FormalGroupLaws -- commutative formal group laws

Description

This package provides elementary functions to deal with commutative formal group laws of dimension one.

Authors

Baptiste Calmès
Viktor Petrov

Version

This documentation describes version 0.2 of FormalGroupLaws.

Citation

If you have used this package in your research, please cite it as follows:

@misc{FormalGroupLawsSource,
  title = {{FormalGroupLaws: commutative formal group laws. Version~0.2}},
  author = {Baptiste Calm{\`e}s and Viktor Petrov},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Types
- FormalGroupLaw -- the class of all formal group laws
- FormalGroupPoint -- the class of all points of a formal group
- FormalSeries -- the class of all formal series
Functions and commands
- compositionInverse -- inverse for composition
- FGL -- constructing a formal group law
- formalGroupPoint -- constructing a formal group point
- series -- constructing a formal series
- universalFGL -- universal formal group law
- universalFGLQ -- universal formal group law over rationals
- valuation -- smallest degree of monomials
Methods
- - FormalGroupPoint -- inverse to a point of a formal group
- - FormalSeries -- minus a formal series
- compositionInverse(FormalSeries) -- inverse for composition of formal series
- FGL(FormalSeries) -- constructing a formal group law
- FormalGroupPoint + FormalGroupPoint -- sum of points of a formal group
- FormalGroupPoint - FormalGroupPoint -- difference of points of a formal group
- 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
- series(RingElement,ZZ) -- constructing a formal series
- substitute(FormalSeries,BasicList) -- compose formal series
- truncate(FormalSeries,ZZ) -- truncate formal series
- universalFGL(ZZ,String,String,String) -- universal formal group law in the Lazard ring
- universalFGLQ(ZZ,String,String,String) -- universal formal group law in the Lazard ring tensor Q
- ZZ * FormalGroupPoint
- ZZ * FormalSeries -- multiplication of a formal series by an integer

For the programmer

The object FormalGroupLaws is a package, defined in FormalGroupLaws.m2.

The source of this document is in FormalGroupLaws.m2:332:0.