Singular Manual: katsura

| #### 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
    ==> // 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
    ==> // 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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