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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