R . 1 : RngLoc, RngInt -> RngElt

Return the generator (indeterminate) for the power series or Laurent series ring R.

elt< R | e, [ a_1, ..., a_(d)], p > : RngIntElt, SeqEnum, RngIntElt -> RngLo

Given a power series ring R[[X]] or Laurent series ring R((X)), integers e and p >= e, and a sequence a=[a_1, ..., a_d] of elements of R, return the series a_1X^e + ... + a_dX^(e + d - 1) + O(X^p). If R is a power series ring, then e must be non-negative. The integer e or the integer p or both may be omitted. If e is omitted, it will be set to zero by default; if p is omitted it will be taken to be e + d, where d is the length of the sequence a.

R ! s : RngLoc, SeqEnum -> RngLocElt

Coerce s into the power series ring or Laurent series ring R. Here s is allowed to be a sequence of elements from (or coercable into) the coefficient ring of R, or just an element from (or coercable into) R. A sequence [a_1, ..., a_d] is converted into the series a_1 + a_2X^1 + ... + a_dX^(d - 1) + O(X^d).

Given a (power or Laurent) series f, this returns the precision that is stored with f. If f is stored with infinite precision the value -1 is returned.

Coefficient(f, i) : FldLocElt, RngIntElt -> RngElt

Coefficient(f, i) : RngLocElt, RngIntElt -> RngElt

Given a series f in R[[X]] or f in R((X)), and an integer i, return the coefficient of the i-th power of the indeterminate X of f. This coefficient is an element of R. The integer i must be less than p, the precision of f; if f is a power series, i must be non-negative.