i1 : -- A Cremona transformation of P^20
ringP20=QQ[t_0..t_20];
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i2 : phi=map(ringP20,ringP20,{t_10*t_15-t_9*t_16+t_6*t_20,t_10*t_14-t_8*t_16+t_5*t_20,t_9*t_14-t_8*t_15+t_4*t_20,t_6*t_14-t_5*t_15+t_4*t_16,t_11*t_13-t_16*t_17+t_15*t_18-t_14*t_19+t_12*t_20,t_3*t_13-t_10*t_17+t_9*t_18-t_8*t_19+t_7*t_20,t_10*t_12-t_2*t_13-t_7*t_16-t_6*t_18+t_5*t_19,t_9*t_12-t_1*t_13-t_7*t_15-t_6*t_17+t_4*t_19,t_8*t_12-t_0*t_13-t_7*t_14-t_5*t_17+t_4*t_18,t_10*t_11-t_3*t_16+t_2*t_20,t_9*t_11-t_3*t_15+t_1*t_20,t_8*t_11-t_3*t_14+t_0*t_20,t_7*t_11-t_3*t_12+t_2*t_17-t_1*t_18+t_0*t_19,t_6*t_11-t_2*t_15+t_1*t_16,t_5*t_11-t_2*t_14+t_0*t_16,t_4*t_11-t_1*t_14+t_0*t_15,t_6*t_8-t_5*t_9+t_4*t_10,t_3*t_6-t_2*t_9+t_1*t_10,t_3*t_5-t_2*t_8+t_0*t_10,t_3*t_4-t_1*t_8+t_0*t_9,t_2*t_4-t_1*t_5+t_0*t_6})
o2 = map(ringP20,ringP20,{t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t , t t - t t + t t })
10 15 9 16 6 20 10 14 8 16 5 20 9 14 8 15 4 20 6 14 5 15 4 16 11 13 16 17 15 18 14 19 12 20 3 13 10 17 9 18 8 19 7 20 10 12 2 13 7 16 6 18 5 19 9 12 1 13 7 15 6 17 4 19 8 12 0 13 7 14 5 17 4 18 10 11 3 16 2 20 9 11 3 15 1 20 8 11 3 14 0 20 7 11 3 12 2 17 1 18 0 19 6 11 2 15 1 16 5 11 2 14 0 16 4 11 1 14 0 15 6 8 5 9 4 10 3 6 2 9 1 10 3 5 2 8 0 10 3 4 1 8 0 9 2 4 1 5 0 6
o2 : RingMap ringP20 <--- ringP20
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i3 : time psi=invertBirMap phi
-- used 0.0810556 seconds
o3 = map(ringP20,ringP20,{- t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t - t t + t t - t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t - t t + t t - t t - t t , t t + t t - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t , - t t + t t - t t + t t - t t , - t t + t t - t t + t t - t t , - t t + t t - t t + t t - t t , - t t + t t - t t })
15 18 14 19 11 20 15 17 13 19 10 20 14 17 13 18 9 20 11 17 10 18 9 19 15 16 3 19 2 20 14 16 3 18 1 20 13 16 3 17 0 20 12 16 8 17 7 18 6 19 5 20 11 16 2 18 1 19 10 16 2 17 0 19 9 16 1 17 0 18 11 13 10 14 9 15 3 12 8 13 7 14 6 15 4 20 3 5 2 6 1 7 0 8 4 16 3 11 2 14 1 15 3 10 2 13 0 15 3 9 1 13 0 14 8 10 7 11 2 12 5 15 4 19 8 9 6 11 1 12 5 14 4 18 7 9 6 10 0 12 5 13 4 17 2 9 1 10 0 11
o3 : RingMap ringP20 <--- ringP20
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i4 : time isInverseMap(phi,psi)
-- used 0.0164138 seconds
o4 = true
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i5 : -- A Cremona transformation of P^26
ringP26=QQ[t_0..t_26];
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i6 : phi=map(ringP26,ringP26,{t_21*t_22-t_20*t_23-t_15*t_24-t_10*t_25-t_0*t_26,t_19*t_22-t_18*t_23-t_16*t_24-t_11*t_25-t_1*t_26,t_19*t_20-t_18*t_21-t_17*t_24-t_12*t_25-t_2*t_26,t_15*t_19-t_16*t_21+t_17*t_23-t_13*t_25-t_3*t_26,t_10*t_19-t_11*t_21+t_12*t_23+t_13*t_24-t_4*t_26,t_0*t_19-t_1*t_21+t_2*t_23+t_3*t_24+t_4*t_25,t_15*t_18-t_16*t_20+t_17*t_22-t_14*t_25-t_5*t_26,t_10*t_18-t_11*t_20+t_12*t_22+t_14*t_24-t_6*t_26,t_0*t_18-t_1*t_20+t_2*t_22+t_5*t_24+t_6*t_25,t_12*t_16-t_11*t_17-t_13*t_18+t_14*t_19-t_7*t_26,t_2*t_16-t_1*t_17-t_3*t_18+t_5*t_19+t_7*t_25,t_12*t_15-t_10*t_17-t_13*t_20+t_14*t_21-t_8*t_26,t_11*t_15-t_10*t_16-t_13*t_22+t_14*t_23-t_9*t_26,t_2*t_15-t_0*t_17-t_3*t_20+t_5*t_21+t_8*t_25,t_1*t_15-t_0*t_16-t_3*t_22+t_5*t_23+t_9*t_25,t_5*t_13-t_3*t_14+t_7*t_15-t_8*t_16+t_9*t_17,t_5*t_12-t_2*t_14-t_6*t_17-t_8*t_18+t_7*t_20,t_3*t_12-t_2*t_13-t_4*t_17-t_8*t_19+t_7*t_21,t_5*t_11-t_1*t_14-t_6*t_16-t_9*t_18+t_7*t_22,t_3*t_11-t_1*t_13-t_4*t_16-t_9*t_19+t_7*t_23,t_2*t_11-t_1*t_12-t_4*t_18+t_6*t_19-t_7*t_24,t_7*t_10-t_8*t_11+t_9*t_12+t_6*t_13-t_4*t_14,t_5*t_10-t_0*t_14-t_6*t_15-t_9*t_20+t_8*t_22,t_3*t_10-t_0*t_13-t_4*t_15-t_9*t_21+t_8*t_23,t_2*t_10-t_0*t_12-t_4*t_20+t_6*t_21-t_8*t_24,t_1*t_10-t_0*t_11-t_4*t_22+t_6*t_23-t_9*t_24,t_4*t_5-t_3*t_6-t_0*t_7+t_1*t_8-t_2*t_9})
o6 = map(ringP26,ringP26,{t t - t t - t t - t t - t t , t t - t t - t t - t t - t t , t t - t t - t t - t t - t t , t t - t t + t t - t t - t t , t t - t t + t t + t t - t t , t t - t t + t t + t t + t t , t t - t t + t t - t t - t t , t t - t t + t t + t t - t t , t t - t t + t t + t t + t t , t t - t t - t t + t t - t t , t t - t t - t t + t t + t t , t t - t t - t t + t t - t t , t t - t t - t t + t t - t t , t t - t t - t t + t t + t t , t t - t t - t t + t t + t t , t t - t t + t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t + t t - t t , t t - t t + t t + t t - t t , t t - t t - t t - t t + t t , t t - t t - t t - t t + t t , t t - t t - t t + t t - t t , t t - t t - t t + t t - t t , t t - t t - t t + t t - t t })
21 22 20 23 15 24 10 25 0 26 19 22 18 23 16 24 11 25 1 26 19 20 18 21 17 24 12 25 2 26 15 19 16 21 17 23 13 25 3 26 10 19 11 21 12 23 13 24 4 26 0 19 1 21 2 23 3 24 4 25 15 18 16 20 17 22 14 25 5 26 10 18 11 20 12 22 14 24 6 26 0 18 1 20 2 22 5 24 6 25 12 16 11 17 13 18 14 19 7 26 2 16 1 17 3 18 5 19 7 25 12 15 10 17 13 20 14 21 8 26 11 15 10 16 13 22 14 23 9 26 2 15 0 17 3 20 5 21 8 25 1 15 0 16 3 22 5 23 9 25 5 13 3 14 7 15 8 16 9 17 5 12 2 14 6 17 8 18 7 20 3 12 2 13 4 17 8 19 7 21 5 11 1 14 6 16 9 18 7 22 3 11 1 13 4 16 9 19 7 23 2 11 1 12 4 18 6 19 7 24 7 10 8 11 9 12 6 13 4 14 5 10 0 14 6 15 9 20 8 22 3 10 0 13 4 15 9 21 8 23 2 10 0 12 4 20 6 21 8 24 1 10 0 11 4 22 6 23 9 24 4 5 3 6 0 7 1 8 2 9
o6 : RingMap ringP26 <--- ringP26
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i7 : time psi=invertBirMap phi
-- used 0.171928 seconds
o7 = map(ringP26,ringP26,{- t t + t t + t t - t t - t t , - t t + t t + t t - t t - t t , - t t + t t + t t - t t - t t , - t t - t t + t t - t t - t t , - t t - t t + t t - t t - t t , - t t - t t + t t - t t - t t , - t t - t t + t t - t t - t t , t t - t t + t t - t t - t t , - t t + t t - t t + t t - t t , - t t + t t - t t + t t - t t , t t - t t + t t + t t - t t , - t t + t t + t t + t t - t t , - t t + t t + t t + t t - t t , - t t - t t + t t + t t - t t , - t t - t t + t t + t t - t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t + t t - t t + t t , t t - t t - t t + t t - t t , - t t + t t + t t - t t + t t , t t - t t - t t + t t - t t })
5 22 8 23 14 24 13 25 0 26 5 18 8 19 14 20 10 25 1 26 5 16 8 17 13 20 10 24 2 26 5 15 14 17 13 19 10 23 3 26 5 21 20 23 19 24 17 25 4 26 8 15 14 16 13 18 10 22 6 26 8 21 20 22 18 24 16 25 7 26 17 18 16 19 15 20 10 21 9 26 13 21 17 22 16 23 15 24 11 26 14 21 19 22 18 23 15 25 12 26 0 21 4 22 7 23 12 24 11 25 4 18 7 19 12 20 1 21 9 25 4 16 7 17 11 20 2 21 9 24 4 15 12 17 11 19 3 21 9 23 7 15 12 16 11 18 6 21 9 22 12 13 11 14 0 15 3 22 6 23 10 12 9 14 1 15 3 18 6 19 10 11 9 13 2 15 3 16 6 17 8 9 7 10 1 16 2 18 6 20 5 9 4 10 1 17 2 19 3 20 8 11 7 13 0 16 2 22 6 24 5 11 4 13 0 17 2 23 3 24 8 12 7 14 0 18 1 22 6 25 5 12 4 14 0 19 1 23 3 25 5 7 4 8 0 20 1 24 2 25 5 6 3 8 0 10 1 13 2 14 4 6 3 7 0 9 1 11 2 12
o7 : RingMap ringP26 <--- ringP26
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i8 : time isInverseMap(phi,psi)
-- used 0.0742329 seconds
o8 = true
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