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# Edit detail for noncommutative Groebner bases revision 2 of 2

 1 2 Editor: hemmecke Time: 2024/01/09 17:15:47 GMT+0 Note: correct according to 96da3341640d9b207218400f485e66c453114241 (remove VarSet from NGroebnerPackage)

changed:
-gPak := NGroebnerPackage(Polynomial(Integer), IndexedExponents(Symbol), Symbol, Pdo)
gPak := NGroebnerPackage(Polynomial(Integer), IndexedExponents(Symbol), Pdo)


FriCAS can compute Groebner bases for noncommutative polynomial rings of solvable type (of category SolvableSkewPolynomialCategory?). Below we give example using partial differential operators:

fricas
(1) -> Pdo := PartialDifferentialOperator(Polynomial(Integer), Symbol)
 (1)
Type: Type
fricas
xx := D(x)$Pdo + y*D(z)$Pdo
 (2)
Type: PartialDifferentialOperator?(Polynomial(Integer),Symbol)
fricas
yy := D(y)$Pdo - x*D(z)$Pdo
 (3)
Type: PartialDifferentialOperator?(Polynomial(Integer),Symbol)
fricas
L := xx*xx + yy*yy
 (4)
Type: PartialDifferentialOperator?(Polynomial(Integer),Symbol)
fricas
gPak := NGroebnerPackage(Polynomial(Integer), IndexedExponents(Symbol), Pdo)
 (5)
Type: Type
fricas
groebner([L, xx])\$gPak
 (6)
Type: List(PartialDifferentialOperator?(Polynomial(Integer),Symbol))