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D.2.8.3 katsura
Procedure from library polylib.lib (see polylib_lib).
- Usage:
- katsura([n]); n integer
- Return:
- katsura(n) : n-th katsura ideal of
(1) newly created and set ring (32003, x(0..n), dp), if
nvars(basering) < n
(2) basering, if nvars(basering) >= n
katsura() : katsura ideal of basering
Example:
| | LIB "polylib.lib";
ring r; basering;
==> // coefficients: ZZ/32003 considered as a field
==> // number of vars : 3
==> // block 1 : ordering dp
==> // : names x y z
==> // block 2 : ordering C
katsura();
==> _[1]=x+2y+2z-1
==> _[2]=x2+2y2+2z2-x
==> _[3]=2xy+2yz-y
katsura(4); basering;
==> _[1]=x(0)+2*x(1)+2*x(2)+2*x(3)-1
==> _[2]=x(0)^2+2*x(1)^2+2*x(2)^2+2*x(3)^2-x(0)
==> _[3]=2*x(0)*x(1)+2*x(1)*x(2)+2*x(2)*x(3)-x(1)
==> _[4]=x(1)^2+2*x(0)*x(2)+2*x(1)*x(3)-x(2)
==> // coefficients: ZZ/32003 considered as a field
==> // number of vars : 5
==> // block 1 : ordering dp
==> // : names x(0) x(1) x(2) x(3) x(4)
==> // block 2 : ordering C
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