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0, 0, 3, 0, 1540, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0 155, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 156 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1570, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0 158, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0; 0, 0, 0, 0, 0, 0, 159 0, 0, 0, 0, 0, 0, 0, 3, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1600; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3; 1, 0, 0, 0, 0, 0, 0, 0, 0 161, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 162 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1630, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0 164, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 1650, 0, 0, 0; 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1660, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 167 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 168 0, -3, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0 169; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 3; 0, 0, 0, 0, 0, 0, 0, 0, 0 170, 0, 0, 0, 0, -3, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0; 0, 1710, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 172 0, 0, 0, 0, 0, 0; 0, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 173 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 174 0, 0, 0, 0, 0; 0, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 175 -3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0 176, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0 177, 0, 0, 0, -3, 0, 3, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 1780, 0; 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1790, 0, 0, 0, 0, 0, 0, 0, -3; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -3; 180 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, -3; 0, 0, 0, 0, 0, 0, 0, 0, 0, 181 0, 0, 0, 0, 0, 3, -3; 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0 182, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1830, 0, 0, 0, 0, 0; 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0 184, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 3, 0, 0, -3, 0, 0, 0, 1850, 0, 0, 0, 0; 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1860, 0, 3, -3, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 187 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 188 0, 0, 3, 0, -3, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0 189, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 3, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0 190, 0, 0, 0, 0, -3, 0, 3, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 3; 1910, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0; 0, -1, 1, 0, 0, 0, 0, 0, 0, 192 0, 0, 0, 0, 0, 0, 0; 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, -1 193, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0 194, 0, 0, 0, 0, 0]], 0, [16, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] 195Suite: all 196Suite: get 197degree: 1 198center: 1 199splitting: 1 200automorphism: 1 201b: 1 202trivial hasse invariants: 1 203charac: 1 204dim: 1 205absdim: 1 206basis: 1 207invbasis: 1 208basis*invbasis: 1 209iscyclic: 1 210radical: 1 211Suite: operations 212radical: 1 213addition: 1 214negation: 1 215soustraction: 1 216multiplication: 1 217non-commutativity: 0 218left division: 1 219right division: 1 220noncommutative left division: 1 221noncommutative right division: 1 222division by non-invertible: error("impossible inverse in algdivl: [Mod(Mod(- 2231, i^2 + 1)*s, s^2 + 2), Mod(Mod(i - 1, i^2 + 1), s^2 + 2)]~.") 224nilpotent: 1 225square: 1 226square j: 1 227inverse: 1 228powers: 1 229negative powers: 1 230multiplication table j: 1 231multiplication table: 1 232characteristic polynomial: 1 233characteristic polynomial j: 1 234trace zero: 1 235trace commutator: 1 236trace: 1 237norm zero: 1 238norm one: 1 239norm j: 1 240norm is multiplicative a*b: 1 241norm is multiplicative b*a: 1 242poleval: 1 243poleval b: 1 244Suite: tensor product of cyclic algebras 245radical 1: 1 246radical 2: 1 247radical 3: 1 248tensor of degree 2 and 3 no mo: 1 249Suite: Grunwald-Wang 250A quadratic over Q, 2 large inert, imaginary: 1 251A quartic over Q, 2 large inert, imaginary: error("sorry, nfgrunwaldwang for 252 nonprime degree is not yet implemented.") 253A : degree 4 over Q(i), local degrees [4,1,1]: 1 254A degree 3 over Q(j), local degrees [3,3] larger primes: 1 255A : degree 3 over Q(sqrt(5)), local degrees [3,3] [0,0], larger primes: 1 256A : degree 5 over Q(sqrt(7)), local degrees [5,5,5,5,5,5,5] [0,0]: 1 257A : degree 9 over Q(zeta_9), local degrees [9,9,9,9]: 1 258A degree 2 over totally real sextic, local degrees [2,2] [2,2,2,2,2,2], larg 259er primes: 1 260A degree 2 over totally real sextic, local degrees [] [2,2,2,2,2,2]: 1 261Suite: more operations 262construct algebra: [[x^3 - 21*x + 7, [1], [49, 1], 27, [7], [], [[1, x + 1, 263x^2 - x - 2], [1, 1/3, Mat(1/9)]], [1, -1, 1; 0, 1, 1; 0, 0, 1], 27, [y, [1, 264 0], 1, 1, [Mat(1), Mat(1), Mat(16), Mat(1), 1, Mat(1), [1, 0], []], [0.E-57 265], [1], Mat(1), Mat(1)], [x^3 - 21*x + 7, 0, 0, y, x^3 - 21*x + 7], [[x^3 - 26621*x + 7, [3, 0], 49, 27, [[1, -1.2469796037174670610500097680084796213, 1.8 267019377358048382524722046390148901023; 1, 0.445041867912628808577805128993589 26851893, -1.2469796037174670610500097680084796213; 1, 1.8019377358048382524722 269046390148901023, 0.44504186791262880857780512899358951893], [1, -1.246979603 2707174670610500097680084796213, 1.8019377358048382524722046390148901023; 1, 0. 27144504186791262880857780512899358951893, -1.246979603717467061050009768008479 2726213; 1, 1.8019377358048382524722046390148901023, 0.445041867912628808577805 27312899358951893], [16, -20, 29; 16, 7, -20; 16, 29, 7], [3, 1, 1; 1, 5, -2; 1 274, -2, 5], [7, 0, 5; 0, 7, 5; 0, 0, 1], [3, -1, -1; -1, 2, 1; -1, 1, 2], [7, 275[2, 1, -1; 1, 3, 1; 0, 1, 2]], [7]~], [-4.7409388111524011831500293040254388 276638, 0.33512560373788642573341538698076855680, 4.405813207414514757416613917 2770446703070], [9, 3*x + 3, x^2 - x - 11], [1, -1, 10; 0, 3, 3; 0, 0, 9], [1, 2780, 0, 0, 1, -1, 0, -1, 2; 0, 1, 0, 1, 1, 1, 0, 1, -1; 0, 0, 1, 0, 1, 0, 1, 0 279, 0]], [[1; 0; 0], Mat(1), 1, Vecsmall([1])]]], [-1/3*x^2 - 2/3*x + 14/3, 1/ 2803*x^2 - 1/3*x - 14/3], Mod(-6, y), Vecsmall([0]), [[[2, [2]~, 1, 1, 1], [3, 281[3]~, 1, 1, 1], [7, [7]~, 1, 1, 1]], Vecsmall([1, 2, 0])], 0, [1, 0, 0, 0, 0 282, 1/7, 0, 2/7, 6/7; 0, 1, 0, 0, 0, 1/7, 0, 1/7, 6/7; 0, 0, 1, 0, 0, 3/7, 0, 2830, 4/7; 0, 0, 0, 1, 0, 5/7, 0, 2/7, 3/7; 0, 0, 0, 0, 1, 5/7, 0, 1/7, 3/7; 0, 284 0, 0, 0, 0, 1/7, 0, 0, 2/7; 0, 0, 0, 0, 0, 0, 1, 2/7, 5/7; 0, 0, 0, 0, 0, 0 285, 0, 1/7, 5/7; 0, 0, 0, 0, 0, 0, 0, 0, 1/7], [1, 0, 0, 0, 0, -1, 0, -2, 6; 0 286, 1, 0, 0, 0, -1, 0, -1, 1; 0, 0, 1, 0, 0, -3, 0, 0, 2; 0, 0, 0, 1, 0, -5, 0 287, -2, 17; 0, 0, 0, 0, 1, -5, 0, -1, 12; 0, 0, 0, 0, 0, 7, 0, 0, -14; 0, 0, 0 288, 0, 0, 0, 1, -2, 5; 0, 0, 0, 0, 0, 0, 0, 7, -35; 0, 0, 0, 0, 0, 0, 0, 0, 7] 289, [[1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 2900, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0 291, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 292 0, 0, 0, 0, 0, 1], [0, 1, -1, 1, 1, 1, 6, 2, 4; 1, 1, 1, 1, 1, 2, 1, 1, 3; 2930, 1, 0, 3, 3, 4, 2, 2, 4; 0, 0, 0, 6, 5, 7, 17, 7, 14; 0, 0, 0, 4, 4, 5, 12 294, 5, 10; 0, 0, 0, -7, -7, -9, -14, -7, -14; 0, 0, 0, 0, 0, 0, 5, 1, 2; 0, 0, 295 0, 0, 0, 0, -35, -9, -21; 0, 0, 0, 0, 0, 0, 7, 2, 5], [0, -1, 2, 0, -1, 0, 296-4, -2, -5; 0, 1, -1, 0, -1, -1, 0, 0, 0; 1, 0, 0, 0, -3, -2, -2, -1, -3; 0, 297 0, 0, 0, -4, -3, -15, -7, -21; 0, 0, 0, 1, -4, -2, -11, -5, -15; 0, 0, 0, 0 298, 7, 5, 14, 7, 21; 0, 0, 0, 0, 0, 0, -2, -1, -3; 0, 0, 0, 0, 0, 0, 28, 12, 3 2995; 0, 0, 0, 0, 0, 0, -7, -3, -9], [0, 0, -1, 0, -2, -1, -6, -2, -4; 0, 0, -1 300, 0, -1, -1, 0, -1, -5; 0, 0, -3, 0, 0, -1, 0, 0, -2; 1, 0, -5, 0, -2, -1, 0 301, 0, 2; 0, 1, -5, 0, -1, -1, 0, 0, 1; 0, 0, 7, 0, 0, 1, 0, 0, 0; 0, 0, 0, 1, 302 -2, 0, 0, 0, 1; 0, 0, 0, 0, 7, 0, 0, 1, -7; 0, 0, 0, 0, 0, 1, 0, 0, 2], [0, 303 -1, 0, -4, -4, -5, 0, -1, 0; 0, -1, 0, 0, 0, 0, 0, -1, -4; 0, -3, 0, -2, -2 304, -3, -6, -3, -8; 0, -4, -1, -15, -15, -20, 0, -7, -12; 1, -4, 1, -11, -11, 305-14, 0, -5, -8; 0, 7, 0, 14, 14, 19, 0, 7, 14; 0, 0, 0, -2, -3, -3, 0, -1, - 3061; 0, 0, 0, 28, 28, 35, 0, 12, 14; 0, 0, 0, -7, -7, -9, 0, -3, -4], [0, -1, 3070, -3, -4, -4, -6, -3, -5; 0, 0, -1, 0, -1, -1, 1, -1, -5; 0, -2, -2, -1, -2 308, -3, -4, -2, -7; 0, -3, -4, -10, -11, -14, -4, -7, -14; 0, -2, -3, -7, -8, 309-10, -3, -5, -10; 1, 5, 5, 9, 10, 14, 4, 7, 17; 0, 0, 0, -1, -3, -2, 0, -1, 310-1; 0, 0, 0, 21, 21, 23, 7, 13, 16; 0, 0, 0, -5, -4, -5, -2, -3, -4], [0, -2 311, 6, -6, 0, -2, 0, -2, 0; 0, -1, 1, 0, -6, -4, 0, -1, -2; 0, 0, 2, 0, 0, 0, 3120, 0, 2; 0, -2, 17, 0, 0, 7, -6, -2, 8; 0, -1, 12, 0, 0, 5, 0, -1, 6; 0, 0, 313-14, 0, 0, -6, 0, 0, -14; 1, -2, 5, 0, 0, 2, 0, 0, 2; 0, 7, -35, 0, 0, -14, 3140, 1, -14; 0, 0, 7, 0, 0, 3, 0, 0, 4], [0, 0, 1, -3, -1, -2, 0, -1, 0; 0, 0, 315 0, 1, -1, 0, 1, 0, -1; 0, 0, 0, 1, 1, 1, 2, 1, 2; 0, 1, 3, -1, -2, 0, 5, 1, 316 8; 0, 1, 2, -1, -1, 0, 6, 1, 6; 0, -1, -2, 1, 1, 0, -8, -2, -10; 0, 0, 1, 0 317, -1, 0, 1, 0, 1; 1, -2, -9, 4, 6, 1, -5, 1, -9; 0, 1, 2, -1, -1, 0, 1, 0, 3 318], [0, 1, 3, -10, -2, -6, 2, -3, 0; 0, 1, 0, 4, -1, 2, 6, 2, 3; 0, 1, 1, 6, 3194, 6, 10, 5, 10; 0, 7, 9, -1, -1, 4, 18, 4, 22; 0, 6, 6, -1, 0, 3, 22, 4, 17 320; 0, -7, -7, 0, 0, -4, -28, -7, -28; 0, 1, 2, -1, -1, 0, 4, 0, 2; 0, -14, -2 3211, 14, 7, 0, -14, 3, -21; 1, 5, 5, -3, -1, 1, 2, 0, 8]], 0, [9, 3, 3, 0, 0, 3223, 0, 3, 12]] 323norm(u): 1 324norm(t): 1 325trace(u): 1 326trace(t): 1 327u+t: 1 328u*t: 1 329u^3: 1 330w^-1 L: 1 331w^-1 R: 1 332w^-1*u: [Mod(0, x^3 - 21*x + 7), Mod(Mod(1, y), x^3 - 21*x + 7), Mod(0, x^3 333- 21*x + 7)]~ 334u*w^-1: [Mod(0, x^3 - 21*x + 7), Mod(Mod(1, y), x^3 - 21*x + 7), Mod(0, x^3 335- 21*x + 7)]~ 336charpol(w): Y^3 - 21*Y^2 + 1179*Y + 9447301/28 337eval charpol: 1 338trace(w): 1 339norm(w): 1 340dim: 1 341absdim: 1 342iscommutative: 1 343issemisimple: 1 344issimple: 1 345algleftmultable w+ww: 1 346algleftmultable w*ww: 1 347alg(basis(w)): 1 348alg(basis(ww)): 1 349basis(w)+ww: 1 350basis(w)-ww: 1 351w+basis(ww): 1 352w-basis(ww): 1 353basis(w)*ww: 1 354w*basis(ww): 1 355basis(w)^2: 1 356basis(ww)^2: 1 357basis(w)\ww: 1 358w\basis(ww): 1 359basis(ww)\w: 1 360wwbasis(w): 1 361basis(w)^-1: 1 362basis(ww)^-1: 1 363basis(w)/ww: 1 364w/basis(ww): 1 365basis(ww)/w: 1 366ww/basis(w): 1 367trace(basis(w)): 1 368trace(basis(ww)): 1 369alg(basis(w)) 2: 1 370alg(basis(ww)) 2: 1 371basis(w)+ww 2: 1 372basis(w)-ww 2: 1 373w+basis(ww) 2: 1 374w-basis(ww) 2: 1 375basis(w)*ww 2: 1 376w*basis(ww) 2: 1 377basis(w)^2 2: 1 378basis(ww)^2 2: 1 379basis(w)ww 2: 1 380wbasis(ww) 2: 1 381basis(ww)w 2: 1 382wwbasis(w) 2: 1 383basis(w)^-1 2: 1 384basis(ww)^-1 2: 1 385basis(w)/ww 2: 1 386w/basis(ww) 2: 1 387basis(ww)/w 2: 1 388ww/basis(w) 2: 1 389trace(basis(w)) 2: 1 390trace(basis(ww)) 2: 1 391alg(basis(w)) 3: 1 392alg(basis(ww)) 3: 1 393basis(w)+ww 3: 1 394basis(w)-ww 3: 1 395w+basis(ww) 3: 1 396w-basis(ww) 3: 1 397basis(w)*ww 3: 1 398w*basis(ww) 3: 1 399basis(w)^2 3: 1 400basis(ww)^2 3: 1 401basis(w)ww 3: 1 402wbasis(ww) 3: 1 403basis(ww)w 3: 1 404wwbasis(w) 3: 1 405basis(w)^-1 3: 1 406basis(ww)^-1 3: 1 407basis(w)/ww 3: 1 408w/basis(ww) 3: 1 409basis(ww)/w 3: 1 410ww/basis(w) 3: 1 411trace(basis(w)) 3: 1 412trace(basis(ww)) 3: 1 413radical: 1 414iscommutative cyc 3: 1 415issemisimple cyc 3: 1 416issimple cyc 3: 1 417algleftmultable/Q w+ww: 1 418algleftmultable/Q w*ww: 1 419alg(basis(w))/Q: 1 420alg(basis(ww))/Q: 1 421basis(w)+ww/Q: 1 422basis(w)-ww/Q: 1 423w+basis(ww)/Q: 1 424w-basis(ww)/Q: 1 425basis(w)*ww/Q: 1 426w*basis(ww)/Q: 1 427basis(w)^2/Q: 1 428basis(ww)^2/Q: 1 429basis(w)ww/Q: 1 430wbasis(ww)/Q: 1 431basis(ww)w/Q: 1 432wwbasis(w)/Q: 1 433basis(w)^-1/Q: 1 434basis(ww)^-1/Q: 1 435basis(w)/ww/Q: 1 436w/basis(ww)/Q: 1 437basis(ww)/w/Q: 1 438ww/basis(w)/Q: 1 439trace(basis(w))/Q: 1 440trace(basis(ww))/Q: 1 441radical/Q: 1 442iscommutative /Q: 1 443issemisimple /Q: 1 444issimple /Q: 1 445Suite: table algebra 446algisassociative 0.0: 1 447algisassociative 0.1: error("incorrect type in algisassociative (mult. table 448) (t_VEC).") 449algisassociative 0.2: 1 450algisassociative 0.3: error("incorrect type in algisassociative (mult. table 451) (t_POL).") 452construction 0: [0, 0, 0, 0, 0, 0, [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 453 1, 0; 0, 0, 1], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [0, 0, 0; 1, 0, 1; 0, 0, 0], 454[0, 0, 0; 0, 0, 0; 1, 0, 1]], 0, [3, 0, 1]] 455iscyclic 0: 1 456dim 0: 1 457dim 0b: 1 458char 0: 1 459a+b 0: 1 460a-b 0: 1 461a*b 0: 1 462b*a 0: 1 463a^2 0: 1 464b^2 0: 1 465e^691691 0: 1 466d^101 0: 1 467multable(a) 0: 1 468multable(b) 0: 1 469divl(d,a) 0: 1 470divl(d,b) 0: 1 471d^-1 0: 1 472divr(a,d) 0: 1 473divr(b,d) 0: 1 474rad(al) 0: 1 475ss(al) 0: 1 476proj(a) idem 0: 1 477idemproj 0: [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]], [0, 0, 0, 478 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]]] 479simple components 0: 1 480center al 0: 1 481center ss 0: 1 482primesubalg ss 0: error("domain error in algprimesubalg: characteristic = 0" 483) 484x^3 - 2*x^2 + x 485charpol annihil(a) 0: 1 486x^3 - x^2 487charpol annihil(b) 0: 1 488x^3 489charpol annihil(c) 0: 1 490x^3 - 4*x^2 + 5*x - 2 491charpol annihil(d) 0: 1 492x^3 - 3*x^2 + 3*x - 1 493charpol annihil(e) 0: 1 494random 0: [1, 0, 0]~ 495algsimpledec 0: 1 496alg_decomposition 0: 1 497iscommutative 0: 1 498issemisimple 0: 1 499issimple 0: 1 500issimple ss 0: 1 501isdivision 0: 1 502algisassociative 2: 1 503construction 2: [0, 0, 0, 0, 0, 0, [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0, 504 1, 0; 0, 0, 1], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [0, 0, 0; 1, 0, 1; 0, 0, 0], 505[0, 0, 0; 0, 0, 0; 1, 0, 1]], 2, [1, 0, 1]] 506iscyclic 2: 1 507dim 2: 1 508char 2: 1 509a+b 2: 1 510a-b 2: 1 511a*b 2: 1 512b*a 2: 1 513a^2 2: 1 514b^2 2: 1 515multable(a) 2: 1 516multable(b) 2: 1 517divl(un,a) 2: 1 518divl(un,b) 2: 1 519un^-1 2: 1 520divr(a,un) 2: 1 521divr(b,un) 2: 1 522rad(al) 2: 1 523ss(al) 2: 1 524proj(a) idem 2: 1 525idemproj 2: [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 2, [1]], [0, 0, 0, 526 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 2, [1]]] 527simple components 2: 1 528center al 2: 1 529center ss 2: 1 530primesubalg ss 2: 1 531x^3 + x 532charpol annihil(a) 2: 1 533x^3 + x^2 534charpol annihil(b) 2: 1 535x^3 536charpol annihil(c) 2: 1 537random 2: [1, 0, 0]~ 538algsimpledec 2: 1 539alg_decomposition 2: 1 540iscommutative 2: 1 541issemisimple 2: 1 542issimple 2: 1 543issimple ss 2: 1 544matrix trace 2: 1 545matrix norm 2: 1 546norm 2: 1 547construction 3: [0, 0, 0, 0, 0, 0, [1, 0; 0, 1], [1, 0; 0, 1], [[1, 0; 0, 1] 548, [0, 0; 1, 0]], 3, [2, 0]] 549iscyclic 3: 1 550dim 3: 1 551char 3: 1 552a+b 3: 1 553a-b 3: 1 554a*b 3: 1 555b*a 3: 1 556a^2 3: 1 557b^2 3: 1 558a^691691 3: 1 559multable(a) 3: 1 560multable(b) 3: 1 561algdivl(a,b) 3: 1 562a^-1 3: 1 563algdivr(b,a) 3: 1 564rad(al) 3: 1 565ss(al) 3: 1 566center al 3: 1 567center ss 3: 1 568primesubalg ss 3: 1 569x^2 + x + 1 570charpol annihil(a) 3: 1 571x^2 572charpol annihil(b) 3: 1 573random 3: [1, 0]~ 574algsimpledec 3: 1 575alg_decomposition 3: 1 576iscommutative 3: 1 577issemisimple 3: 1 578issemisimple ss 3: 1 579issimple 3: 1 580issimple ss 3: 1 581construction 3c: [0, 0, 0, 0, 0, 0, [1, 0, 0; 0, 1, 0; 0, 0, 1], [1, 0, 0; 0 582, 1, 0; 0, 0, 1], [[1, 0, 0; 0, 1, 0; 0, 0, 1], [0, 0, 0; 1, 0, 0; 0, 1, 0], 583 [0, 0, 0; 0, 0, 0; 1, 0, 0]], 3, [0, 0, 0]] 584iscyclic 3c: 1 585dim 3c: 1 586char 3c: 1 587a+b 3c: 1 588a-b 3c: 1 589a*b 3c: 1 590b*a 3c: 1 591a^2 3c: 1 592b^2 3c: 1 593a^691691 3c: 1 594multable(a) 3c: 1 595multable(b) 3c: 1 596algdivl(a,b) 3c: 1 597a^-1 3c: 1 598algdivr(b,a) 3c: 1 599rad(al) 3c: 1 600ss(al) 3c: 1 601center al 3c: 1 602center ss 3c: 1 603primesubalg ss 3c: 1 604x^3 + 2 605charpol annihil(a) 3c: 1 606x^3 607charpol annihil(b) 3c: 1 608random 3c: [1, 0, 0]~ 609algsimpledec 3c: 1 610alg_decomposition 3c: 1 611iscommutative 3c: 1 612issemisimple 3c: 1 613issemisimple ss 3c: 1 614issimple 3c: 1 615issimple ss 3c: 1 616construction 2b: [0, 0, 0, 0, 0, 0, [1, 0; 0, 1], [1, 0; 0, 1], [[1, 0; 0, 1 617], [0, 1; 1, 1]], 2, [0, 1]] 618iscyclic 2b: 1 619dim 2b: 1 620char 2b: 1 621a+b 2b: 1 622a-b 2b: 1 623a*b 2b: 1 624b*a 2b: 1 625a^2 2b: 1 626b^2 2b: 1 627a^691691 2b: 1 628multable(a) 2b: 1 629multable(b) 2b: 1 630divl(a,b) 2b: 1 631a^-1 2b: 1 632divr(b,a) 2b: 1 633rad(al) 2b: 1 634center al 2b: 1 635primesubalg al 2b: 1 636x^2 + x + 1 637charpol annihil(a) 2b: 1 638x^2 + x + 1 639charpol annihil(b) 2b: 1 640random 2b: [1, 0]~ 641algsimpledec 2b: 1 642alg_decomposition 2b: 1 643iscommutative 2b: 1 644issemisimple 2b: 1 645issimple 2b: 1 646issimple,1 2b: 1 647construction 3b: [0, 0, 0, 0, 0, 0, [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 6480, 0, 1], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [[1, 0, 0, 0; 0, 649 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, 1, 0, 0; 1, 0, 0, 0; 0, 0, 1, 0; 0, 0 650, 0, 2], [0, 0, 0, 2; 0, 0, 0, 2; 1, 2, 0, 0; 0, 0, 0, 0], [0, 0, 2, 0; 0, 0 651, 1, 0; 0, 0, 0, 0; 1, 1, 0, 0]], 3, [1, 0, 0, 0]] 652iscyclic 3b: 1 653dim 3b: 1 654char 3b: 1 655a+b 3b: 1 656a-b 3b: 1 657a*b 3b: 1 658b*a 3b: 1 659a^2 3b: 1 660b^2 3b: 1 661a^691691 3b: 1 662b^691691 3b: 1 663multable(a) 3b: 1 664multable(b) 3b: 1 665divl(a,b) 3b: 1 666a^-1 3b: 1 667divr(b,a) 3b: 1 668rad(al) 3b: 1 669center al 3b: 1 670primesubalg al 3b: 1 671x^4 + x^2 + 1 672charpol annihil(a) 3b: 1 673x^4 + 2*x^3 + x^2 674charpol annihil(b) 3b: 1 675x^4 676charpol annihil(c) 3b: 1 677random 3b: [1, 0, 0, 1]~ 678algsimpledec 3b: 1 679alg_decomposition 3b: 1 680iscommutative 3b: 1 681issemisimple 3b: 1 682issimple 3b: 1 683construction 2c: [0, 0, 0, 0, 0, 0, [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 6840, 0, 1], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [[1, 0, 0, 0; 0, 685 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, 0, 1, 0; 1, 0, 0, 1; 0, 0, 0, 0; 0, 0 686, 1, 0], [0, 0, 0, 0; 0, 0, 0, 0; 1, 0, 0, 0; 0, 1, 0, 0], [0, 0, 0, 0; 0, 0 687, 0, 0; 0, 0, 1, 0; 1, 0, 0, 1]], 2, [0, 0, 0, 0]] 688iscyclic 2c: 1 689dim 2c: 1 690char 2c: 1 691a+b 2c: 1 692a-b 2c: 1 693a*b 2c: 1 694b*a 2c: 1 695a^2 2c: 1 696b^2 2c: 1 697a^691691 2c: 1 698b^691691 2c: 1 699c^691691 2c: 1 700multable(a) 2c: 1 701multable(b) 2c: 1 702divl(c,a) 2c: 1 703divl(c,b) 2c: 1 704c^-1 2c: 1 705divr(a,c) 2c: 1 706divr(b,c) 2c: 1 707rad(al) 2c: 1 708center al 2c: 1 709primesubalg al 2c: 1 710x^4 711charpol annihil(a) 2c: 1 712x^4 + x^2 713charpol annihil(b) 2c: 1 714x^4 + x^2 + 1 715charpol annihil(c) 2c: 1 716random 2c: [1, 0, 0, 1]~ 717algsimpledec 2c: 1 718alg_decomposition 2c: 1 719iscommutative 2c: 1 720issemisimple 2c: 1 721issimple 2c: 1 722construction 5: [0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 5, [1]] 723iscyclic 5: 1 724dim 5: 1 725char 5: 1 726a+b 5: 1 727a-b 5: 1 728a*b 5: 1 729b*a 5: 1 730a^2 5: 1 731b^2 5: 1 732a^691691 5: 1 733multable(a) 5: 1 734multable(b) 5: 1 735divl(a,b) 5: 1 736a^-1 5: 1 737divr(a,b) 5: 1 738rad(al) 5: 1 739center al 5: 1 740primesubalg al 5: 1 741x + 3 742charpol annihil(a) 5: 1 743x + 2 744charpol annihil(b) 5: 1 745random 5: [1]~ 746algsimpledec 5: 1 747alg_decomposition 5: 1 748iscommutative 5: 1 749issemisimple 5: 1 750issimple 5: 1 751construction 0b: [0, 0, 0, 0, 0, 0, [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 7520, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 753 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [[1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 7541, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [0, 0, 1, 0, 0; 1, 0, 0, 1, 0; 0, 0, 755 0, 0, 0; 0, 0, -1, 0, 0; 0, 1, -1, -1, 1], [0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 1 756, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 0, 0, 0], [0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 7570, 0, 1, 0, 0; 1, 0, 0, 1, 0; 0, 0, 0, 0, 0], [0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 758 0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 1, 1, 0, 0, 1]], 0, [5, 1, 0, 2, 1]] 759iscyclic 0b: 1 760dim 0b: 1 761char 0b: 1 762a+b 0b: 1 763a-b 0b: 1 764a*b 0b: 1 765b*a 0b: 1 766a^2 0b: 1 767b^2 0b: 1 768a^691691 0b: 1 769b^691 0b: 1 770multable(a) 0b: 1 771multable(b) 0b: 1 772divl(b,a) 0b: 1 773b^-1 0b: 1 774divr(a,b) 0b: 1 775rad(al) 0b: 1 776idemproj 0b: [[0, 0, 0, 0, 0, 0, [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 7770, 1], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [[1, 0, 0, 0; 0, 1, 778 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, 0, 1, 0; 1, 0, 0, 1; 0, 0, 0, 0; 0, 0, - 7791, 0], [0, 0, 0, 0; 0, 0, 0, 0; 1, 0, 0, 0; 0, 1, 0, 0], [0, 0, 0, 0; 0, 0, 7800, 0; 0, 0, 1, 0; 1, 0, 0, 1]], 0, [4, 0, 0, 2]], [0, 0, 0, 0, 0, 0, Mat(1), 781 Mat(1), [Mat(1)], 0, [1]]] 782simple components 0b: 1 783mt M2 component 0b: 1 784center al 0b: 1 785primesubalg al 0b: error("domain error in algprimesubalg: characteristic = 0 786") 787x^5 - 4*x^4 + 6*x^3 - 4*x^2 + x 788charpol annihil(a) 0b: 1 789x^5 - 6*x^4 + 14*x^3 - 16*x^2 + 9*x - 2 790charpol annihil(b) 0b: 1 791random 0b: [1, 0, 0, 1, 1]~ 792algsimpledec 0b: 1 793alg_decomposition 0b: 1 794subalg M2(Q): 1 795iscommutative 0b: 1 796issemisimple 0b: 1 797issimple 0b: 1 798construction 3d: [0, 0, 0, 0, 0, 0, [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 7990, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 1, 800 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [[1, 0, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 8011, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1], [0, 0, 1, 0, 0; 1, 0, 0, 1, 0; 0, 0, 802 0, 0, 0; 0, 0, 2, 0, 0; 0, 1, 2, 2, 1], [0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 1, 0 803, 0, 0, 0; 0, 1, 0, 0, 0; 0, 0, 0, 0, 0], [0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 0, 8040, 1, 0, 0; 1, 0, 0, 1, 0; 0, 0, 0, 0, 0], [0, 0, 0, 0, 0; 0, 0, 0, 0, 0; 0, 805 0, 0, 0, 0; 0, 0, 0, 0, 0; 1, 1, 0, 0, 1]], 3, [2, 1, 0, 2, 1]] 806iscyclic 3d: 1 807dim 3d: 1 808char 3d: 1 809a+b 3d: 1 810a-b 3d: 1 811a*b 3d: 1 812b*a 3d: 1 813a^2 3d: 1 814b^2 3d: 1 815a^691691 3d: 1 816b^691 3d: 1 817multable(a) 3d: 1 818multable(b) 3d: 1 819divl(b,a) 3d: 1 820b^-1 3d: 1 821divr(a,b) 3d: 1 822rad(al) 3d: 1 823idemproj 3d: [[0, 0, 0, 0, 0, 0, [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 8240, 1], [1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [[1, 0, 0, 0; 0, 1, 825 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, 0, 1, 0; 1, 0, 0, 1; 0, 0, 0, 0; 0, 0, 2 826, 0], [0, 0, 0, 0; 0, 0, 0, 0; 1, 0, 0, 0; 0, 1, 0, 0], [0, 0, 0, 0; 0, 0, 0 827, 0; 0, 0, 1, 0; 1, 0, 0, 1]], 3, [1, 0, 0, 2]], [0, 0, 0, 0, 0, 0, Mat(1), 828Mat(1), [Mat(1)], 3, [1]]] 829simple components 3d: 1 830mt M2 component 3d: 1 831center al 3d: 1 832primesubalg al 3d: 1 833x^5 + 2*x^4 + 2*x^2 + x 834charpol annihil(a) 3d: 1 835x^5 + 2*x^3 + 2*x^2 + 1 836charpol annihil(b) 3d: 1 837random 3d: [1, 0, 0, 1, 1]~ 838algsimpledec 3d: 1 839alg_decomposition 3d: 1 840subalg M2(F3): 1 841iscommutative 3d: 1 842issemisimple 3d: 1 843issimple 3d: 1 844issimple,1 3d: 1 845maxorder assoc: 1 846natorder assoc: 1 847spl(1): 1 848spl(i): 1 849spl(j): 1 850spl(k): 1 851spl(basis(1)): 1 852spl(basis(i)): 1 853spl(basis(j)): 1 854spl(basis(k)): 1 855spl(a*1): 1 856spl(a*i): 1 857spl(a*j): 1 858spl(a*k): 1 859spl(b*1): 1 860spl(b*i): 1 861spl(b*j): 1 862spl(b*k): 1 863nattomax 1: 1 864nattomax 2: 1 865ord*invord=id: 1 866spl additive: 1 867spl multiplicative: 1 868changebasis bug 1: 1 869changebasis bug 2: 1 870changebasis bug 3: 1 871changebasis bug 4: 1 872algtableinit segfault bug: 8731 874center of CSA: 1 875radical of CSA: 1 876decomposition of CSA: 1 877alg_decomposition of CSA: 1 878alsimple bug 8790 880tests for al_CSA: 8811 8821 883algebra: 884csa getcenter: 1 885csa getsplitting: 1 886getrelmultable: 1 887getsplittingdata: 8881 8891 8901 8911 8921 8931 8941 8951 8961 8971 8981 8991 9001 9011 9021 9031 9041 9051 9061 9071 9081 9091 9101 9111 9121 9131 9141 915hasse invariants: 916hassei csa: error("sorry, computation of Hasse invariants over table CSA is 917not yet implemented.") 918hassef cas: error("sorry, computation of Hasse invariants over table CSA is 919not yet implemented.") 920hasse csa: error("sorry, computation of Hasse invariants over table CSA is n 921ot yet implemented.") 922csa splitting pol: 1 923csa basis: 1 924csa invbasis: 1 925csa absdim: 1 926csa char: 1 927csa deg: 1 928csa dim: 1 929csa absdim: 1 930csa type: 1 931csa iscommutative: 1 932csa issemisimple: 1 933elements: 934[0, Mod(y, y^3 - y + 1), 0, 0]~ 935[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]~ 936csa add: 1 937csa neg: 1 938csa neg 2: 1 939csa sub: 1 940csa mul: 1 941csa mul 2: 1 942csa sqr: 1 943csa sqr 2: 1 944csa mt: 1 945csa inv: 1 946csa inv 2: 1 947csa divl: 1 948csa pow: 1 949csa mul 3: 1 950csa mul 4: 1 951csa pow 2: 1 952csa sub 2: 1 953csa sub 3: 1 954csa inv 3: 1 955csa inv 4: 1 956csa inv 5: 1 957csa trace: 1 958csa trace 2: 1 9591 960testcharpol 9611 9621 9631 964testcharpol2 9651 9661 9671 968testnorm 9691 9701 9711 972testnorm2 9731 9741 9751 976examples from docu 9770 978[2, 2]~ 9790 9801 981[Mod(Mod(-1/3, y), x^2 + 1), Mod(Mod(2/3, y), x^2 + 1)]~ 9820 9831 9841 985[Mod(-2/5*x - 1/5, x^2 + 1), 0]~ 986[0, 2, 0, -1, 2, 0, 0, 0]~ 987[Mod(Mod(y, y^2 - 5), x^2 - 2), 1]~ 988[Mod(Mod(-1/2*y - 2, y^2 - 5)*x + Mod(-1/4*y + 5/4, y^2 - 5), x^2 - 2), Mod( 989Mod(-3/4*y + 7/4, y^2 - 5), x^2 - 2)]~ 990[0, 1, 0, 0, 2, -3, 0, 0]~ 991[[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 2, [1]], [0, 0, 0, 0, 0, 0, [1 992, 0; 0, 1], [1, 0; 0, 1], [[1, 0; 0, 1], [0, 1; 1, 1]], 2, [0, 1]]] 993 994[1 0] 995 996[0 1] 997 998[0 0] 999 1000[0, 0, 0, 0, 0, 0, [1, 0; 0, 1], [1, 0; 0, 1], [[1, 0; 0, 1], [0, 1; 1, 1]], 1001 2, [0, 1]] 1002[[0, 0, 0, 0, 0, 0, [1, 0; 0, 1], [1, 0; 0, 1], [[1, 0; 0, 1], [0, 1; 1, 1]] 1003, 2, [0, 1]], [1, 0; 0, 0; 0, 1]] 10041 10050 10060 10070 10080 10091 1010[[[2, [2, 0]~, 1, 2, 1], [3, [3, 0]~, 1, 2, 1]], Vecsmall([0, 1])] 101112960000 101212960000 101312 1014y^3 - y + 1 10152 10164 1017-1/3*x^2 - 4/3*x + 26/3 1018Mod(5929, y) 101913 10201 1021[[[2, [2, 0]~, 1, 2, 1], [19, [-9, 2]~, 1, 1, [-8, 2; 2, -10]]], Vecsmall([0 1022, 1])] 1023Vecsmall([1, 0]) 10241/2 10250 10261/2 10270 10282 10291 10302 10311 10322 10331 10340 10351 10360 10371 10380 10391 10400 10411 10420 10431 10440 10451 10460 10471 1048[1, [2, [2, 0]~, 1, 2, 1]] 1049x^2 + Mod(-y + 13, y^2 - 5) 1050 1051[1 0 0 -1] 1052 1053[0 1 0 -1] 1054 1055[0 0 1 -1] 1056 1057[0 0 0 2] 1058 1059 1060[1 0 0 1/2] 1061 1062[0 1 0 1/2] 1063 1064[0 0 1 1/2] 1065 1066[0 0 0 1/2] 1067 1068[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, -1, 1, 0; 1, 0, 1, 1; 1069 0, 0, 1, 1; 0, 0, -2, -1], [0, -1, -1, -1; 0, -1, 0, -1; 1, -1, 0, 0; 0, 2, 1070 0, 1], [0, -1, 0, -1; 0, 0, 1, 0; 0, -1, 1, 0; 1, 1, -1, 1]] 1071[1/2, -1/2, 0, 0]~ 1072[2, 3, 5, -4]~ 1073 1074[0 -1 1 0] 1075 1076[1 0 1 1] 1077 1078[0 0 1 1] 1079 1080[0 0 -2 -1] 1081 1082 1083[-1 0 0 -1] 1084 1085[-1 0 1 0] 1086 1087[-1 -1 0 -1] 1088 1089[ 2 0 0 1] 1090 1091[-1, -1, 0, 0]~ 1092 1093[Mod(x + 1, x^2 + 1) Mod(x - 1, x^2 + 1)] 1094 1095[Mod(x + 1, x^2 + 1) Mod(-x + 1, x^2 + 1)] 1096 1097[8, -8, 0, 0]~ 1098[0, 1, -1, 0]~ 109911 11003 1101[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, y, 0, 0; 1, 0, 0, 0; 11020, 0, 0, y; 0, 0, 1, 0], [0, 0, y^2, 0; 0, 0, 0, -y^2; 1, 0, 0, 0; 0, -1, 0, 1103 0], [0, 0, 0, -5; 0, 0, y^2, 0; 0, -y, 0, 0; 1, 0, 0, 0]] 1104x^2 - y 1105[[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]~, [1, 0; 0, -1; 0, 0; 0, 0; 0, 0; 0, 0 1106; 0, 1; 0, 0; 0, 0; 0, 0; 0, 0; 0, 0], [1, Mod(x^2, x^6 - 5), Mod(x^4, x^6 - 1107 5), Mod(x, x^6 - 5), Mod(1/2*x^4 + 1/2*x^3 + 1/2*x + 1/2, x^6 - 5), Mod(1/2 1108*x^5 + 1/2*x^4 + 1/2*x^2 + 1/2*x, x^6 - 5), Mod(x^2, x^6 - 5), Mod(x^4, x^6 1109- 5), Mod(x^4 + x^2 + 1, x^6 - 5), 3, Mod(x^2, x^6 - 5), Mod(x^4, x^6 - 5); 11100, 0, 0, 0, 0, 0, 1, Mod(x^2, x^6 - 5), Mod(1/10*x^4 + 1/2*x^2 + 1/2, x^6 - 11115), Mod(1/2*x^4 - 1/2*x, x^6 - 5), Mod(-1/10*x^3 + 1/2, x^6 - 5), Mod(-1/10* 1112x^5 + 1/2*x^2, x^6 - 5)]] 11132 111418 111518 11161 11171 11181 1119matrices over algebras 1120 1121[[1, 0, 2, 2, 2, 2, 0, -2]~ [-2, -1, 1, 0, -1, -2, -1, 1]~] 1122 1123[[1, 2, 0, -2, 2, 1, 2, 2]~ [2, -2, -2, 0, -2, 2, -1, 2]~] 1124 1125 1126[[-2, 0, -2, 2, 0, 2, 0, -2]~ [0, 2, -1, 0, -2, -2, -1, -1]~] 1127 1128[[0, 2, 0, -2, -1, 1, 1, -1]~ [0, 2, 0, 2, 0, 1, 0, 1]~] 1129 1130mul alM: [[30, 1, -15, 6, -9, -30, -41, 37]~, [62, -3, -20, 6, -11, -16, -49 1131, 20]~; [247, 49, -39, 122, -43, 31, -265, 73]~, [168, 74, -22, 68, -91, 48, 1132 -136, 32]~] 1133sqr alM: 1 1134divl alM: 1 1135divr alM: 1 1136isinv alM: 1 1137isinv alM 2: 1 1138inv alM: 1 1139inv alM 2: 1 1140neg alM: 1 1141sub alM: 1 1142add alM: 1 1143algtobasis basistoalg alM 1: 1 1144algtobasis basistoalg alM 2: 1 1145algleftmultable add alM: 1 1146algleftmultable mul alM: 1 1147algleftmultable sqr alM: 1 1148algsplitm add alM: 1 1149algsplitm mul alM: 1 1150algsplitm sqr alM: 1 1151algsplitm sqr alM 2: 1 1152algtrace alM: 1 1153algtrace alM 2: 1 1154algtrace prod alM: 1 1155algnorm alM: 1 1156algnorm alM 2: 1 1157algcharpoly alM: 1 1158algcharpoly alM 2: 1 1159pow alM: 1 1160pow alM 2: 1 1161pow 0 alM: 1 1162 1163[[Mod(Mod(-1/2*y - 1/2, y^2 - 5)*x + Mod(1/2*y + 1/2, y^2 - 5), x^2 + 1), Mo 1164d(Mod(1/14*y + 3/14, y^2 - 5)*x + Mod(-1/14*y + 3/14, y^2 - 5), x^2 + 1)]~ [ 1165Mod(-2*x + Mod(3/4*y - 17/4, y^2 - 5), x^2 + 1), Mod(Mod(-1/28*y - 3/4, y^2 1166- 5)*x - 6/7, x^2 + 1)]~] 1167 1168[[Mod(13/2*x + Mod(1/2*y + 4, y^2 - 5), x^2 + 1), Mod(Mod(-1/14*y + 11/7, y^ 11692 - 5)*x + Mod(1/7*y + 53/14, y^2 - 5), x^2 + 1)]~ [Mod(Mod(-1/4*y - 3/4, y^ 11702 - 5)*x + Mod(-1/2*y + 7/2, y^2 - 5), x^2 + 1), Mod(Mod(-1/14*y + 23/14, y^ 11712 - 5)*x + Mod(1/28*y + 43/28, y^2 - 5), x^2 + 1)]~] 1172 1173 1174[[Mod(Mod(-1/2*y - 3/2, y^2 - 5)*x + Mod(-3/2*y - 1/2, y^2 - 5), x^2 + 1), M 1175od(Mod(1/14*y + 3/14, y^2 - 5)*x + Mod(-1/14*y - 11/14, y^2 - 5), x^2 + 1)]~ 1176 [Mod(Mod(1/2*y - 1, y^2 - 5)*x + Mod(-3/4*y - 7/4, y^2 - 5), x^2 + 1), Mod( 1177Mod(1/28*y - 43/28, y^2 - 5)*x + Mod(-1/14*y - 22/7, y^2 - 5), x^2 + 1)]~] 1178 1179[[Mod(Mod(y + 5/2, y^2 - 5)*x + Mod(-1/4*y + 5/4, y^2 - 5), x^2 + 1), Mod(Mo 1180d(1/28*y + 1/4, y^2 - 5)*x - 9/14, x^2 + 1)]~ [Mod(Mod(-5/4*y + 9/4, y^2 - 5 1181)*x + Mod(1/4*y + 3/4, y^2 - 5), x^2 + 1), Mod(Mod(-1/28*y + 25/28, y^2 - 5) 1182*x + Mod(1/28*y + 39/28, y^2 - 5), x^2 + 1)]~] 1183 1184mul scalar alM: 1 1185 1186[ [2, 1, 0, 2]~ [-1, -1, 2, -1]~] 1187 1188[[2, 1, -1, -2]~ [1, -1, 0, -1]~] 1189 1190 1191[ [-2, 2, 2, 1]~ [-2, -2, 2, 1]~] 1192 1193[[-1, -2, 1, 1]~ [0, 1, 0, -1]~] 1194 1195mul alM t: [[-10, 4, 7, 3]~, [-4, -13, -3, -1]~; [-4, 5, 5, 11]~, [2, -2, 7, 1196 5]~] 1197sqr alM t: 1 1198divl alM t: 1 1199divr alM t: 1 1200isinv alM t: 1 1201isinv alM t 2: 1 1202inv alM t: 1 1203inv alM t 2: 1 1204neg alM t: 1 1205sub alM t: 1 1206add alM t: 1 1207algleftmultable add alM t: 1 1208algleftmultable mul alM t: 1 1209algleftmultable sqr alM t: 1 1210algtrace alM t: 1 1211algtrace alM t 2: 1 1212algtrace prod alM t: 1 1213algnorm alM t: 1 1214algnorm alM t 2: 1 1215algcharpoly alM t: 1 1216algcharpoly alM t 2: 1 1217pow alM t: 1 1218pow alM 2 t: 1 1219pow 0 alM t: 1 1220csa al2 1221al2 contains nfabs: 1 1222[[x^2 + (-2*y^2 + 2*y)*x + (6*y^2 - 5*y + 5), [292133, -1964*x^5 + 4725*x^4 1223- 14044*x^3 - 95698*x^2 - 164828*x - 456632, -1406*x^5 + 4870*x^4 - 7674*x^3 1224 - 64939*x^2 - 119188*x + 52103], [[412, 92, 376; 0, 4, 0; 0, 0, 4], [-7, -4 1225, 2]~], 1, [2, 103], [], [[1, x], [1, 1]], [1, 0; 0, 1], 1, [y^3 - y + 1, [1 1226, 1], -23, 1, [[1, 0.75487766624669276004950889635852869189, -1.324717957244 12277460259609088544780973407; 1, -0.87743883312334638002475444817926434595 + 0. 122874486176661974423659317042860439236724*I, 0.66235897862237301298045442723904 1229867037 + 0.56227951206230124389918214490937306150*I], [1, 0.7548776662466927 12306004950889635852869189, -1.3247179572447460259609088544780973407; 1, -0.1325 12317706650360214343158401957487197871, 1.2246384906846742568796365721484217319; 1232 1, -1.6223005997430906166179248767836567132, 0.1000794665600717690812722823 12332967560887], [16, 12, -21; 16, -2, 20; 16, -26, 2], [3, -1, 0; -1, 1, -3; 0, 1234 -3, 2], [23, 16, 10; 0, 1, 0; 0, 0, 1], [7, -2, -3; -2, -6, -9; -3, -9, -2] 1235, [23, [-10, -1, 8; -7, -3, 1; 1, 7, -10]], [23]], [-1.324717957244746025960 12369088544780973407, 0.66235897862237301298045442723904867037 + 0.5622795120623 12370124389918214490937306150*I], [1, y^2 - 1, y], [1, 0, 1; 0, 0, 1; 0, 1, 0], 1238[1, 0, 0, 0, 0, -1, 0, -1, 1; 0, 1, 0, 1, -1, 0, 0, 0, 1; 0, 0, 1, 0, -1, 0, 1239 1, 0, 0]], [x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191, -1406/292 1240133*x^5 + 4870/292133*x^4 - 7674/292133*x^3 - 64939/292133*x^2 - 119188/2921 124133*x + 52103/292133, 0, y^3 - y + 1, x^2 + (-2*y^2 + 2*y)*x + (6*y^2 - 5*y + 1242 5)], [0, [[1, 0, 0; 0, -1, 0; 0, 0, 1; 0, 0, 0; 0, 0, 0; 0, 0, 0], [1, 0, 0 1243; 0, -1, 0; 0, 0, 1], 1, Vecsmall([1, 2, 3])]]], [[1, 0, 0, 0; 0, 1, 0, 0; 0 1244, 0, 1, 0; 0, 0, 0, 1], [0, 0, 1, 0; 1, 0, 0, 1; 0, 0, 0, 0; 0, 0, -1, 0], [ 12450, 0, 0, 0; 0, 0, 0, 0; 1, 0, 0, 0; 0, 1, 0, 0], [0, 0, 0, 0; 0, 0, 0, 0; 0, 1246 0, 1, 0; 1, 0, 0, 1]], [[0, 1, -1, -1, -2, 2, 0, 0, -2, 2, 0, 0]~, [1, 0; 0 1247, 0; 0, 0; 0, 0; 0, 0; 0, 0; 0, 1; 0, 0; 0, 0; 0, 0; 0, 0; 0, 0], [1, Mod(-1 1248964/292133*x^5 + 4725/292133*x^4 - 14044/292133*x^3 - 95698/292133*x^2 - 164 1249828/292133*x - 456632/292133, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x 1250 + 191), Mod(-1406/292133*x^5 + 4870/292133*x^4 - 7674/292133*x^3 - 64939/29 12512133*x^2 - 119188/292133*x + 52103/292133, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 1 125220*x^2 + 36*x + 191), Mod(-516/6719059*x^5 + 59549/6719059*x^4 - 144104/6719 1253059*x^3 + 56369/6719059*x^2 + 2656099/6719059*x + 5563831/6719059, x^6 - 4*x 1254^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), Mod(-54291/6719059*x^5 + 21048 12559/6719059*x^4 - 786258/6719059*x^3 - 905381/6719059*x^2 - 6840464/6719059*x 1256- 4510816/6719059, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), Mo 1257d(-48132/6719059*x^5 + 241931/6719059*x^4 - 785055/6719059*x^3 - 523468/6719 1258059*x^2 - 1628025/6719059*x + 4121552/6719059, x^6 - 4*x^5 + 15*x^4 + 14*x^3 1259 + 120*x^2 + 36*x + 191), 0, 0, 0, 0, 0, 0; 0, 0, 0, Mod(-499864/154538357*x 1260^5 - 232506/154538357*x^4 + 2075504/154538357*x^3 - 39252216/154538357*x^2 - 1261 107292314/154538357*x - 129681996/154538357, x^6 - 4*x^5 + 15*x^4 + 14*x^3 1262+ 120*x^2 + 36*x + 191), Mod(1153778/154538357*x^5 - 4109402/154538357*x^4 + 1263 13244560/154538357*x^3 + 24564582/154538357*x^2 + 151883496/154538357*x - 1 12640149974/154538357, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), Mo 1265d(171940/154538357*x^5 - 3019052/154538357*x^4 + 13537158/154538357*x^3 - 30 1266710744/154538357*x^2 - 25903390/154538357*x - 175396598/154538357, x^6 - 4*x 1267^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), 1, Mod(-1964/292133*x^5 + 4725 1268/292133*x^4 - 14044/292133*x^3 - 95698/292133*x^2 - 164828/292133*x - 456632 1269/292133, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), Mod(-1406/29 12702133*x^5 + 4870/292133*x^4 - 7674/292133*x^3 - 64939/292133*x^2 - 119188/292 1271133*x + 52103/292133, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), 1272 Mod(-516/6719059*x^5 + 59549/6719059*x^4 - 144104/6719059*x^3 + 56369/67190 127359*x^2 + 2656099/6719059*x + 5563831/6719059, x^6 - 4*x^5 + 15*x^4 + 14*x^3 1274+ 120*x^2 + 36*x + 191), Mod(-54291/6719059*x^5 + 210489/6719059*x^4 - 78625 12758/6719059*x^3 - 905381/6719059*x^2 - 6840464/6719059*x - 4510816/6719059, x^ 12766 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 191), Mod(-48132/6719059*x^5 1277+ 241931/6719059*x^4 - 785055/6719059*x^3 - 523468/6719059*x^2 - 1628025/671 12789059*x + 4121552/6719059, x^6 - 4*x^5 + 15*x^4 + 14*x^3 + 120*x^2 + 36*x + 1 127991)]], 0, 0, 0, [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 1280 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 12810, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 1282, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 1283 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 12840, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 1285 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 12860, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1 1287, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1288 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 12890, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0 1290, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [[1, 0, 0, 0, 0, 0, 0, 0, 0, 1291 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 12920, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 1293; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 1294 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 12950, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0 1296, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, -1, 0, 0 1297, 0, 0, 0, 0, 0, 0, 0, 0; 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0 1298, -1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, -1, 1299 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1300 1, -1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0 1301, 0, 0, 0, 0, -1; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0; 0, 0, 0, 0, 0, 0, 0, 13020, 0, 0, -1, 0], [0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 13030, 0, 0, 0, 0; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, -1, 1, 0, 0, 13040, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 1305, 0, 0; 0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 1306, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1 1307; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1; 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], [ 13080, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0 1309, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 1, 0, 1310 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1; 0, 0, 0, 0, 13110, 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 1312, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0 1313, -1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0 1314, 0, -1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1315-1, 0, 0, 0, 0; 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1; 1, -1, 0, 0, 0, 0, 0, 13160, 0, 1, -1, 0; 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0; 0, 0, 0, 0, 0, 0, 0, 0 1317, 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, 1318 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 1319 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, -1, 1, 0, 13200, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 1321; 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1; 13221, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0 1323, 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, 1324 0, 0, 0, 0, 1, -1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0; 0, 0, 0, 0 1325, 0, 0, -1, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1326 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, 13270, 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 1328, 0, 0, 0, 0, 0; 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 1329 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 13300, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 1331, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13320; 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 1333, 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, 1334 -1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, -1, 13350, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 13361, -1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 13370, 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 1338, 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, 1339 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, -1, 1, 0, 0, 0, 0, 1340 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0; 1, 0, 0, 0, 0, 0, 0, 0, 13410, 0, 0, 0; 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0, 13420, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1343 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, 13440; 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 1345, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 1346 0, 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 1, 0, 0, 13470, 0, 0, 0, 0, 0, 1, 0, 0; 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 1, 0, 0 1348, 0, 0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 13490, 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 1350, 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, 1351 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, -1, 0 1352, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0; 0, 0, -1, 0, 0, 0, 0, 0, 0, 13530, 0, -1; 1, -1, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0; 0, -1, 0, 0, 0, 0, 0, 0, 0, 13540, -1, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 1355, 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, 1356 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; 13570, 0, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 13580, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, -1, 1; 0, 0, 1359 1, 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]], 0, [12, 1360 -4, 0, 0, 0, 0, 0, 0, 0, 6, -2, 0]] 1361csa al3 1362al3 contains nfabs: 1 1363trivial algebra over a quadratic field 1364[[x, [1, -x], [1, 1], 1, [], [], [[1], [1]], Mat(1), 1, [y^2 + 1, [0, 1], -4 1365, 1, [Mat([1, 0.E-57 + 1.0000000000000000000000000000000000000*I]), [1, 1.00 136600000000000000000000000000000000000; 1, -1.000000000000000000000000000000000 13670000], [16, 16; 16, -16], [2, 0; 0, -2], [2, 0; 0, 2], [1, 0; 0, -1], [1, [0 1368, -1; 1, 0]], [2]], [0.E-57 + 1.0000000000000000000000000000000000000*I], [1 1369, y], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, 0]], [x^2 + 1, -x, -1, y^2 + 1, x 1370], [[x^2 + 1, [0, 1], -4, 1, [Mat([1, 0.E-57 + 1.000000000000000000000000000 13710000000000*I]), [1, 1.0000000000000000000000000000000000000; 1, -1.000000000 13720000000000000000000000000000], [16, 16; 16, -16], [2, 0; 0, -2], [2, 0; 0, 2 1373], [1, 0; 0, -1], [1, [0, -1; 1, 0]], [2]~], [0.E-57 + 1.0000000000000000000 1374000000000000000000*I], [1, x], [1, 0; 0, 1], [1, 0, 0, -1; 0, 1, 1, 0]], [[1 1375, 0; 0, -1], [1, 0; 0, -1], 1, Vecsmall([1, 2])]]], [Mod(y, y^2 + 1)], Mod(1 1376, y^2 + 1), Vecsmall([]), [[], Vecsmall([])], 0, [1, 0; 0, 1], [1, 0; 0, 1], 1377 [[1, 0; 0, 1], [0, -1; 1, 0]], 0, [2, 0]] 1378[y]~ 1379[-2*y + 1]~ 1380[-3, 1]~ 1381[-y + 1]~ 1382[-3, 2]~ 1383[Mod(Mod(y + 2, y^2 + 1), x)]~ 1384[-1/5, 7/5]~ 1385[-1/5, 7/5]~ 1386[Mod(Mod(-y, y^2 + 1), x)]~ 1387[1, 2]~ 1388 1389[Mod(Mod(y, y^2 + 1), x)] 1390 1391 1392[ 0 1] 1393 1394[-1 0] 1395 1396x + Mod(2*y - 1, y^2 + 1) 1397Mod(-y - 3, y^2 + 1) 1398Mod(-y - 3, y^2 + 1) 13991 14001 14011 14020 14030 14041 14051 14061 14070 1408[] 1409trivial algebra over Q 1410[[x, [1], [1, 1], 1, [], [], [[1], [1]], Mat(1), 1, [y, [1, 0], 1, 1, [Mat(1 1411), Mat(1), Mat(16), Mat(1), 1, Mat(1), [1, 0], []], [0.E-57], [1], Mat(1), M 1412at(1)], [x, 0, 0, y, x], [[x, [1, 0], 1, 1, [Mat(1), Mat(1), Mat(16), Mat(1) 1413, 1, Mat(1), [1, 0], []~], [0.E-77], [1], Mat(1), Mat(1)], [Mat(1), Mat(1), 14141, Vecsmall([1])]]], [0], Mod(1, y), Vecsmall([0]), [[], Vecsmall([])], 0, M 1415at(1), Mat(1), [Mat(1)], 0, [1]] 1416[-2]~ 1417[1/3]~ 1418[4/5]~ 1419[-5/3]~ 1420[14/5]~ 1421[-2/3]~ 1422[12/5]~ 1423[12/5]~ 1424[-1/2]~ 1425[1/3]~ 1426 1427[-2] 1428 1429 1430[Mod(1/3, x)] 1431 1432x - 1/3 14334/5 14344/5 14351 14361 14371 14380 14390 14401 14411 14421 14430 1444[] 1445trivial CSA over Q 1446[Mod(9, y)]~ 1447[4]~ 1448nontrivial CSA over Q 1449[Mod(0, y), Mod(12, y), Mod(6, y), Mod(12, y)]~ 1450[-81, 27, 36, 45]~ 1451empty matrices 1452-v: 1 1453v^(-1): 1 1454v^n: 1 1455v^0: 1 1456mt(v)1 1457spl(v)1 1458trace(v): 1 1459norm(v): 1 1460charpoly(v): 1 1461v+v: 1 1462v-v: 1 1463v*v: 1 1464v/v: 1 1465v\v: 1 1466v*nv: 1 1467v*v 2: 1 1468trace(v) char 2: 1 1469[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]] 1470[12]~ 1471[-1/7]~ 1472[83/7]~ 1473[85/7]~ 1474[-12/7]~ 1475[-12]~ 1476[1/12]~ 1477[1/49]~ 1478[-1/84]~ 147912 1480-1/7 1481x - 12 1482 1483[-1/7] 1484 1485[1]~ 14861 14871 14881 14891 1490trivial tensor product 14911 14921 1493splitting a nasty commutative algebra 14941 14951 14961 14971 1498non associative algebra 14990 1500csa without maximal order 1501simplify bug #1671 1502testing simplify: degree 1 cyclic over Q 15031 15041 15051 15061 15071 15081 15091 15101 15111 15121 15131 15141 15151 15161 15171 15181 15191 15201 15211 15221 15231 15241 15251 15261 15271 15281 15291 1530testing simplify: degree 1 cyclic over Q(i) 15311 15321 15331 15341 15351 15361 15371 15381 15391 15401 15411 15421 15431 15441 15451 15461 15471 15481 15491 15501 15511 15521 15531 15541 15551 15561 15571 1558testing simplify: degree 1 csa over Q 15591 15601 15611 15621 15631 15641 15651 15661 15671 15681 15691 15701 15711 15721 15731 15741 15751 15761 15771 15781 15791 15801 15811 15821 15831 15841 15851 1586testing simplify: degree 1 csa over Q(i) 15871 15881 15891 15901 15911 15921 15931 15941 15951 15961 15971 15981 15991 16001 16011 16021 16031 16041 16051 16061 16071 16081 16091 16101 16111 16121 16131 1614testing simplify: quatalg over Q(s5) 16151 16161 16171 16181 16191 16201 16211 16221 16231 16241 16251 16261 16271 16281 16291 16301 16311 16321 16331 16341 16351 16361 16371 16381 16391 16401 16411 1642testing simplify: quatalg csa over Q 16431 16441 16451 16461 16471 16481 16491 16501 16511 16521 16531 16541 16551 16561 16571 16581 16591 16601 16611 16621 16631 16641 16651 16661 16671 16681 16691 1670 1671[1 0] 1672 1673[0 0] 1674 1675[0 1/2] 1676 1677[0 0] 1678 1679 *** at top-level: algsplittingfield(almt) 1680 *** ^----------------------- 1681 *** algsplittingfield: incorrect type in alg_get_splittingfield [use alginit] (t_VEC). 1682 *** at top-level: algdegree(almt) 1683 *** ^--------------- 1684 *** algdegree: incorrect type in alg_get_degree [use alginit] (t_VEC). 1685 *** at top-level: alghassei(almt) 1686 *** ^--------------- 1687 *** alghassei: incorrect type in alg_get_hasse_i [use alginit] (t_VEC). 1688 *** at top-level: alghassef(almt) 1689 *** ^--------------- 1690 *** alghassef: incorrect type in alg_get_hasse_f [use alginit] (t_VEC). 1691 *** at top-level: algrandom(1,1) 1692 *** ^-------------- 1693 *** algrandom: incorrect type in checkalg [please apply alginit()] (t_INT). 1694 *** at top-level: algrandom(1,I) 1695 *** ^-------------- 1696 *** algrandom: incorrect type in algrandom (t_COMPLEX). 16970 1698 *** at top-level: algdim([1,[1],0,0,0,0,0,0,0,0]) 1699 *** ^------------------------------- 1700 *** algdim: incorrect type in checkalg [please apply alginit()] (t_VEC). 1701 *** at top-level: algdim([1,[1],0,0,0,0,0,0,0,0],1) 1702 *** ^--------------------------------- 1703 *** algdim: incorrect type in checkalg [please apply alginit()] (t_VEC). 1704 *** at top-level: algtensor(al,al2) 1705 *** ^----------------- 1706 *** algtensor: incorrect type in checkalg [please apply alginit()] (t_VEC). 1707 *** at top-level: algtensor(al2,al) 1708 *** ^----------------- 1709 *** algtensor: incorrect type in checkalg [please apply alginit()] (t_VEC). 1710 *** at top-level: algtensor(1,z,1) 1711 *** ^---------------- 1712 *** algtensor: incorrect type in checkalg [please apply alginit()] (t_INT). 1713 *** at top-level: algisassociative([1],0) 1714 *** ^----------------------- 1715 *** algisassociative: incorrect type in algisassociative (mult. table) (t_VEC). 17160 1717 *** at top-level: algmul(almt,a,b) 1718 *** ^---------------- 1719 *** algmul: incorrect type in alg_model (t_COL). 1720 *** at top-level: algtomatrix(almt,a,1) 1721 *** ^--------------------- 1722 *** algtomatrix: incorrect type in alg_model (t_COL). 1723 *** at top-level: alginv(almt,a) 1724 *** ^-------------- 1725 *** alginv: incorrect type in alg_model (t_COL). 1726 *** at top-level: algalgtobasis(almt,a) 1727 *** ^--------------------- 1728 *** algalgtobasis: incorrect type in algalgtobasis [use alginit] (t_VEC). 1729 *** at top-level: algbasistoalg(almt,[0,0,0,0]~) 1730 *** ^------------------------------ 1731 *** algbasistoalg: incorrect type in algbasistoalg [use alginit] (t_VEC). 1732 *** at top-level: algpoleval(almt,1,a) 1733 *** ^-------------------- 1734 *** algpoleval: incorrect type in algpoleval (t_INT). 1735 *** at top-level: algadd(almt,[zero;zero],m) 1736 *** ^-------------------------- 1737 *** algadd: inconsistent dimensions in alM_add (rows). 1738 *** at top-level: algadd(almt,[zero;zero;zero],[zero;zero]) 1739 *** ^----------------------------------------- 1740 *** algadd: inconsistent dimensions in alM_add (columns). 1741 *** at top-level: algsub(almt,[zero;zero],m) 1742 *** ^-------------------------- 1743 *** algsub: inconsistent dimensions in alM_sub (rows). 1744 *** at top-level: algsub(almt,[zero;zero;zero],[zero;zero]) 1745 *** ^----------------------------------------- 1746 *** algsub: inconsistent dimensions in alM_sub (columns). 1747 *** at top-level: algmul(almt,m,[zero;zero;zero]) 1748 *** ^------------------------------- 1749 *** algmul: inconsistent dimensions in alM_mul. 1750 *** at top-level: algsqr(almt,[zero;zero]) 1751 *** ^------------------------ 1752 *** algsqr: inconsistent dimensions in alM_mul. 1753 *** at top-level: algdivl(almt,m,zero) 1754 *** ^-------------------- 1755 *** algdivl: forbidden division t_MAT (1x2) \ t_COL (4 elts). 1756 *** at top-level: algdivl(almt,m,[zero,zero;zero,zero]) 1757 *** ^------------------------------------- 1758 *** algdivl: inconsistent dimensions in algdivl. 1759 *** at top-level: algdivl(almt,m,m) 1760 *** ^----------------- 1761 *** algdivl: inconsistent dimensions in algdivl (nonsquare). 1762 *** at top-level: alginv(almt,m) 1763 *** ^-------------- 1764 *** alginv: inconsistent dimensions in alginv_i (nonsquare). 1765 *** at top-level: algtomatrix(almt,m,1) 1766 *** ^--------------------- 1767 *** algtomatrix: inconsistent dimensions in algleftmultable_mat (nonsquare). 1768 *** at top-level: algpow(almt,m,3) 1769 *** ^---------------- 1770 *** algpow: inconsistent dimensions in alM_mul. 1771 *** at top-level: algtrace(almt,m) 1772 *** ^---------------- 1773 *** algtrace: inconsistent dimensions in algtrace_mat (nonsquare). 1774 *** at top-level: algcharpoly(almt,m) 1775 *** ^------------------- 1776 *** algcharpoly: inconsistent dimensions in algleftmultable_mat (nonsquare). 1777 *** at top-level: algcharpoly(alginit(nfinit(y),[-1,-1]),m) 1778 *** ^----------------------------------------- 1779 *** algcharpoly: incorrect type in easychar (t_MAT). 1780 *** at top-level: algnorm(almt,m) 1781 *** ^--------------- 1782 *** algnorm: inconsistent dimensions in algleftmultable_mat (nonsquare). 1783 *** at top-level: algnorm(alginit(nfinit(y),[-1,-1]),m) 1784 *** ^------------------------------------- 1785 *** algnorm: inconsistent dimensions in det. 1786 *** at top-level: alginit(nfinit(y),[2,[[],[]],[x]]) 1787 *** ^---------------------------------- 1788 *** alginit: incorrect type in Hasse invariant (t_POL). 1789 *** at top-level: alginit(nfinit(y),[2,[],[1,1]]) 1790 *** ^------------------------------- 1791 *** alginit: incorrect type in checkhasse [hf] (t_VECSMALL). 1792 *** at top-level: alginit(nfinit(y),[2,[[],[]],Vecsmall([1])]) 1793 *** ^-------------------------------------------- 1794 *** alginit: domain error in checkhasse: sum(Hasse invariants) != 0 1795 *** at top-level: alginit(y,[2,[[],[]],[1]]) 1796 *** ^-------------------------- 1797 *** alginit: incorrect type in alginit (t_POL). 1798 *** at top-level: alginit(nfinit(y),y) 1799 *** ^-------------------- 1800 *** alginit: incorrect type in alginit (t_POL). 1801 *** at top-level: alginit(nfinit(y),[1,2,3,4]) 1802 *** ^---------------------------- 1803 *** alginit: incorrect type in alginit (t_VEC). 1804 *** at top-level: algtableinit(mt,y) 1805 *** ^------------------ 1806 *** algtableinit: incorrect type in algtableinit (t_POL). 1807 *** at top-level: alginit(nfinit(y^2+1),-3) 1808 *** ^------------------------- 1809 *** alginit: domain error in alg_matrix: n <= 0 1810 *** at top-level: alginit(nfinit(x^2+1),3) 1811 *** ^------------------------ 1812 *** alginit: incorrect priority in alginit: variable x >= x 1813 *** at top-level: alginit(nfinit(highvar^2+1),3) 1814 *** ^------------------------------ 1815 *** alginit: incorrect priority in alginit: variable x >= highvar 1816 *** at top-level: ...t(nfinit(y^2-2),[-1,-1]);algrandom(al,-10) 1817 *** ^----------------- 1818 *** algrandom: domain error in algrandom: b < 0 1819 *** at top-level: algrelmultable(al) 1820 *** ^------------------ 1821 *** algrelmultable: incorrect type in alg_get_relmultable [algebra not given via mult. table] (t_VEC). 1822 *** at top-level: algsplittingdata(al) 1823 *** ^-------------------- 1824 *** algsplittingdata: incorrect type in alg_get_splittingdata [algebra not given via mult. table] (t_VEC). 1825 *** at top-level: alghasse(almt,1) 1826 *** ^---------------- 1827 *** alghasse: incorrect type in alghasse [use alginit] (t_VEC). 1828 *** at top-level: algindex(almt,1) 1829 *** ^---------------- 1830 *** algindex: incorrect type in algindex [use alginit] (t_VEC). 1831 *** at top-level: algisdivision(almt) 1832 *** ^------------------- 1833 *** algisdivision: sorry, algisdivision for table algebras is not yet implemented. 1834 *** at top-level: algissplit(almt) 1835 *** ^---------------- 1836 *** algissplit: incorrect type in algissplit [use alginit] (t_VEC). 1837 *** at top-level: algisramified(almt) 1838 *** ^------------------- 1839 *** algisramified: incorrect type in algisramified [use alginit] (t_VEC). 1840 *** at top-level: algramifiedplaces(almt) 1841 *** ^----------------------- 1842 *** algramifiedplaces: incorrect type in algramifiedplaces [use alginit] (t_VEC). 1843 *** at top-level: alghasse(al,-1) 1844 *** ^--------------- 1845 *** alghasse: domain error in is_place_emb: pl <= 0 1846 *** at top-level: alghasse(al,3) 1847 *** ^-------------- 1848 *** alghasse: domain error in is_place_emb: pl > 2 1849 *** at top-level: alghasse(al,2^100) 1850 *** ^------------------ 1851 *** alghasse: domain error in is_place_emb: pl > 2 1852 *** at top-level: alghasse(al,[]) 1853 *** ^--------------- 1854 *** alghasse: incorrect type in is_place_emb (t_VEC). 1855 *** at top-level: alghasse(al,1/3) 1856 *** ^---------------- 1857 *** alghasse: incorrect type in is_place_emb (t_FRAC). 1858 *** at top-level: algtableinit([matid(2),[0,1/2;1,0]]) 1859 *** ^------------------------------------ 1860 *** algtableinit: domain error in algtableinit: denominator(mt) != 1 1861 *** at top-level: alginit(Q,[matid(2),[0,1/2;1,0]]) 1862 *** ^--------------------------------- 1863 *** alginit: domain error in alg_csa_table: denominator(mt) != 1 1864 *** at top-level: alginit(Q,[-1/2,-1]) 1865 *** ^-------------------- 1866 *** alginit: domain error in alg_hilbert: denominator(a) != 1 1867 *** at top-level: alginit(Q,[-1,-1/2]) 1868 *** ^-------------------- 1869 *** alginit: domain error in alg_hilbert: denominator(b) != 1 1870 *** at top-level: alginit(rnfinit(Q,x^2+1),[-x,-1/2]) 1871 *** ^----------------------------------- 1872 *** alginit: domain error in alg_cyclic: denominator(b) != 1 1873 *** at top-level: algsqr([0,0,0,0,0,0,0,0,0,0,0],[]~) 1874 *** ^----------------------------------- 1875 *** algsqr: incorrect type in checkalg [please apply alginit()] (t_VEC). 1876 *** at top-level: algsqr([0,0,0,0,0,0,0,0,[],0,0],[]~) 1877 *** ^------------------------------------ 1878 *** algsqr: incorrect type in checkalg [please apply alginit()] (t_VEC). 1879 *** at top-level: algsqr([0,0,0,0,0,0,0,0,[0],0,0],[]~) 1880 *** ^------------------------------------- 1881 *** algsqr: incorrect type in checkalg [please apply alginit()] (t_VEC). 1882 *** at top-level: algsqr([0,0,0,0,0,0,0,0,[[;]],0,0],[]~) 1883 *** ^--------------------------------------- 1884 *** algsqr: incorrect type in alg_model (t_COL). 1885 *** at top-level: algsqr([[],0,0,0,0,0,0,0,[[;]],0,0],[]~) 1886 *** ^---------------------------------------- 1887 *** algsqr: incorrect type in checkalg [please apply alginit()] (t_VEC). 1888 *** at top-level: algsqr([[],[0],0,0,0,0,0,0,[[;]],0,0],[]~) 1889 *** ^------------------------------------------ 1890 *** algsqr: incorrect type in checkalg [please apply alginit()] (t_VEC). 1891 *** at top-level: algdim([[],[0],0,0,0,0,0,0,[[;]],0,0]) 1892 *** ^-------------------------------------- 1893 *** algdim: incorrect type in checkalg [please apply alginit()] (t_VEC). 1894 *** at top-level: algdegree([[],[0],0,0,0,0,0,0,[[;]],0,0]) 1895 *** ^----------------------------------------- 1896 *** algdegree: incorrect type in checkalg [please apply alginit()] (t_VEC). 1897 *** at top-level: algdegree([rnfinit(nfinit(y),x),[[]],0,0,0,0,0 1898 *** ^---------------------------------------------- 1899 *** algdegree: incorrect type in alg_get_degree [use alginit] (t_VEC). 1900 *** at top-level: algcenter([rnfinit(nfinit(y),x),[[]],0,0,0,0,0 1901 *** ^---------------------------------------------- 1902 *** algcenter: incorrect type in alg_get_center [use alginit] (t_VEC). 1903 *** at top-level: algcentralproj(almt,0) 1904 *** ^---------------------- 1905 *** algcentralproj: incorrect type in alcentralproj (t_INT). 1906 *** at top-level: algcentralproj(almt,[zero,zero]) 1907 *** ^-------------------------------- 1908 *** algcentralproj: incorrect type in alcentralproj [z[i]'s not surjective] (t_VEC). 1909 *** at top-level: algsubalg(almt,0) 1910 *** ^----------------- 1911 *** algsubalg: incorrect type in algsubalg (t_INT). 1912 *** at top-level: algisassociative([]) 1913 *** ^-------------------- 1914 *** algisassociative: incorrect type in algisassociative (mult. table) (t_VEC). 1915 *** at top-level: algisassociative([matid(2),Mat([1,1])]) 1916 *** ^--------------------------------------- 1917 *** algisassociative: incorrect type in algisassociative (mult. table) (t_VEC). 19180 1919 *** at top-level: algisassociative([matid(1)],[]) 1920 *** ^------------------------------- 1921 *** algisassociative: incorrect type in algisassociative (t_VEC). 1922 *** at top-level: algsqr(algtableinit([matid(1)]),[1,2]~) 1923 *** ^--------------------------------------- 1924 *** algsqr: incorrect type in alg_model (t_COL). 1925 *** at top-level: algsqr(al,vector(691)~) 1926 *** ^----------------------- 1927 *** algsqr: incorrect type in alg_model (t_COL). 1928 *** at top-level: algsqr(al,[1,2,3,4,5,6,7,f^2]~) 1929 *** ^------------------------------- 1930 *** algsqr: incorrect type in checkalgx (t_POL). 1931 *** at top-level: algsqr(al,[f^3,[]]~) 1932 *** ^-------------------- 1933 *** algsqr: incorrect type in checkalgx (t_VEC). 1934 *** at top-level: algmul(al,[;],[1,2]~) 1935 *** ^--------------------- 1936 *** algmul: incorrect type in algmul (t_COL). 1937 *** at top-level: algdivl(al,[;],matid(1)) 1938 *** ^------------------------ 1939 *** algdivl: impossible inverse in algdivl: [;]. 1940 *** at top-level: algdivl(al,matid(1),matrix(1,2)) 1941 *** ^-------------------------------- 1942 *** algdivl: inconsistent dimensions in algdivl (nonsquare). 1943 *** at top-level: alginv(al,[0,0]~) 1944 *** ^----------------- 1945 *** alginv: impossible inverse in alginv: [0, 0]~. 1946 *** at top-level: algalgtobasis(al0mt,[1]~) 1947 *** ^------------------------- 1948 *** algalgtobasis: incorrect type in algalgtobasis [use alginit] (t_VEC). 1949 *** at top-level: algbasistoalg(al0mt,[1]~) 1950 *** ^------------------------- 1951 *** algbasistoalg: incorrect type in algbasistoalg [use alginit] (t_VEC). 1952 *** at top-level: nfgrunwaldwang(nfinit(y),0,[],[],'x) 1953 *** ^------------------------------------ 1954 *** nfgrunwaldwang: incorrect type in nfgrunwaldwang (t_INT). 1955 *** at top-level: nfgrunwaldwang(nfinit(y),[2],'x-'x,[1]) 1956 *** ^--------------------------------------- 1957 *** nfgrunwaldwang: incorrect type in nfgrunwaldwang (t_POL). 1958 *** at top-level: alginit(rnfinit(nfinit(y),x),0) 1959 *** ^------------------------------- 1960 *** alginit: incorrect type in alginit (t_INT). 1961 *** at top-level: alginit(rnfinit(nfinit(y),x),[1,2,3,4]) 1962 *** ^--------------------------------------- 1963 *** alginit: incorrect type in alginit (t_VEC). 1964 *** at top-level: alginit(nfinit(y),[matid(2),matid(2)]) 1965 *** ^-------------------------------------- 1966 *** alginit: incorrect type in alg_csa_table (t_VEC). 1967 *** at top-level: alginit(nfinit(y),[matid(2),[0,1;1,0]]) 1968 *** ^--------------------------------------- 1969 *** alginit: domain error in alg_csa_table: (nonsquare) dimension != 1 1970 *** at top-level: nfgrunwaldwang(nfinit(y),0,[],[0]) 1971 *** ^---------------------------------- 1972 *** nfgrunwaldwang: incorrect type in nfgrunwaldwang (t_INT). 1973 *** at top-level: nfgrunwaldwang(nfinit(y),[2],[],[0]) 1974 *** ^------------------------------------ 1975 *** nfgrunwaldwang: inconsistent dimensions in nfgrunwaldwang [#Lpr != #Ld]. 1976 *** at top-level: nfgrunwaldwang(nfinit(y),[2],[2],[]) 1977 *** ^------------------------------------ 1978 *** nfgrunwaldwang: domain error in nfgrunwaldwang [pl should have r1 components]: #pl != 1 1979 *** at top-level: nfgrunwaldwang(nfinit(y),[2],[6],[0]) 1980 *** ^------------------------------------- 1981 *** nfgrunwaldwang: sorry, nfgrunwaldwang for non prime-power local degrees (a) is not yet implemented. 1982 *** at top-level: nfgrunwaldwang(nfinit(y),[2,3],[2,3],[0]) 1983 *** ^----------------------------------------- 1984 *** nfgrunwaldwang: sorry, nfgrunwaldwang for non prime-power local degrees (b) is not yet implemented. 1985 *** at top-level: nfgrunwaldwang(nfinit(y),[2],[3],[-1]) 1986 *** ^-------------------------------------- 1987 *** nfgrunwaldwang: sorry, nfgrunwaldwang for non prime-power local degrees (c) is not yet implemented. 1988 *** at top-level: nfgrunwaldwang(nfinit(y),[[]~],[3],[-1]) 1989 *** ^---------------------------------------- 1990 *** nfgrunwaldwang: incorrect type in checkprid (t_COL). 1991 *** at top-level: nfgrunwaldwang(nfinit(y),[2],[9],[0]) 1992 *** ^------------------------------------- 1993 *** nfgrunwaldwang: sorry, nfgrunwaldwang for nonprime degree is not yet implemented. 1994 *** at top-level: algdegree(A) 1995 *** ^------------ 1996 *** algdegree: incorrect type in alg_get_degree [use alginit] (t_VEC). 1997 *** at top-level: algsub(A,1,1) 1998 *** ^------------- 1999 *** algsub: incorrect type in alg_model (t_INT). 2000 *** at top-level: algadd(A,1,1) 2001 *** ^------------- 2002 *** algadd: incorrect type in alg_model (t_INT). 2003 *** at top-level: algneg(A,1) 2004 *** ^----------- 2005 *** algneg: incorrect type in alg_model (t_INT). 2006 *** at top-level: algmul(A,1,1) 2007 *** ^------------- 2008 *** algmul: incorrect type in alg_model (t_INT). 2009 *** at top-level: algsqr(A,1) 2010 *** ^----------- 2011 *** algsqr: incorrect type in alg_model (t_INT). 2012 *** at top-level: algdivl(A,1,1) 2013 *** ^-------------- 2014 *** algdivl: incorrect type in alg_model (t_INT). 2015 *** at top-level: algdivr(A,1,1) 2016 *** ^-------------- 2017 *** algdivr: incorrect type in alg_model (t_INT). 2018 *** at top-level: alginv(A,1) 2019 *** ^----------- 2020 *** alginv: incorrect type in alg_model (t_INT). 2021 *** at top-level: ...;PR=idealprimedec(K,2);A=alginit(K,[3,[PR,[1]] 2022 *** ^--------------------- 2023 *** alginit: domain error in checkhasse: Hasse invariant at real place [must be 0 or 1/2] != 0 2024 *** at top-level: ...;P3=idealprimedec(K,3);A=alginit(K,[3,[concat( 2025 *** ^--------------------- 2026 *** alginit: domain error in checkhasse: Hasse invariant at real place [must be 0 or 1/2] != 0 2027 *** at top-level: algtensor(alginit(nfinit(y),2),alginit(nfinit( 2028 *** ^---------------------------------------------- 2029 *** algtensor: inconsistent tensor product [not the same center] t_VEC (11 elts) , t_VEC (11 elts). 2030 *** at top-level: algtensor(alginit(nfinit(y),2),alginit(nfinit( 2031 *** ^---------------------------------------------- 2032 *** algtensor: sorry, tensor of cylic algebras of noncoprime degrees is not yet implemented. 2033 *** at top-level: alginit(nf,[2,[[p2,p2],[1/2,1/2]],[0]]) 2034 *** ^--------------------------------------- 2035 *** alginit: error in checkhasse [duplicate prime ideal]. 2036 *** at top-level: alginit(nf,[2,[[p2,p3],[1/2,1/2]],[0,0]]) 2037 *** ^----------------------------------------- 2038 *** alginit: domain error in checkhasse [hi should have r1 components]: #hi != 1 2039 *** at top-level: alginit(nf,[2,[[p2,p3],[1/2,1/2],0],[0]]) 2040 *** ^----------------------------------------- 2041 *** alginit: incorrect type in Hasse invariant (t_VEC). 2042 *** at top-level: alginit(nf,[2,[0,[1/2,1/2]],[0]]) 2043 *** ^--------------------------------- 2044 *** alginit: incorrect type in Hasse invariant (t_VEC). 2045 *** at top-level: alginit(nf,[2,[[p2,p3],0],[0]]) 2046 *** ^------------------------------- 2047 *** alginit: incorrect type in Hasse invariant (t_INT). 2048 *** at top-level: alginit(nf,[2,[[p2,p3],[1/2,1/2,0]],[0]]) 2049 *** ^----------------------------------------- 2050 *** alginit: inconsistent dimensions in checkhasse [Lpr and Lh should have same length]. 2051 *** at top-level: alginit(nf,[2,[[p2,p3],[1/2,1/2]],[1/3]]) 2052 *** ^----------------------------------------- 2053 *** alginit: domain error in hasseconvert [degree should be a denominator of the invariant]: denom(h) ndiv 2 2054 *** at top-level: algcharpoly(al,a,'z) 2055 *** ^-------------------- 2056 *** algcharpoly: incorrect priority in algredcharpoly: variable z >= y 2057 *** at top-level: algcharpoly(al,[1,2,3]~) 2058 *** ^------------------------ 2059 *** algcharpoly: incorrect type in alg_model (t_COL). 2060 *** at top-level: algindex(1,1) 2061 *** ^------------- 2062 *** algindex: incorrect type in checkalg [please apply alginit()] (t_INT). 2063 *** at top-level: algsqr(al,[Mod(1,y),Mod(2,y)]~) 2064 *** ^------------------------------- 2065 *** algsqr: incorrect type in alg_model (t_COL). 2066 *** at top-level: algsqr(al,[Mod(1,y),Mod(2,y)]~) 2067 *** ^------------------------------- 2068 *** algsqr: incorrect type in alg_model (t_COL). 2069 *** at top-level: alfail=alginit(nf,[0,0],'x) 2070 *** ^-------------------- 2071 *** alginit: domain error in rnfequation: issquarefree(B) = 0 2072 *** at top-level: algb(al) 2073 *** ^-------- 2074 *** algb: incorrect type in alg_get_b [noncyclic algebra] (t_VEC). 2075 *** at top-level: algaut(al) 2076 *** ^---------- 2077 *** algaut: incorrect type in alg_get_aut [noncyclic algebra] (t_VEC). 2078 *** at top-level: algtableinit([Mat(1)],1) 2079 *** ^------------------------ 2080 *** algtableinit: not a prime number in algtableinit: 1. 2081 *** at top-level: algtableinit([Mat(1)],4) 2082 *** ^------------------------ 2083 *** algtableinit: not a prime number in algtableinit: 4. 2084 *** at top-level: algpoleval(al,x+1,"toto") 2085 *** ^------------------------- 2086 *** algpoleval: incorrect type in alg_model (t_STR). 2087 *** at top-level: algpoleval(al,x+1,[1,2,3]) 2088 *** ^-------------------------- 2089 *** algpoleval: incorrect type in algpoleval [vector must be of length 2] (t_VEC). 2090 *** at top-level: algpoleval(al,x+1,[1,2]) 2091 *** ^------------------------ 2092 *** algpoleval: incorrect type in algpoleval [mx must be the multiplication table of x] (t_INT). 2093 *** at top-level: algpoleval(al,x+1,[a,mb]) 2094 *** ^------------------------- 2095 *** algpoleval: incorrect type in algpoleval [mx must be the multiplication table of x] (t_MAT). 2096 *** at top-level: algpoleval(al,x+1,[1,mb]) 2097 *** ^------------------------- 2098 *** algpoleval: incorrect type in algpoleval [mx must be the multiplication table of x] (t_MAT). 2099 *** at top-level: alginit(nfinit(y),["a",[[],[]],[]]) 2100 *** ^----------------------------------- 2101 *** alginit: incorrect type in alginit [degree should be an integer] (t_STR). 2102 *** at top-level: alginit(nfinit(y),[1,[[],[]],[]]) 2103 *** ^--------------------------------- 2104 *** alginit: domain error in alg_hasse: degree <= 1 2105 *** at top-level: alginit(nfinit(y),[0,[[],[]],[]]) 2106 *** ^--------------------------------- 2107 *** alginit: domain error in alg_hasse: degree <= 1 2108new algsimpledec 21090 2110[0, [[[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]], Mat([1, 1, 0]), 2111[0; 1; 0]], [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]], Mat([1, 0 2112, 0]), [1; -1; -1]], [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]], 2113Mat([1, 0, 1]), [0; 0; 1]]]] 21140 2115[0, [[[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 5, [1]], Mat([1, 1, 0]), 2116[0; 1; 0]], [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 5, [1]], Mat([1, 0 2117, 1]), [0; 0; 1]], [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 5, [1]], Ma 2118t([1, 0, 0]), [1; 4; 4]]]] 2119[[0; 0; 1], [[[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]], Mat([1, 21200, 0]), [1; -1; 0]], [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 0, [1]], 2121Mat([1, 1, 0]), [0; 1; 0]]]] 2122[[0; 0; 1], [[[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 5, [1]], Mat([1, 21231, 0]), [0; 1; 0]], [[0, 0, 0, 0, 0, 0, Mat(1), Mat(1), [Mat(1)], 5, [1]], M 2124at([1, 0, 0]), [1; 4; 0]]]] 2125norm(,1) 212616 2127Mod(-y + 1, y^2 - 5) 212816 212916/6561 2130223225143999841/5764801 21311 21321 2133trace(,1) 2134Mod(2*y + 2, y^2 - 5) 21358 21368 21371 21381 21391 21401 2141charpoly(,1) 2142x^2 - 2*y*x - 4*y 2143x^8 - 40*x^6 - 160*x^5 + 240*x^4 + 3200*x^3 + 9600*x^2 + 12800*x + 6400 2144x^8 - 40*x^6 - 160*x^5 + 240*x^4 + 3200*x^3 + 9600*x^2 + 12800*x + 6400 21451 21461 21471 2148more al_MAT tests 2149add 21501 21511 21521 21531 2154alg/basis 21551 21561 21571 21581 21591 21601 21611 21621 2163charpoly 21641 21651 21661 21671 21681 21691 21701 21711 21721 21731 21741 21751 21761 21771 21781 21791 21801 21811 2182inv/div 21831 21841 21851 21861 21871 21881 21891 21901 21911 21921 21931 21941 21951 21961 21971 21981 21991 22001 22011 22021 22031 22041 22051 22061 2207mul 22081 22091 22101 2211neg 22121 22131 22141 2215norm 22161 22171 22181 2219pow 22201 22211 22221 2223sqr 22241 22251 22261 2227sub 22281 22291 22301 2231trace 22321 22331 22341 2235algtomatrix 22361 22371 22381 22391 22401 22411 22421 22431 2244algleftmultable 22451 22461 22471 22481 22491 22501 22511 22521 22531 22541 22551 22561 2257more al_CSA tests 22581 22591 22601 22611 2262charpoly 22631 22641 22651 22661 22671 22681 22691 22701 22711 22721 22731 22741 22751 22761 22771 22781 22791 22801 2281inv/div 22821 22831 22841 22851 22861 22871 22881 22891 2290mul 22911 22921 22931 2294neg 22951 22961 22971 2298norm 22991 23001 23011 2302pow 23031 23041 23051 2306sqr 23071 23081 23091 2310sub 23111 23121 23131 2314trace 23151 23161 23171 2318algtomatrix 23191 23201 23211 23221 23231 23241 23251 23261 2327algleftmultable 23281 23291 23301 23311 23321 23331 23341 23351 23361 23371 2338csa pol/polmod bugs 2339[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, -1, 0, 0; 1, 0, 0, 0; 2340 0, 0, 0, -1; 0, 0, 1, 0], [0, 0, y, 0; 0, 0, 0, -y; 1, 0, 0, 0; 0, -1, 0, 0 2341], [0, 0, 0, y; 0, 0, y, 0; 0, 1, 0, 0; 1, 0, 0, 0]] 2342[Mod(1000/9*y + 4400/81, y^2 - 5), Mod(1000/9*y, y^2 - 5), Mod(1000/9*y, y^2 2343 - 5), Mod(1000/27*y, y^2 - 5)]~ 2344[Mod(927/1936*y + 2025/1936, y^2 - 5), Mod(-729/1936*y - 8343/9680, y^2 - 5) 2345, Mod(-729/1936*y - 8343/9680, y^2 - 5), Mod(-243/1936*y - 2781/9680, y^2 - 23465)]~ 2347[Mod(50/9*y, y^2 - 5), Mod(10, y^2 - 5), Mod(10, y^2 - 5), Mod(10/3, y^2 - 5 2348)]~ 23491 23501 23511 23521 23531 23541 23551 2356csa: denom over Z[y] but not over ZK 2357[[1, 0, 0, 0; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [0, -1, 0, 0; 1, 0, 0, 0; 2358 0, 0, 0, -1; 0, 0, 1, 0], [0, 0, 1/2*y - 1/2, 0; 0, 0, 0, -1/2*y + 1/2; 1, 23590, 0, 0; 0, -1, 0, 0], [0, 0, 0, 1/2*y - 1/2; 0, 0, 1/2*y - 1/2, 0; 0, 1, 0, 2360 0; 1, 0, 0, 0]] 2361 *** at top-level: al=alginit(nf,mt*Mod(1,nf.pol)) 2362 *** ^---------------------------- 2363 *** alginit: domain error in alg_csa_table: denominator(mt) != 1 2364al_MAT over al_CSA 23651 23661 23671 23681 23691 23701 23711 23721 23731 23741 23751 23761 23771 23781 23791 23801 2381algleftmultable 23821 23831 23841 23851 23861 23871 2388nfgrunwaldwang SEGV #1669 2389x^2 + Mod(-17, y) 2390 *** at top-level: nfgrunwaldwang(nfinit(x),[2,3],[1,2],Vecsmall( 2391 *** ^---------------------------------------------- 2392 *** nfgrunwaldwang: incorrect priority in nfgrunwaldwang: variable x >= x 2393 2394[1] 2395 2396 2397[1] 2398 2399 2400[1] 2401 2402 2403[1/2] 2404 2405 2406[1/2] 2407 24081 2409GW modified arguments 24101 2411 *** at top-level: algpoleval(al,pol,a)==0 2412 *** ^----------------------- 2413 *** algpoleval: sorry, algpoleval with x in basis form and pol not in Q[x] is not yet implemented. 2414 *** at top-level: algpoleval(al,pol,[;]) 2415 *** ^---------------------- 2416 *** algpoleval: incorrect type in algpoleval (t_MAT). 24171 24181 2419 *** at top-level: al2=algtensor(al,al) 2420 *** ^---------------- 2421 *** algtensor: sorry, tensor of noncyclic algebras is not yet implemented. 2422 *** at top-level: al2=algtensor(al,al) 2423 *** ^---------------- 2424 *** algtensor: sorry, tensor of noncyclic algebras is not yet implemented. 2425Total time spent: 1280 2426