# 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)
• Outputs:
• N, , whose entries form a partial subalgebra basis

## Description

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