## 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;
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