CASA Function: mgbasis
Compute the normed reduced Groebner basis.
- GB := mgbasis(F, X)
- GB := mgbasis(F, X, torder1)
- GB := mgbasis(F, X, torder1, torder2)
- F : list(list(polynom(rational)))
- A list of polynomial tuples.
- X : list(name)
- A list of indeterminates.
- torder1 : name
- A power-product-tuple ordering. Either term (for term first) or index (for index first - default).
- torder2 : name
- A power-product ordering. Either plex (for pure lexicographic) or tdeg (for total degree - default).
- GB : list(list(polynom(rational)))
- The normed reduced Groebner basis of F.
- The command mgbasis(F, X, torder1, torder2) computes the normed reduced Groebner basis of F with respect to the indeterminates X and the given orderings. The algorithm used in mgbasis is described as Alg.13 in .
- The polynomial tuples in F are represented as lists of polynomials.
- If X has the form [x1, x2, ..., xn], then using the pure lexicographic ordering this is interpreted as x1 > x2 > ... > xn. Within the total degree ordering, ties are broken by inverse lexicographic order.
> F := [[x*y-1,x+2], [y^2+x+1,y-1]]:
> mgbasis(F, [x,y]);
> mgbasis(F, [y,x], term, plex);