assert ( 8 == rank coker (random (ZZ^11, ZZ^3, MaximalRank => true) * matrix "2,,;,5,;,,11" * random(ZZ^3,ZZ^5,MaximalRank => true))) assert ( 8 == rank coker (random (QQ^11, QQ^3, MaximalRank => true) * matrix "2,,;,5,;,,11" * random(QQ^3,QQ^5,MaximalRank => true))) assert ( 3 == rank (random (ZZ^11, ZZ^3, MaximalRank => true) * matrix "2,,;,5,;,,11" * random(ZZ^3,ZZ^5,MaximalRank => true))) assert ( 3 == rank (random (QQ^11, QQ^3, MaximalRank => true) * matrix "2,,;,5,;,,11" * random(QQ^3,QQ^5,MaximalRank => true))) R = ZZ/101[x_0..x_4]/(x_0^5 + x_1^5 + x_2^5 + x_3^5 + x_4^5 + 2*x_0*x_1*x_2*x_3*x_4); M = cokernel map((R)^{{ -2},{ -2},{ -1},{ -1},{ -1},{ -1}},(R)^{{ -4},{ -4}},{{4*x_3^2, x_0^2+10*x_2^2}, {9*x_0^2+x_2^2, x_1^2}, {8*x_2^3, 9*x_2^3}, {2*x_3^3, 7*x_3^3}, {4*x_1^3, 9*x_1^3+x_2^3}, {9*x_1^3, x_1^3+7*x_4^3}}); assert ( rank M == 4 ) end R = QQ[x,y] r = rank coker (random (R^11, R^3, MaximalRank => true) * matrix "x3+2,,;,5,;,,x+1" * random(R^3,R^5,MaximalRank => true)) assert ( 3 == r ) -- git issue 359. For awhile, this gave the incorrect answer of 12. k = ZZ/101 x = symbol x; R = k[x_0..x_5] M = random(R^6, R^{6:-1}) M = M - transpose M S = R/pfaffians(6,M) N = sub(M,S) assert(rank N == 4)

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