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Question: For-loop seems to affect the Defined tensor expression

Question:For-loop seems to affect the Defined tensor expression

Michael_Watson 125
define physics tensor
September 28 2015
1

 

restart; with(Physics); with(Tetrads)

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

 (1)

Physics:-Setup(coordinatesystems = {X}, mathematicalnotation = true)

[coordinatesystems = {X}, mathematicalnotation = true]

 (2)

Physics:-Define(Ybar[a], Y[a], 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]), RiemannT[k, l, m, n] = %d_[k](GammaT[m, n, l])-%d_[l](GammaT[m, n, k])+Physics:-`*`(GammaT[`~a`, m, l], GammaT[a, n, k])-Physics:-`*`(GammaT[`~a`, m, k], GammaT[a, n, l])+Physics:-`*`(GammaT[m, n, a], GammaT[`~a`, k, l]-GammaT[`~a`, l, k]))

RicciT[1, 3]

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

 (3)

for a to 4 do for b to 4 do RicciT[a, b] end do end do

Error, (in index/PhysicsTensor) expected summation indices of type symbol, received: 1

  

 

Now, if I type the RicciT from (3) it displays the same result. However,......

 

RicciT[1, 3]

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

 (4)

 

If I type a different RicciT, then ...

 

RicciT[2, 3]

Error, (in index/PhysicsTensor) expected summation indices of type symbol, received: 1

  

 

The for loop is changing the tetrad definition of RicciT.

 

NULL

 

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