Compute a partial fraction decomposition of :

Compute a partial fraction decomposition of :

Partial fraction decomposition of a rational function:

Check that this is equivalent to the input:

Partial fraction decomposition involving a polynomial denominator that does not factor over the rationals:

Use ExtensionReals to put complex conjugate roots together into a quadratic denominator:

Compute a partial fraction decomposition of a rational function with a nonzero polynomial part:

A rational function:

Rewrite it as a sum of partial fractions over the reals:

This is the same as specifying the "Decomposition" in PartialFractionElements:

Obtain the polynomial part:

Obtain the fractional part:

Integrate a rational function:

Now compute its partial fraction decomposition over the reals:

Integrating term-wise shows where the terms from the integral arise:

Sum a rational function:

Now compute its partial fraction decomposition:

Summing term-wise shows where the individual terms arise:

InverseLaplaceTransform of a rational function:

Now compute its partial fraction decomposition:

Inverting term-wise shows where the terms from the sum arise:

A rational function:

Write it as a sum of partial fractions but allowing no extension field:

Apart gives essentially the same result:

PartialFractionElements with the "Decomposition" setting also gives the same result:

PartialFractions by default does a full factorization of the denominator and thus can give a result that uses Root objects:

Use ExtensionNone to avoid this factorization: