Known Bugs and Weaknesses in the Packages of the Mgfun Family

In the future versions of Mgfun (2.2 and later), I plan to fix all known bugs and weaknesses for which I provide a description of the origin below. (Last update: Feb 5, 1999.)
[August 14, 2002: version 3.2 of Mgfun has now been released. This page is now very obsolete! I should consider updating it.]

Ore_algebra Package

  • Unknown functions in the coefficients of skew polynomials are not accepted together with algebraic numbers in the same algebra.

    This is due to the internal use of Gröbner basis calculations which cannot accomodate unknown functions.

  • Wrong result in a call to skew_pdiv in the case of commutations of the type euler=[Tx,x].

    The code is correct in the case of the elimination of Tx, but not in the cas of the elimination of x.

  • Various crashes with message: 'Error, (in collect) cannot collect, q^n'.

    The internal normalizer for elements in an Ore algebra is not correctly implemented. This functionality is not exported to the user (yet), but the bug hinders certain types of Gröbner basis calculations (inducing weaknesses in Groebner).

    Groebner Package

  • Gröbner basis calculation does not terminate for the matrix-defined term order 'matrix'([[1,0,0,0],[0,1,0,0]],[x,y,z,t]).

    The bug is a lack of type-checking: term orderings defined by a matrix have to be defined by a matrix of full rank in order to be total orderings (which is needed for the termination of the algorithm).

  • Lack of type-checking when calling termorder in the case of an algebra declared by poly_algebra.

    All indeterminates that have been declared polynomial in an algebra have to be sorted by the term order description. Without this type-checking, one has a real pain realizing that one misspelled an indeterminate.

  • Output is not a Gröbner basis (ideal case in the non-commutative case with polynomial coefficients):

    In the Weyl algebra Q<x,Dx>, Dx and x2 yield the S-polynomial 2x which is not considered by gbasis: for a strange reason, Buchberger's first criterion which is known not to apply in the non commutative case was mistakenly used.

  • Output is not a Gröbner basis (module case):

    The code for Gröbner bases for modules is wrong in Maple V Release 5. This is due to a subtle interaction between the module structure and the improved selection strategy.

    [This bug is present in the release 5, but not in version 2.1 of Mgfun, which is available for release 4 only.]

  • The Groebner package crashes when computing with algebras involving the predefined commutation type dual_q_shift (and similar ones).

    Maple's data structure for polynomials will confuse me till the end of my life. Easy fix.

  • Wrong type-ckecking in termorder makes is impossible to input user-defined term orders.

    Easy fix.

    Holonomy Package

    (None at the moment.)

    Mgfun Package

    (None at the moment.)