))^3*Zbar*Zbar(Z1+Zbar1)^2/(Z+Zbar)^2-(exp(P))^3*Zbar*Z(Z1+Zbar1)^2/(Z+Zbar)^2+(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^2*Zbar1(Z+Zbar)/(Z+Zbar)^2+(exp(3*P))(Z+Zbar)*Zbar(Z+Zbar)^2*Z1(Z+Zbar)/(Z+Zbar)^2-3*(exp(P))^3*Ybar3*Zbar^4/(Z+Zbar)^2-2*(exp(P))^3*Z^3*Z1/(Z+Zbar)^2-3*(exp(P))^3*P1*Z^4/(Z+Zbar)^2+3*(exp(P))^3*P1*Zbar^4/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^3/(Z+Zbar)^2+3*P1(Z+Zbar)*(exp(3*P))(Z+Zbar)*Zbar(Z+Zbar)^3/(Z+Zbar)^2+3*(exp(3*P))(Z+Zbar)*Z(Z+Zbar)^2*Z1(Z+Zbar)/(Z+Zbar)^2+3*(exp(3*P))(Z+Zbar)*Zbar(Z+Zbar)^2*Zbar1(Z+Zbar)/(Z+Zbar)^2 = 0, P1)

Error, (in solve) cannot solve for an unknown function with other operations in its arguments

  

NULL

``


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Using a Defined Tetrad...

Michael_Watson 125
define tensor physics
October 09 2015
1 0

 

I am trying to use the Define() funtion for the tetrad form of the Ricci Tensor. I use the Setup() function to define the tetradmetric and the tetrad labels. However, the function continues do some strange things with the d_ . It should be just a simple sum over the repeated indices, but I am getting imaginary terms.

 

  restart; with(Physics); with(Tetrads)

0, "%1 is not a command in the %2 package", Tetrads, Physics

 (1)

Physics:-Setup(coordinatesystems = {X}, spacetimeindices = greek, tetradindices = lowercaselatin, tetradmetric = Matrix([[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]], shape = symmetric), mathematicalnotation = true)

[coordinatesystems = {X}, mathematicalnotation = true, spacetimeindices = greek, tetradindices = lowercaselatin, tetradmetric = {(1, 2) = 1, (3, 4) = 1}]

 (2)

Physics:-Define(GammaT[a, b, c], RicciT[b, c] = -%d_[c](GammaT[`~a`, b, a])+%d_[a](GammaT[`~a`, b, c])-Physics:-`*`(GammaT[`~m`, b, a], GammaT[`~a`, m, c])+Physics:-`*`(GammaT[`~m`, b, c], GammaT[`~a`, m, a])-Physics:-`*`(GammaT[`~a`, b, m], GammaT[`~m`, c, a]-GammaT[`~m`, a, c]))

{Physics:-Dgamma[mu], GammaT[a, b, c], Physics:-Psigma[mu], RicciT[b, c], Physics:-d_[mu], Physics:-Tetrads:-eta_[a, b], Physics:-g_[mu, nu], Physics:-Tetrads:-l_[mu], Physics:-Tetrads:-m_[mu], Physics:-Tetrads:-mb_[mu], Physics:-Tetrads:-n_[mu], Physics:-KroneckerDelta[mu, nu], Physics:-LeviCivita[alpha, beta, mu, nu], Physics:-SpaceTimeVector[mu](X)}

 (3)

RicciT[1, 2]

-%d_[2](GammaT[`~1`, 1, 1]+GammaT[`~2`, 1, 2]+GammaT[`~3`, 1, 3]+GammaT[`~4`, 1, 4])-GammaT[`~1`, 1, 3]*GammaT[`~3`, 2, 1]-GammaT[`~3`, 1, 3]*GammaT[`~3`, 2, 3]-GammaT[`~4`, 1, 3]*GammaT[`~3`, 2, 4]+GammaT[`~4`, 1, 2]*GammaT[`~1`, 4, 1]+GammaT[`~4`, 1, 2]*GammaT[`~3`, 4, 3]+GammaT[`~4`, 1, 2]*GammaT[`~4`, 4, 4]+GammaT[`~1`, 1, 2]*GammaT[`~3`, 1, 3]+GammaT[`~1`, 1, 2]*GammaT[`~4`, 1, 4]+GammaT[`~2`, 1, 2]*GammaT[`~1`, 2, 1]+GammaT[`~2`, 1, 2]*GammaT[`~3`, 2, 3]+GammaT[`~2`, 1, 2]*GammaT[`~4`, 2, 4]+GammaT[`~3`, 1, 2]*GammaT[`~1`, 3, 1]+GammaT[`~3`, 1, 2]*GammaT[`~3`, 3, 3]+GammaT[`~3`, 1, 2]*GammaT[`~4`, 3, 4]-GammaT[`~1`, 1, 4]*GammaT[`~4`, 2, 1]-GammaT[`~3`, 1, 4]*GammaT[`~4`, 2, 3]-GammaT[`~4`, 1, 4]*GammaT[`~4`, 2, 4]-GammaT[`~1`, 1, 1]*GammaT[`~1`, 2, 1]-GammaT[`~3`, 1, 1]*GammaT[`~1`, 2, 3]-GammaT[`~4`, 1, 1]*GammaT[`~1`, 2, 4]-GammaT[`~1`, 1, 2]*GammaT[`~2`, 2, 1]-GammaT[`~3`, 1, 2]*GammaT[`~2`, 2, 3]-GammaT[`~4`, 1, 2]*GammaT[`~2`, 2, 4]-(1/2)*2^(1/2)*%d_[3](GammaT[`~2`, 1, 2])+(1/2)*2^(1/2)*%d_[3](GammaT[`~1`, 1, 2])+GammaT[`~2`, 3, 2]*GammaT[`~3`, 1, 2]+GammaT[`~2`, 4, 2]*GammaT[`~4`, 1, 2]+GammaT[`~1`, 1, 1]*GammaT[`~1`, 1, 2]+GammaT[`~1`, 1, 2]*GammaT[`~2`, 1, 2]-GammaT[`~1`, 2, 2]*GammaT[`~2`, 1, 1]-GammaT[`~2`, 1, 3]*GammaT[`~3`, 2, 2]-GammaT[`~2`, 1, 4]*GammaT[`~4`, 2, 2]+((1/2)*I)*2^(1/2)*%d_[1](GammaT[`~4`, 1, 2])-((1/2)*I)*2^(1/2)*%d_[4](GammaT[`~4`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[1](GammaT[`~3`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[4](GammaT[`~3`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[2](GammaT[`~2`, 1, 2])+((1/2)*I)*2^(1/2)*%d_[2](GammaT[`~1`, 1, 2])

 (4)

 

``

 

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