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Question: Length of Output Exceeded Error when using tetrads

Question:Length of Output Exceeded Error when using tetrads

Michael_Watson 125 Maple 18
physics tetrads
December 16 2014
2

I am using the SumOverRepeatedIndices and get a Length of Output Exceeded error. Sometimes if I close the file and restart the program then I get a result and no error.  However, if I recalculate then I get the error.

 


restart; with(Physics); with(Tetrads)

[e_, eta_, gamma_, l_, lambda_, m_, mb_, n_]

 (1)

`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))` := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(zeta, zetabar, u, v)), (du+Physics:-`*`(Ybar(zeta, zetabar, u, v), dzeta)+Physics:-`*`(Y(zeta, zetabar, u, v), dzetabar)-Physics:-`*`(Physics:-`*`(Y(zeta, zetabar, u, v), Ybar(zeta, zetabar, u, v)), dv))^2)

2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2

 (2)

X = [zeta, zetabar, u, v]

X = [zeta, zetabar, u, v]

 (3)

PDEtools:-declare(`#msup(mi("ds",mathcolor = "#af00af"),mn("2",mathcolor = "#af00af"))`)

Ybar(zeta, zetabar, u, v)*`will now be displayed as`*Ybar

 (4)

Setup(coordinates = (X = [zeta, zetabar, u, v]), metric = 2*dzeta*dzetabar+2*du*dv+2*H(zeta, zetabar, u, v)*(du+Ybar(zeta, zetabar, u, v)*dzeta+Y(zeta, zetabar, u, v)*dzetabar-Y(zeta, zetabar, u, v)*Ybar(zeta, zetabar, u, v)*dv)^2)

[coordinatesystems = {X}, metric = {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}]

 (5)

g_[]

g_[mu, nu] = (Matrix(4, 4, {(1, 1) = 2*H(X)*Ybar(X)^2, (1, 2) = 1+2*H(X)*Ybar(X)*Y(X), (1, 3) = 2*H(X)*Ybar(X), (1, 4) = -2*H(X)*Ybar(X)^2*Y(X), (2, 1) = 1+2*H(X)*Ybar(X)*Y(X), (2, 2) = 2*H(X)*Y(X)^2, (2, 3) = 2*H(X)*Y(X), (2, 4) = -2*H(X)*Y(X)^2*Ybar(X), (3, 1) = 2*H(X)*Ybar(X), (3, 2) = 2*H(X)*Y(X), (3, 3) = 2*H(X), (3, 4) = 1-2*H(X)*Ybar(X)*Y(X), (4, 1) = -2*H(X)*Ybar(X)^2*Y(X), (4, 2) = -2*H(X)*Y(X)^2*Ybar(X), (4, 3) = 1-2*H(X)*Ybar(X)*Y(X), (4, 4) = 2*H(X)*Y(X)^2*Ybar(X)^2}))

 (6)

NULL

``

eqn1 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[1, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

 (7)

eqn2 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[2, `~mu`])) = 0

`[Length of output exceeds limit of 1000000]`

 (8)

eqn3 := SumOverRepeatedIndices(Physics:-`*`(d_[mu](Y(Zeta, zetabar, u, v)), e_[4, `~mu`])) = x

(1/2)*(-(diff(Y(Zeta, zetabar, u, v), zetabar))*(Y(X)*Ybar(X)+1)*2^(1/2)+(diff(Y(Zeta, zetabar, u, v), u))*2^(1/2)*(Y(X)-Ybar(X))-(diff(Y(Zeta, zetabar, u, v), v))*2^(1/2)*(Y(X)-Ybar(X)))/((-(Ybar(X)^2+1)*(Y(X)^2+1)/(Y(X)-Ybar(X))^2)^(1/2)*(Y(X)-Ybar(X))) = x

 (9)

eqn1 := `[Length of output exceeds limit of 1000000]` = 0

`[Length of output exceeds limit of 1000000]` = 0

 (10)

algsubs(`[Length of output exceeds limit of 1000000]` = 0, `[Length of output exceeds limit of 1000000]`)

0

 (11)

``

simplify(`[Length of output exceeds limit of 1000000]`)

``


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