Kronecker delta

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Kronecked delta is maths object that has some formulas.

First, resolve deltas into one by taking symmetric and anti-symmetric combinations:

is equivalent to . So deltas can be combined into: .

Then, since the coefficients are order-1 in , the trick is to insert some quantity of into some order-1 expression in :

.

Now solve for with and , which will be 4 equations in 3 unknowns. These equations must have one degeneracy or else it will not be possible to reduce the form.

General formula[edit]

Order 1 coefficients[edit]

If

then combined form will be

where the equations to solve are:

This will be solvable if and and to:

or, if and and to:

Thus:

or:

otherwise not reducible to one kronecker delta.

Order 2 coefficients[edit]

If

then combined form will be

where the equations to solve are:

This will be solvable if and and to:


or, if Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha_1 = \beta_1 \neq 0} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_2 = b_2} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \alpha_0 \neq \beta_0} to:


otherwise not reducible to one kronecker delta.

Order 3 coefficients[edit]

If

then combined form will be

You do algebra yourself.