# subalgebraBasis -- Compute subalgebra basis (sagbi basis) generators

## Synopsis

• Usage:
N = subalgebraBasis M
N = subalgebraBasis A
N = subalgebraBasis L
N = subalgebraBasis B
• Inputs:
• A, an instance of the type Subring,
• M, , of generators for a subring of
• L, a list, containing generators for a subring of
• B, an instance of the type SAGBIBasis, containing a partial computation of a sagbi basis
• Optional inputs:
• AutoSubduce => , default value true, a flag indicating when to perform autosubduction on the generators before performing the Sagbi basis computation (See: AutoSubduce)
• ReduceNewGenerators => , default value true, a flag indicating whether to apply gaussian elimination to new sagbi generators before adding them to the current sagbi basis (See: ReduceNewGenerators)
• StorePending => , default value true, a flag that indicates whether the pending list should be stored in the result. (See: StorePending)
• Strategy => , default value "Master", the update strategy at the beginning of each loop: \"DegreeByDegree\", \"Incremental\", and \"Master\". The strategy \"Master\" is a hybrid that combines the other two; starting with \"DegreeByDegree\" for low degrees and switching to \"Incremental\". (See: Strategy)
• SubductionMethod => , default value "Top", the method used for subduction either: \"Top\" or \"Engine\". (See: SubductionMethod)
• Limit => an integer, default value 100, a degree limit for the binomial S-pairs that are computed internally.
• AutoSubduceOnPartialCompletion => , default value false, apply autosubduction to the sagbi generators the first time no new generators are added. Use this only if very few new sagbi generators are expected. (See: AutoSubduceOnPartialCompletion)
• PrintLevel => an integer, default value 0, When this is greater than zero, information is printed about the progress of the computation (See: PrintLevel)
• Recompute => , default value false, if true then the computation will resume otherwise it starts at the beginning
• RenewOptions => , default value false, if true then the computation will use the options specified otherwise it will use the previously selected options (except for the following, which may always be specified: PrintLevel, Limit, Recompute, and RenewOptions)
• Outputs:
• N, , whose entries form a partial subalgebra basis

## Description

The command subalgebraBasis A is equivalent to the command generators sagbi A.

• sagbi -- Compute a subalgebra basis (sagbi basis)
• AutoSubduce -- Flag for autosubduction before the Sagbi algorithm
• ReduceNewGenerators -- Flag for reducing new generators in Sagbi algorithm
• StorePending -- Flag for storing the pending list to the result of the Sagbi algorithm
• Strategy -- an optional argument
• SubductionMethod -- Subduction method for the Sagbi algorithm
• Limit -- an optional argument
• AutoSubduceOnPartialCompletion -- Subduct sagbi generators at the end of the Sagbi algorithm
• PrintLevel -- Levels of information displayed during Sagbi algorithm
• Recompute -- Flag for restarting a sagbi computation
• RenewOptions -- Flag for reselecting the options for a sagbi computation

## Ways to use subalgebraBasis :

• "subalgebraBasis(List)"
• "subalgebraBasis(Matrix)"
• "subalgebraBasis(Subring)"

## For the programmer

The object subalgebraBasis is .