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Macaulay2 web site
FormalGroupLaws
::
FormalGroupLaws
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.
Source code
The source code from which this documentation is derived is in the file
FormalGroupLaws.m2
.
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
substitute(FormalSeries,BasicList)
-- compose formal series
truncate(FormalSeries,ZZ)
-- truncate formal series
ZZ * FormalGroupPoint
-- a binary operator, usually used for multiplication
ZZ * FormalSeries
-- multiplication of a formal series by an integer