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D.15.1.5 autXhat

Procedure from library autgradalg.lib (see autgradalg_lib).

Usage:
autXhat(RL, w0, TOR): RL is an ideal, w an intvec, TOR a list of integers

Assume:
the basering is multigraded, the elements of TOR stand for the torsion rows of the matrix getVariableWeights(), w is an ample class or the free part of such a class.

Purpose:
compute an ideal J such that V(J) in some GL(n) is isomorphic to the H-equivariant automorphisms \widehat X --> \widehat X.

Example:
 
LIB "autgradalg.lib";
intmat Q[3][5] =
1,1,1,1,1,
1,-1,0,0,1,
1,1,1,0,0;
list TOR = 2;
ring R = 0,T(1..5),dp;
setBaseMultigrading(Q);
ideal I = T(1)*T(2) + T(3)^2 + T(4)^2;
intvec w0 = 2,1,0;
def RR = autXhat(I, w0, TOR);
==> (T(1),T(2))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(4)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> // coefficients: QQ
==> // number of vars : 30
==> //        block   1 : ordering dp
==> //                  : names    T(1) T(2) T(3) T(4) T(5) Y(1) Y(2) Y(3) Y(\
   4) Y(5) Y(6) Y(7) Y(8) Y(9) Y(10) Y(11) Y(12) Y(13) Y(14) Y(15) Y(16) Y(1\
   7) Y(18) Y(19) Y(20) Y(21) Y(22) Y(23) Y(24) Y(25)
==> //        block   2 : ordering C
==> // ** redefining adMons (  list adMons;) autgradalg.lib::autKS:2324
==> // ** redefining k (int k = 1;) autgradalg.lib::stabilizer:1975
==> (T(1),T(2))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(4)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(4)
==>    [2]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(3)
==>    [2]:
==>       T(4)
==>    [3]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(2)
==>    [2]:
==>       T(3)
==>    [3]:
==>       T(4)
==>    [4]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
==> (T(1),T(2),T(3),T(4),T(5))
==> [1]:
==>    0
==> [2]:
==>    [1]:
==>       T(1)
==>    [2]:
==>       T(2)
==>    [3]:
==>       T(3)
==>    [4]:
==>       T(4)
==>    [5]:
==>       T(5)
==> [3]:
==>    [1]:
==>       [1]:
==>          wp
==>       [2]:
==>          1,1,1,1,1
==>    [2]:
==>       [1]:
==>          C
==>       [2]:
==>          0
==> [4]:
==>    _[1]=0
setring RR;
RES;
==> [1]:
==>    [1]:
==>       _[1,1]=Y(1)
==>       _[1,2]=0
==>       _[1,3]=0
==>       _[1,4]=0
==>       _[1,5]=0
==>       _[2,1]=0
==>       _[2,2]=Y(7)
==>       _[2,3]=0
==>       _[2,4]=0
==>       _[2,5]=0
==>       _[3,1]=0
==>       _[3,2]=0
==>       _[3,3]=Y(13)
==>       _[3,4]=0
==>       _[3,5]=0
==>       _[4,1]=0
==>       _[4,2]=0
==>       _[4,3]=0
==>       _[4,4]=Y(19)
==>       _[4,5]=0
==>       _[5,1]=0
==>       _[5,2]=0
==>       _[5,3]=0
==>       _[5,4]=0
==>       _[5,5]=Y(25)
==>    [2]:
==>       1,0,0,
==>       0,1,0,
==>       0,0,1 
==>    [3]:
==>       _[1]=Y(2)
==>       _[2]=Y(3)
==>       _[3]=Y(4)
==>       _[4]=Y(5)
==>       _[5]=Y(6)
==>       _[6]=Y(8)
==>       _[7]=Y(9)
==>       _[8]=Y(10)
==>       _[9]=Y(11)
==>       _[10]=Y(12)
==>       _[11]=Y(14)
==>       _[12]=Y(15)
==>       _[13]=Y(16)
==>       _[14]=Y(17)
==>       _[15]=Y(18)
==>       _[16]=Y(20)
==>       _[17]=Y(21)
==>       _[18]=Y(22)
==>       _[19]=Y(23)
==>       _[20]=Y(24)
==>       _[21]=Y(1)*Y(7)*Y(13)*Y(19)*Y(25)*Z-1
==>       _[22]=Y(13)^2-Y(19)^2
==>       _[23]=Y(1)*Y(7)-Y(13)^2
==> [2]:
==>    [1]:
==>       _[1,1]=Y(1)
==>       _[1,2]=0
==>       _[1,3]=0
==>       _[1,4]=0
==>       _[1,5]=0
==>       _[2,1]=0
==>       _[2,2]=Y(7)
==>       _[2,3]=0
==>       _[2,4]=0
==>       _[2,5]=0
==>       _[3,1]=0
==>       _[3,2]=0
==>       _[3,3]=0
==>       _[3,4]=Y(14)
==>       _[3,5]=0
==>       _[4,1]=0
==>       _[4,2]=0
==>       _[4,3]=Y(18)
==>       _[4,4]=0
==>       _[4,5]=0
==>       _[5,1]=0
==>       _[5,2]=0
==>       _[5,3]=0
==>       _[5,4]=0
==>       _[5,5]=Y(25)
==>    [2]:
==>       1,0,0,
==>       0,1,0,
==>       1,1,1 
==>    [3]:
==>       _[1]=Y(2)
==>       _[2]=Y(3)
==>       _[3]=Y(4)
==>       _[4]=Y(5)
==>       _[5]=Y(6)
==>       _[6]=Y(8)
==>       _[7]=Y(9)
==>       _[8]=Y(10)
==>       _[9]=Y(11)
==>       _[10]=Y(12)
==>       _[11]=Y(13)
==>       _[12]=Y(15)
==>       _[13]=Y(16)
==>       _[14]=Y(17)
==>       _[15]=Y(19)
==>       _[16]=Y(20)
==>       _[17]=Y(21)
==>       _[18]=Y(22)
==>       _[19]=Y(23)
==>       _[20]=Y(24)
==>       _[21]=-Y(1)*Y(7)*Y(14)*Y(18)*Y(25)*Z-1
==>       _[22]=-Y(14)^2+Y(18)^2
==>       _[23]=Y(1)*Y(7)-Y(18)^2
kill RR, Q, R;