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# FormalSeries -- the class of all formal series

## Description

An object of the class FormalSeries is a list \{P,n\} where P is an element of a polynomial ring and n is an integer representing the precision (the terms in degree strictly greater than n are considered zero).

## Types of FormalSeries:

- FormalGroupLaw -- the class of all formal group laws

## Methods that use an object of class FormalSeries:

- - FormalSeries -- minus a formal series
- compositionInverse(FormalSeries) -- inverse for composition of formal series
- FGL(FormalSeries) -- constructing a formal group law
- formalGroupPoint(FormalGroupLaw,FormalSeries) -- constructing a formal group point
- FormalSeries * FormalSeries -- multiplication of formal series
- FormalSeries + FormalSeries -- addition of formal series
- FormalSeries - FormalSeries -- difference of formal series
- FormalSeries == FormalSeries -- equality of formal series
- FormalSeries ^ ZZ -- powers of formal series
- inverse(FormalSeries) -- multiplicative inverse of formal series
- RingElement * FormalSeries -- multiplication of a formal series by a constant
- substitute(FormalSeries,BasicList) -- compose formal series
- truncate(FormalSeries,ZZ) -- truncate formal series
- ZZ * FormalSeries -- multiplication of a formal series by an integer

## For the programmer

The object FormalSeries is a type, with ancestor classes BasicList < Thing.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/FormalGroupLaws.m2:342:0.