i4 : phi=map(ringP8,ringP14,gens minors(2,matrix pack(6,for i to 11 list random(1,ringP8))))
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
o4 = map(ringP8,ringP14,{- 37x - 163x x + 64x - 153x x - 147x x + 91x - 159x x + 70x x + 133x x + 62x + 111x x - 24x x - 129x x + 62x x + 7x + 11x x - 54x x + 7x x + 95x x + 105x x - 63x - 30x x + 65x x + 145x x + 13x x - 99x x + 29x x + 92x + 89x x + 51x x - 137x x - 111x x + 126x x - 127x x - 80x x - 28x - 19x x - 27x x - 59x x + 141x x + 24x x + 66x x + 107x x + 100x x - 116x , 67x + 26x x - 96x + 110x x - 11x x - 41x + 46x x - 142x x + 87x x + 40x - 160x x - 159x x + 73x x - 130x x + 123x + 114x x + 18x x - 124x x - 152x x - 26x x + 12x + 52x x - 40x x - 120x x + 62x x + 84x x + 58x x + 122x + 152x x - 23x x - 110x x + 120x x + 157x x + 8x x + 141x x - 108x - 74x x - 155x x + 130x x + 65x x - 127x x + 40x x - 116x x + 159x x - 89x , - 21x + 116x x + 133x + 155x x + 79x x - 148x - 61x x - 115x x - 70x x + 25x + 86x x - 68x x - 41x x + 145x x - 11x + 137x x - 6x x - 114x x - 26x x + 114x x + 3x - 84x x - 17x x - 160x x - 32x x + 46x x + 132x x - 153x - 109x x + 160x x - 74x x + 114x x - 114x x - 109x x - 65x x - 7x - 120x x - 151x x + 157x x + 21x x - 14x x - 40x x - 71x x + 132x x - 21x , 106x + 34x x - 118x + 143x x + 120x x - 27x - 114x x - 162x x + 67x x + 144x + 106x x + 83x x - 62x x - 36x x - 102x + 160x x + 147x x + 42x x + 12x x - 65x x + 52x + 108x x - 37x x - 127x x - 90x x + 84x x - 6x x - 33x + 160x x + 14x x - 10x x + 114x x + 84x x + 86x x - 37x x + 66x + 104x x - 83x x - 71x x - 149x x - 131x x + 19x x - 143x x + 61x x - 164x , - 33x + 37x x + 35x - 152x x - 55x x + 130x - 23x x + 81x x - 136x x + 161x + 57x x - 77x x - 5x x + 47x x - 120x - 106x x - 150x x + 86x x + 89x x + 160x x - 115x + 43x x - 143x x + 16x x + 150x x + 75x x + 106x x + 15x + 165x x + 154x x + 112x x + 23x x + 134x x - 107x x + 153x x - 151x + 85x x - 33x x - 2x x - 29x x - 70x x - 44x x - 125x x - 11x x - 148x , 98x - 82x x + 141x + 7x x + 3x - 37x x - 146x x - 98x x - 93x + 118x x - 113x x + 96x x - 24x x - 141x + 34x x - 61x x + 153x x + 101x x + 122x x - 149x - 64x x + 126x x - 161x x - 162x x + 10x x + 110x x - 17x + 72x x - 59x x - 114x x - 28x x + 10x x - 50x x - 122x x + 134x - 20x x + 120x x - 4x x + 154x x + 75x x - 28x x - 72x x + 100x x + 133x , 64x - 127x x + 51x + 67x x + 126x x - 42x + 9x x - 2x x - 150x x - 141x + 69x x + 10x x + 35x x + 126x x + 65x + 127x x + 47x x - 102x x + 53x x - 36x x + 77x - 51x x - 12x x - 102x x + 4x x - 124x x - 15x x - 26x + 72x x - 14x x - 137x x - 12x x - 86x x - 24x x - 103x x + 58x + 141x x + 68x x - 156x x + 42x x + 82x x - 93x x + 163x x + 53x x + 2x , - 30x - 122x x + 151x + 26x x - 43x x + 63x + 40x x + 40x x + 38x x - 38x + 144x x - 83x x - 62x x + 151x x + 31x + 27x x + 53x x - 148x x + 57x x - 6x x + 134x - 92x x + 136x x - 86x x - 66x x + 146x x - 92x x + 104x + 120x x + 10x x - 161x x - 159x x + 148x x - 30x x + 34x x - 60x + 119x x + 32x x - 47x x + 71x x - 76x x - 75x x - 110x x + 49x x - 144x , 18x - 155x x - 17x - 8x x + 135x x + 107x + 90x x - 141x x - 84x x + 27x + 122x x - 115x x + 39x x + 50x x - 157x - 153x x - 46x x + 56x x - 56x x - 21x x + 120x - 119x x + 47x x - 69x x + 133x x + 95x x + 89x x - 114x + 24x x - 30x x + 46x x + 163x x + 47x x + 38x x + 56x x + 156x + 36x x - 85x x - 88x x - 78x x - 155x x - 135x x + 103x x - 107x x + 9x , - 159x + 65x x + 154x + 90x x + 148x x - 86x - 162x x + 145x x + 59x + 137x x - 34x x - 126x x - 40x x - 94x + 120x x - 65x x - 106x x + 30x x + 147x x - 41x + 90x x - 105x x - 96x x - 20x x + 51x x - 120x x - 141x - 98x x - 37x x - 34x x + 145x x + 26x x + 137x x - 113x x + 136x - 100x x - 118x x - 80x x - 85x x - 121x x + 63x x + 131x x + 15x x - 92x , - 103x + 14x x - 104x - 94x x - 92x x + 17x - 99x x + 151x x + 13x x - 25x - 84x x + 85x x - 120x x + 32x x + 46x - 147x x + 113x x + 138x x - 109x x - 160x x - 26x - 36x x - 66x x - 16x x - 102x x + 13x x - 79x x - 25x - 22x x - 89x x + 14x x - 93x x + 18x x - 133x x - 154x x + 51x + 132x x - 120x x - 46x x - 86x x + 89x x - 124x x + 40x x - 30x x + 37x , - 52x + 26x x + 5x + 32x x + 89x x - 110x - 5x x - 121x x + 79x x - 32x - 154x x - 48x x + 81x x - 86x x - 47x + 80x x + 9x x - 45x x + 157x x - 112x x - 34x - 59x x - 101x x - 153x x - 3x x - 134x x + 27x x - 130x - 157x x + 74x x + 147x x - 160x x - 164x x + 54x x - 67x x + 155x - 79x x - 70x x + 117x x - 31x x - 32x x - 20x x - 131x x - 9x x + 49x , 90x - 58x x - 81x - 99x x - 156x x - 21x - 96x x - 71x x + 26x x - 112x - 154x x + 11x x + 29x x - 7x x + 3x + 102x x - 144x x - 139x x - 101x x + 140x x + 21x + 66x x + 4x x + 84x x - 89x x + 152x x - 138x x - 160x + 91x x - 136x x + 119x x - 74x x + 3x x - 141x x - 21x x - 136x + 82x x + 11x x - 73x x - 60x x - 150x x + 58x x + 76x x - 6x x - 49x , - 117x - 83x x + 58x - 45x x - 164x x + 52x - 117x x - 16x x + x x + 60x + 57x x + 152x x + 6x x - x x - 87x - 96x x + 121x x + 40x x + 137x x + 52x x + 44x - 155x x - 46x x + 85x x + 96x x + 30x x - 157x x - 104x - 127x x - 74x x - 56x x - 147x x - 112x x + 95x x - 5x x + 128x + 114x x - 53x x + 140x x - 153x x + 165x x - 131x x + 46x x - 35x , 84x - 140x x + 58x - 90x x + 25x x + 39x - 165x x + 159x x - 41x x - 60x + 50x x - 46x x + 143x x - 108x x - 120x + 127x x + 81x x + 95x x - 48x x + 142x x - 19x - 155x x + 14x x + 148x x + 51x x - 5x x + 25x x + 65x + 26x x - 150x x + 35x x - 56x x + 115x x - 101x x - 49x x - 123x - 84x x - 146x x + 95x x - 31x x - 21x x - 31x x - 64x x + 16x })
0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 5 8 6 8 7 8 8
o4 : RingMap ringP8 <--- ringP14
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i6 : -- Compose phi:P^8--->P^14 with a linear projection P^14--->P^8 from a general subspace of P^14
-- of dimension 5 (so that the composition phi':P^8--->P^8 must have degree equal to deg(G(1,5))=14)
phi'=phi*map(ringP14,ringP8,for i to 8 list random(1,ringP14))
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
o6 = map(ringP8,ringP8,{- 43x - 58x x + 98x - 163x x + 110x x - 158x + 158x x - 131x x + 88x x + 57x + 68x x + 35x x + 21x x - 8x x + 116x - 67x x + 121x x - 23x x - 119x x + 153x x - 51x - 26x x + 71x x - 57x x + 87x x + 61x x - 101x x + 61x - 151x x - 121x x + 28x x + 132x x - 78x x - 78x x - 157x x + 55x - 115x x - 37x x + 95x x + 116x x - 60x x - 81x x - 123x x - 23x x + 156x , - 120x + 111x x + 117x + 151x x - 58x x + 96x - 86x x + 136x x + 111x x + 109x - 20x x + 109x x + 122x x - 34x x + 35x + 133x x + 160x x - 143x x + 116x x + 113x x + 129x - 126x x + 112x x - 86x x + 33x x + 19x x - 5x x + 107x + 32x x + 128x x - 78x x - 134x x - 113x x - 49x x - 102x x + 9x + 98x x + 58x x - 148x x + 113x x - 44x x + 107x x + x x - 6x x - 109x , 74x - 8x x + 33x - 96x x - 128x x + 41x + 79x x + 138x x - 141x x + 29x + 137x x - 122x x + 114x x + 44x x - 141x - 25x x + 115x x - 164x x + 22x x - 148x x - 58x + 31x x + 145x x - 117x x + 133x x + 121x x - 21x x + 88x + 135x x + 97x x - 132x x + 48x x + 34x x - 74x x + 129x x + 61x - 117x x + 20x x - 147x x + 66x x + 43x x + 46x x - 61x x + 134x x + 17x , - 47x - 116x x - 73x - 50x x - 120x x - 26x - 135x x - 39x x + 155x x + 162x - 134x x - 102x x + 86x x + 66x x - 69x + 131x x + 74x x + 6x x + 72x x - 120x x - 23x - 42x x + 39x x - 3x x + 125x x + 37x x - 89x x + 62x - 77x x + 163x x - 134x x - 135x x - 107x x + 109x x + 27x x + 138x - 67x x + 89x x - 32x x - 26x x + 48x x + 13x x - 118x x + 100x x + 74x , - 75x - x x + 68x - 153x x - 2x x - 79x + 148x x - 87x x + 61x x + 129x - 38x x + 58x x - 127x x + 91x x - 32x - 61x x + 126x x - 10x x - 63x x - 39x x + 163x + 96x x - 20x x + 94x x + 136x x + 86x x + 111x x - 35x + 163x x - 22x x - 49x x - 93x x + 34x x - 135x x - 62x x - 101x + 151x x + 21x x - 79x x - 22x x - 77x x - 137x x - 92x x + 47x x + 113x , - 96x + 161x x - 118x - 25x x - 144x x - 125x - 107x x + 98x x - 28x x + 104x + 46x x + 18x x + 11x x - 65x x - 98x + 163x x - 26x x - 140x x + 90x x + 60x x - 63x + 41x x - 136x x - 61x x + 133x x - 157x x - 22x x - 29x + 161x x - 56x x + 148x x - 30x x + 79x x - 116x x - 63x x - 140x - 36x x + 141x x + 155x x - 46x x + 9x x - 16x x - 36x x + 85x x - 77x , - 146x + 6x x + 79x - 162x x - 104x x + 29x + 66x x - 86x x - 66x x + 133x + 8x x - 84x x - 134x x - 107x x + 74x + 94x x + 89x x + 124x x - 88x x - 108x x - 54x - 80x x - 150x x - 47x x - 22x x + 104x x - 50x x + 164x + 11x x - 113x x + 74x x + 43x x - 75x x - 84x x - 25x x - 67x + 122x x - 13x x - 29x x - 124x x + 53x x + 62x x + 101x x - 58x x - 91x , 81x + 141x x - 62x - 108x x - 30x x + 93x + 86x x - 160x x + 50x x + 148x - 138x x + 124x x - 162x x + 81x x - 149x + 134x x + 20x x - 71x x + 121x x + 126x x - 47x + 104x x - 37x x + 146x x - 111x x - 161x x + 79x x - 109x - 21x x + 58x x - 133x x + 54x x - 125x x + 14x x - 25x x + 91x - 4x x - 98x x - 134x x - 56x x + 152x x + 41x x + 109x x - 73x x + 141x , 12x - 91x x + 107x - 85x x + 58x x - 103x + 28x x + 165x x + 71x x - 164x + 12x x - 83x x - 12x x + 40x x + 122x + 43x x + 115x x + 93x x + 39x x - 49x x + 142x + 165x x - 84x x + 76x x - 18x x - 87x x - 52x x + 38x + 46x x + 131x x - 54x x + 95x x + 163x x + 149x x - 87x x + 109x - 104x x + 137x x - 50x x + 31x x - 50x x - 110x x + 152x x + 28x x - 149x })
0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8 0 0 1 1 0 2 1 2 2 0 3 1 3 2 3 3 0 4 1 4 2 4 3 4 4 0 5 1 5 2 5 3 5 4 5 5 0 6 1 6 2 6 3 6 4 6 5 6 6 0 7 1 7 2 7 3 7 4 7 5 7 6 7 7 0 8 1 8 2 8 3 8 4 8 5 8 6 8 7 8 8
o6 : RingMap ringP8 <--- ringP8
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