- #1
Kevin McHugh
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Given: Ra[bcd] = 0
What permutations of bcd make this expression 0? TIA for your response.
What permutations of bcd make this expression 0? TIA for your response.
Rabcd+Racdb+Radbc=0Kevin McHugh said:Given: Ra[bcd] = 0
What permutations of bcd make this expression 0? TIA for your response.
Ibix said:I think this is an anti-symmetrised tensor, not a symmetrised one, isn't it?
Samy_A said:Rabcd+Racdb+Radbc=0
Ibix said:The latter is ##R_{abcd}- R_{acbd} +R_{acdb} -R_{adcb} +R_{adbc} -R_{abdc}=0##.
Any combination (if we interpret the expression as I did in post ##2).Kevin McHugh said:Am I not being clear in my question? Nobody has yet answered it. What combinations of [bcd] make Ra[bcd] zero?
Kevin McHugh said:Am I not being clear in my question? Nobody has yet answered it. What combinations of [bcd] make Ra[bcd] zero?
To elaborate on this, the first Bianchi identity Rabcd+Racdb+Radbc=0 is true for any combination of indices, but not all combination yield interesting information.Samy_A said:Any combination (if we interpret the expression as I did in post ##2).
The equation "Ra[bcd]=0" is a mathematical expression that indicates a system of equations with unknown variables, represented by the letters a, b, c, and d, that need to be solved in order to obtain a solution that makes the whole expression equal to 0.
A permutation is an arrangement of objects in a specific order. In the context of solving equations, a permutation refers to a specific arrangement of the unknown variables that can be used to solve the equation.
In order to determine which permutations work, you can plug each permutation into the equation and see if it results in a solution that makes the equation equal to 0. The permutations that work will result in a solution, while the ones that do not work will result in a non-zero value.
There are some strategies that can help you find the correct permutations more efficiently. For example, you can use the properties of the equation, such as symmetry or patterns, to eliminate certain permutations and focus on the ones that are more likely to work.
Yes, you can use a computer or a mathematical software program to solve equations with unknown variables, such as "solve Ra[bcd]=0". These tools use algorithms to quickly find the solutions, making the process more efficient and accurate.