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B.7.0.9 Fin_dim_algebra
Procedure from library nctools.lib (see nctools_lib).
- Usage:
- Fin_dim_algebra(M,[r]); M a matrix, r an optional ring.
- Return:
- nothing. Creates finite dimensional algebra structure in a ring r
(if it is given) or in a basering (by default) from the matrix M. Exports the ideal called Quot for further qring definition.
- Note:
- matrix M will be read according to relations x_j*x_i = M[i,j]; Quot is not given in its two-sided Groebner basis.
Example:
| LIB "nctools.lib";
ring r=(0,a,b),(x(1..3)),dp;
matrix S[3][3];
S[2,3]=a*x(1); S[3,2]=-b*x(1);
Fin_dim_algebra(S);
Quot = twostd(Quot);
qring Qr = Quot;
Qr;
==> // characteristic : 0
==> // 2 parameter : a b
==> // minpoly : 0
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x(1) x(2) x(3)
==> // block 2 : ordering C
==> // noncommutative relations:
==> // x(3)x(2)=(-b)/(a)*x(2)*x(3)
==> // quotient ring from ideal
==> _[1]=x(3)^2
==> _[2]=x(2)*x(3)+(-a)*x(1)
==> _[3]=x(1)*x(3)
==> _[4]=x(2)^2
==> _[5]=x(1)*x(2)
==> _[6]=x(1)^2
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