A formal series of the form

\[ \sum_{e \in I} a_e x^e \]

such that the set of indices \(e\) for which \(a_e\) is non-zero is left-finite: for any \(i\), the set of indices \(e < i\) for which \(a_e\) is non-zero is finite.

Addition of indices is required to preserve the ordering.

term i a is a series consisting of the term \(a x^i\).

term i a * term j b = term (i+j) (a*b)

Power series representing a constant value \(c\)

constant a = term 0 a

Identity function, i.e. the indeterminate \(x\)

identity = term 1 1

Construct a power series from a list in ascending order of index

fromTerms ts = sum [term i a | (i, a) <- ts]

Power series formed from a list of coefficients of indices 0, 1, ... If the list is finite, the remaining coefficients are zero.

The smallest exponent with a non-zero coefficient (undefined on zero)

Indices with non-zero coefficients, in ascending order

A formal power series with integer indices, of which finitely many are negative.

A Laurent series with coefficients starting from the given index

The Levi-Civita field.