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7.3.24 ringlist (plural)
Syntax:
ringlist ( ring_expression )
ringlist ( qring_expression )
Type:
- list
Purpose:
- decomposes a ring/qring into a list of 6 (or 4 in the commutative case)
components.
The first 4 components are common both for the commutative and for the
non-commutative cases, the 5th and the 6th appear only in the non-commutative case.
- upper triangle square matrix with nonzero upper triangle, containing
structural coefficients of a G-algebra (this corresponds to the
matrix C from the definition of G-algebras)
- square matrix, containing structural polynomials of a G-algebra
(this corresponds to the matrix D from the definition of G-algebras)
Note: After modifying a list aquired with ringlist, one can construct a corresponding ring with ring(list).
Example:
| | // consider the quantized Weyl algebra
ring r = (0,q),(x,d),Dp;
def RS=nc_algebra(q,1);
setring RS; RS;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : 0
==> // number of vars : 2
==> // block 1 : ordering Dp
==> // : names x d
==> // block 2 : ordering C
==> // noncommutative relations:
==> // dx=(q)*xd+1
list l = ringlist(RS);
l;
==> [1]:
==> [1]:
==> 0
==> [2]:
==> [1]:
==> q
==> [3]:
==> [1]:
==> [1]:
==> lp
==> [2]:
==> 1
==> [4]:
==> _[1]=0
==> [2]:
==> [1]:
==> x
==> [2]:
==> d
==> [3]:
==> [1]:
==> [1]:
==> Dp
==> [2]:
==> 1,1
==> [2]:
==> [1]:
==> C
==> [2]:
==> 0
==> [4]:
==> _[1]=0
==> [5]:
==> _[1,1]=0
==> _[1,2]=(q)
==> _[2,1]=0
==> _[2,2]=0
==> [6]:
==> _[1,1]=0
==> _[1,2]=1
==> _[2,1]=0
==> _[2,2]=0
// now, change the relation d*x = q*x*d +1
// into the relation d*x=(q2+1)*x*d + q*d + 1
matrix S = l[5]; // matrix of coefficients
S[1,2] = q^2+1;
l[5] = S;
matrix T = l[6]; // matrix of polynomials
T[1,2] = q*d+1;
l[6] = T;
def rr = ring(l);
setring rr; rr;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : 0
==> // number of vars : 2
==> // block 1 : ordering Dp
==> // : names x d
==> // block 2 : ordering C
==> // noncommutative relations:
==> // dx=(q2+1)*xd+(q)*d+1
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See also
ring (plural);
ringlist.
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