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Signature






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Integer Functions > Signature[{n1,n2,...,nd}] > Introduction to the tensor functions





Definitions of the tensor functions


For all possible values of their arguments, the discrete delta functions and , Kronecker delta functions and , and signature (Levi–Civita symbol) are defined by the formulas:

In other words, the Kronecker delta function is equal to 1 if all its arguments are equal.

In the case of one variable, the discrete delta function coincides with the Kronecker delta function . In the case of several variables, the discrete delta function coincides with Kronecker delta function :

where is the number of permutations needed to go from the sorted version of to .





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