<< [x-variables] [d-variables] [p c l m n cc ll mm nn next] order-matrix [(keyword) value (keyword) value ....] set_up_ring@ >> <<next>> is the optional argument. The last argument is also optional. Keywords are mpMult, coeffient ring, valuation, characteristic, schreyer, ringName. 1.When [x[0] .... x[n-1]] [D[0] .... D[n-1]] is given as the lists of variables, D[0] is usually used as the variable for homogenization and x[n-1] is used for the variable for the graduation. 2.Order matrix should be given in the order x[n-1] ... x[0], D[n-1]...D[0] 3.0<=i<c : commutative; c<=i<l : q-difference; l<=i<m : difference(better not to use it); m<=i<n : differential; 4.Graduation variables : cc<=i<c : commutative; ll<=i<l : q-difference; mm<=i<m : difference; nn<=i<n : differential; If you do not use graduation variables, set, for example, cc=c. 5.c-cc>0 or l-ll>0 or m-mm>0 or n-nn>0 must be held. Example: [$H$ $x$ $y$ $e$] [$h$ $Dx$ $Dy$ $E$] [0 1 1 1 4 1 1 1 3] ( e y x H E Dy Dx h ) [[1 1 1 1 1 1 1 0] [1 0 0 0 0 0 0 0] [0 0 0 0 0 1 0 0] ........ cf. polynomial_ring, ring_of_..., groebner.

Nobuki Takayama 2020-11-24