The AlPI (Algoritmi Pisa) system is a small polynomial algebra system. It was designed and implemented by the first author in MuLISP-86. It is now (almost) ported by the second author in Lucid COMMON-LISP, in such a way that only a few macros are needed to transport it in any COMMON-LISP dialect (MuLISP included). Its main aim is the experimentation on the Buchberger Griibner basis completion algorithm with its different versions, and on Mora tangent cone algorithm. It is driven by a menu, and has a series of facilities to manipulate lists of polynomials. After a description of the system and of the versions of the algorithms presently implemented, we give a series of experimental results (for the MuLISP version). These results, and results of the same kind to obtain with further experimentation, can give suggestions on the versions of the algorithm to choose as default for other implementations of the algorithms. The research was done with the contribution of C. N. R., “Progetto strategic0 Software Matematico”
[1]
H. M. Möller,et al.
New Constructive Methods in Classical Ideal Theory
,
1986
.
[2]
Rüdiger Gebauer,et al.
On an Installation of Buchberger's Algorithm
,
1988,
J. Symb. Comput..
[3]
D. Bayer.
The division algorithm and the hilbert scheme
,
1982
.
[4]
Ferdinando Mora,et al.
An Algorithm to Compute the Equations of Tangent Cones
,
1982,
EUROCAM.
[5]
Heinz Kredel,et al.
Some Examples for Solving Systems of Algebraic Equations by Calculating Groebner Bases
,
1986,
J. Symb. Comput..
[6]
Harvey Cohn,et al.
An explicit modular equation in two variables and Hilbert’s twelfth problem
,
1982
.
[7]
André Galligo,et al.
Greater Easy Common Divisor and Standard Basis Completion Algorithms
,
1988,
ISSAC.
[8]
Carlo Traverso,et al.
Gröbner Trace Algorithms
,
1988,
ISSAC.