set_up_ring@

<< [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