9 Algorithms

For constructing Gröbner Bases the following function is used:

basis( algorithm, divisionInterface, system)
returns object of class Basis which is an involutive basis for system system
algorithm:
the string defining the algorithm used

Value of algorithm Algorithm used
"IB" algorithm Involutive Basis http://arXiv.org/math.AC/0501111 for any admissible order
"JBI" algorithm Janet Basis I http://arXiv.org/math.AC/0603161 for degree compatible orders (see. 4)
"JBII/highest" algorithm Janet Basis II http://arXiv.org/math.AC/0603161 with the option ``highest'' in its subalgorithm Update and for degree compatible orders (see. 4)
"JBII/lowest" algorithm Janet Basis II http://arXiv.org/math.AC/0603161 with the option ``lowest'' in its subalgorithm Update and for degree compatible orders (see. 4)

divisionInterface:
specifies an interface for the involutive division (see. 8.1) that is used in the construction of an involutive basis

system:
the list representing the polynomials as objects of class Poly or their initialization strings (see. 6.2)



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