i10 : minimalPresentation J
-- ker (36) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (36) returned CacheFunction: -*a cache function*-
-- ker (36) called with Matrix: 0
-- 1
-- ker (36) returned Module: R
assert( ker(map(R^0,R^{{12}},0)) === (R^{{12}}))
-- ker (37) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (37) returned CacheFunction: -*a cache function*-
-- ker (37) called with Matrix: 0
-- 4
-- ker (37) returned Module: R
assert( ker(map(R^0,R^{{5}, {8}, {9}, {10}},0)) === (R^{{5}, {8}, {9}, {10}}))
-- ker (38) called with OptionTable: OptionTable{SubringLimit => infinity}
-- ker (38) returned CacheFunction: -*a cache function*-
-- ker (38) called with Matrix: {-24} | 0 0 0 0 a13 0 0 0 0 0 0 0 0 0 0 0 |
-- {-23} | -a2b10 -b13 0 0 0 a13 0 0 0 0 0 0 0 0 0 0 |
-- {-22} | 0 0 -b13 0 0 0 a13 0 0 0 0 0 0 0 0 0 |
-- {-19} | 0 0 0 -b13 0 0 0 a13 0 0 0 0 0 0 0 0 |
-- {-24} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-23} | 0 0 0 0 0 0 0 0 a2b10 b13 0 0 0 0 0 0 |
-- {-22} | 0 0 0 0 -a2c9 -b3c9 -c13 0 0 0 b13 0 0 0 0 0 |
-- {-19} | 0 0 0 0 0 0 0 -c13 0 0 0 b13 0 0 0 0 |
-- {-24} | 0 0 0 0 0 0 0 0 a13 0 0 0 0 0 0 0 |
-- {-23} | 0 0 0 0 0 0 0 0 0 a13 0 0 0 0 0 0 |
-- {-22} | -a2c9 -b3c9 -c13 0 0 0 0 0 0 0 a13 0 0 0 0 0 |
-- {-19} | 0 0 0 -c13 0 0 0 0 0 0 0 a13 0 0 0 0 |
-- {-24} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-23} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-22} | 0 0 0 0 0 0 0 0 0 0 0 0 a2c9 b3c9 c13 0 |
-- {-19} | 0 0 0 0 0 0 0 0 -a2d6 -b3d6 -c4d6 -d13 0 0 0 c13 |
-- {-24} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-23} | 0 0 0 0 0 0 0 0 0 0 0 0 a2b10 b13 0 0 |
-- {-22} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b13 0 |
-- {-19} | 0 0 0 0 -a2d6 -b3d6 -c4d6 -d13 0 0 0 0 0 0 0 b13 |
-- {-24} | 0 0 0 0 0 0 0 0 0 0 0 0 a13 0 0 0 |
-- {-23} | 0 0 0 0 0 0 0 0 0 0 0 0 0 a13 0 0 |
-- {-22} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a13 0 |
-- {-19} | -a2d6 -b3d6 -c4d6 -d13 0 0 0 0 0 0 0 0 0 0 0 a13 |
-- ker (38) returned Module: subquotient ({-11} | b3 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 0 0 0 0 0 a11 |, {-11} | b3 c4 0 d7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |)
-- {-10} | -a2 0 0 0 0 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 0 0 | {-10} | -a2 0 c4 0 d7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-9} | 0 0 0 0 -a2 0 0 0 -b3 0 0 0 0 0 0 0 0 0 0 0 d7 0 0 0 0 | {-9} | 0 -a2 -b3 0 0 d7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-6} | 0 0 0 0 0 0 0 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 -c4 0 0 0 0 | {-6} | 0 0 0 -a2 -b3 -c4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-11} | 0 b3 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 0 0 0 0 0 | {-11} | 0 0 0 0 0 0 b3 c4 0 d7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-10} | 0 -a2 0 0 0 0 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 b10 | {-10} | 0 0 0 0 0 0 -a2 0 c4 0 d7 0 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-9} | 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 0 0 0 0 0 0 0 0 d7 0 0 0 | {-9} | 0 0 0 0 0 0 0 -a2 -b3 0 0 d7 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 -c4 0 0 0 | {-6} | 0 0 0 0 0 0 0 0 0 -a2 -b3 -c4 0 0 0 0 0 0 0 0 0 0 0 0 |
-- {-11} | 0 0 b3 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 0 0 0 0 | {-11} | 0 0 0 0 0 0 0 0 0 0 0 0 b3 c4 0 d7 0 0 0 0 0 0 0 0 |
-- {-10} | 0 0 -a2 0 0 0 0 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 | {-10} | 0 0 0 0 0 0 0 0 0 0 0 0 -a2 0 c4 0 d7 0 0 0 0 0 0 0 |
-- {-9} | 0 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 0 0 0 0 0 0 0 0 d7 0 c9 | {-9} | 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 -b3 0 0 d7 0 0 0 0 0 0 |
-- {-6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 -c4 0 0 | {-6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 -b3 -c4 0 0 0 0 0 0 |
-- {-11} | 0 0 0 b3 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 0 0 0 0 | {-11} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 b3 c4 0 d7 0 0 |
-- {-10} | 0 0 0 -a2 0 0 0 0 0 0 0 c4 0 0 0 0 0 0 0 d7 0 0 0 0 0 | {-10} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 0 c4 0 d7 0 |
-- {-9} | 0 0 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 0 0 0 0 0 0 0 0 d7 0 | {-9} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 -b3 0 0 d7 |
-- {-6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 0 0 0 -b3 0 0 0 -c4 d6 | {-6} | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -a2 -b3 -c4 |
assert( ker(map(cokernel(map(R^{{24}, {23}, {22}, {19}, {24}, {23}, {22}, {19}, {24}, {23}, {22}, {19}, {24}, {23}, {22}, {19}, {24}, {23}, {22}, {19}, {24}, {23}, {22}, {19}},R^{{21}, {20}, {19}, {17}, {16}, {15}, {21}, {20}, {19}, {17}, {16}, {15}, {21}, {20}, {19}, {17}, {16}, {15}, {21}, {20}, {19}, {17}, {16}, {15}, {21}, {20}, {19}, {17}, {16}, {15}, {21}, {20}, {19}, {17}, {16}, {15}},{{b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4}})),cokernel(map(R^{{11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}},R^{{8}, {7}, {6}, {4}, {3}, {2}, {8}, {7}, {6}, {4}, {3}, {2}, {8}, {7}, {6}, {4}, {3}, {2}, {8}, {7}, {6}, {4}, {3}, {2}},{{b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4}})),{{0,0,0,0,a^13,0,0,0,0,0,0,0,0,0,0,0}, {-a^2*b^10,-b^13,0,0,0,a^13,0,0,0,0,0,0,0,0,0,0}, {0,0,-b^13,0,0,0,a^13,0,0,0,0,0,0,0,0,0}, {0,0,0,-b^13,0,0,0,a^13,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,a^2*b^10,b^13,0,0,0,0,0,0}, {0,0,0,0,-a^2*c^9,-b^3*c^9,-c^13,0,0,0,b^13,0,0,0,0,0}, {0,0,0,0,0,0,0,-c^13,0,0,0,b^13,0,0,0,0}, {0,0,0,0,0,0,0,0,a^13,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,a^13,0,0,0,0,0,0}, {-a^2*c^9,-b^3*c^9,-c^13,0,0,0,0,0,0,0,a^13,0,0,0,0,0}, {0,0,0,-c^13,0,0,0,0,0,0,0,a^13,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,a^2*c^9,b^3*c^9,c^13,0}, {0,0,0,0,0,0,0,0,-a^2*d^6,-b^3*d^6,-c^4*d^6,-d^13,0,0,0,c^13}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,a^2*b^10,b^13,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,b^13,0}, {0,0,0,0,-a^2*d^6,-b^3*d^6,-c^4*d^6,-d^13,0,0,0,0,0,0,0,b^13}, {0,0,0,0,0,0,0,0,0,0,0,0,a^13,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,a^13,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,a^13,0}, {-a^2*d^6,-b^3*d^6,-c^4*d^6,-d^13,0,0,0,0,0,0,0,0,0,0,0,a^13}})) === (subquotient(map(R^{{11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}},R^{{8}, {8}, {8}, {8}, {7}, {7}, {7}, {7}, {6}, {6}, {6}, {6}, {4}, {4}, {4}, {4}, {3}, {3}, {3}, {3}, {2}, {2}, {2}, {2}, {0}},{{b^3,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,a^11}, {-a^2,0,0,0,0,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0,0,0}, {0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,0,0,0,0,0,0,0,0,d^7,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,-c^4,0,0,0,0}, {0,b^3,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0}, {0,-a^2,0,0,0,0,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0,b^10}, {0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,0,0,0,0,0,0,0,0,d^7,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,-c^4,0,0,0}, {0,0,b^3,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0,0,0,0,0}, {0,0,-a^2,0,0,0,0,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0}, {0,0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,0,0,0,0,0,0,0,0,d^7,0,c^9}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,-c^4,0,0}, {0,0,0,b^3,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0,0,0,0,0}, {0,0,0,-a^2,0,0,0,0,0,0,0,c^4,0,0,0,0,0,0,0,d^7,0,0,0,0,0}, {0,0,0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,0,0,0,0,0,0,0,0,d^7,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,0,0,-b^3,0,0,0,-c^4,d^6}}),map(R^{{11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}, {11}, {10}, {9}, {6}},R^{{8}, {7}, {6}, {4}, {3}, {2}, {8}, {7}, {6}, {4}, {3}, {2}, {8}, {7}, {6}, {4}, {3}, {2}, {8}, {7}, {6}, {4}, {3}, {2}},{{b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,b^3,c^4,0,d^7,0,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,0,c^4,0,d^7,0}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,0,0,d^7}, {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-a^2,-b^3,-c^4}}))))
1
o10 = OO
X
o10 : coherent sheaf on X, free
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