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[1, x]
[1, x, 1/2*x^2 + 1/2, 1/4*x^3 + 1/4*x^2 - 1/4*x - 1/4]
-4
3392
Mod(0, 4)
206105552
[1, x, 1/4*x^2 + 1/4, 1/4*x^3 + 1/4*x]
[1, x, 1/2*x^2 + 1/2, 1/4*x^3 + 1/4*x^2 + 1/4*x + 1/4]
12
[1, x, x^2, x^3]
27648
1
[1 2.6720881244151097674232871083920323733 + 0.37423915433885206387815653913250097460*I I -0.37423915433885206387815653913250097460 + 2.6720881244151097674232871083920323733*I]
[1 2.6720881244151097674232871083920323733 - 0.37423915433885206387815653913250097460*I -I -0.37423915433885206387815653913250097460 - 2.6720881244151097674232871083920323733*I]
[1 -2.6720881244151097674232871083920323733 - 0.37423915433885206387815653913250097460*I I 0.37423915433885206387815653913250097460 - 2.6720881244151097674232871083920323733*I]
[1 -2.6720881244151097674232871083920323733 + 0.37423915433885206387815653913250097460*I -I 0.37423915433885206387815653913250097460 + 2.6720881244151097674232871083920323733*I]
13568.000000000000000000000000000000000 + 0.E-34*I
[1, x, 1/2*x^2 + 1/2, 1/4*x^3 + 1/4*x^2 + 1/4*x + 1/4]
[1, x, 1/2*x^2 + 1/2, 1/4*x^3 + 1/4*x^2 - 1/4*x - 1/4]
[1, x, x^2, x^3]
[1, x, 1/8*x^2 + 1/2*x - 3/8, 1/40*x^3 - 11/40*x + 1/2]
[1, x, 1/5*x^2 + 2/5, 1/5*x^3 + 2/5*x]
[1, x, 1/4*x^2 + 1/2*x + 1/2, 1/8*x^3 - 1/4*x + 1/2]
[1, x, 1/4*x^2 + 1/2, 1/20*x^3 - 1/10*x]
[1, x, 1/2*x^2, 1/4*x^3]
[1 1.5537739740300373073441589530631469482 + 0.64359425290558262473544343741820980892*I 1 + I 0.45508986056222734130435775782246856962 + 1.0986841134678099660398011952406783786*I]
[1 1.5537739740300373073441589530631469482 - 0.64359425290558262473544343741820980892*I 1 - I 0.45508986056222734130435775782246856962 - 1.0986841134678099660398011952406783785*I]
[1 -1.5537739740300373073441589530631469482 - 0.64359425290558262473544343741820980892*I 1 + I -0.45508986056222734130435775782246856962 - 1.0986841134678099660398011952406783786*I]
[1 -1.5537739740300373073441589530631469482 + 0.64359425290558262473544343741820980892*I 1 - I -0.45508986056222734130435775782246856962 + 1.0986841134678099660398011952406783785*I]
512.00000000000000000000000000000000000 + 4.255744136770140078 E-36*I
512
[1 0.77688698701501865367207947653157347408 + 0.32179712645279131236772171870910490446*I I -0.64359425290558262473544343741820980892 + 1.5537739740300373073441589530631469482*I]
[1 0.77688698701501865367207947653157347408 - 0.32179712645279131236772171870910490446*I -I -0.64359425290558262473544343741820980892 - 1.5537739740300373073441589530631469482*I]
[1 -0.77688698701501865367207947653157347408 - 0.32179712645279131236772171870910490446*I I 0.64359425290558262473544343741820980892 - 1.5537739740300373073441589530631469482*I]
[1 -0.77688698701501865367207947653157347408 + 0.32179712645279131236772171870910490446*I -I 0.64359425290558262473544343741820980892 + 1.5537739740300373073441589530631469482*I]
512.00000000000000000000000000000000000 - 4.255744136770140078 E-36*I
[1 2.6720881244151097674232871083920323733 + 0.37423915433885206387815653913250097460*I I 0.37423915433885206387815653913250097460 - 3.6720881244151097674232871083920323733*I]
[1 2.6720881244151097674232871083920323733 - 0.37423915433885206387815653913250097460*I -I 0.37423915433885206387815653913250097460 + 3.6720881244151097674232871083920323733*I]
[1 -2.6720881244151097674232871083920323733 - 0.37423915433885206387815653913250097460*I I -0.37423915433885206387815653913250097460 + 1.6720881244151097674232871083920323733*I]
[1 -2.6720881244151097674232871083920323733 + 0.37423915433885206387815653913250097460*I -I -0.37423915433885206387815653913250097460 - 1.6720881244151097674232871083920323733*I]
13568.000000000000000000000000000000000 + 0.E-34*I
[1 0.45508986056222734130435775782246856962 + 1.0986841134678099660398011952406783786*I I -1.0986841134678099660398011952406783785 + 0.45508986056222734130435775782246856962*I]
[1 0.45508986056222734130435775782246856962 - 1.0986841134678099660398011952406783785*I -I -1.0986841134678099660398011952406783785 - 0.45508986056222734130435775782246856962*I]
[1 -0.45508986056222734130435775782246856962 - 1.0986841134678099660398011952406783786*I I 1.0986841134678099660398011952406783785 - 0.45508986056222734130435775782246856962*I]
[1 -0.45508986056222734130435775782246856962 + 1.0986841134678099660398011952406783785*I -I 1.0986841134678099660398011952406783785 + 0.45508986056222734130435775782246856962*I]
511.99999999999999999999999999999999999 + 0.E-35*I
12
[1 1.4553466902253548081226618397096970699 + 0.34356074972251246413856574391455856847*I I -0.34356074972251246413856574391455856847 + 1.4553466902253548081226618397096970699*I]
[1 1.4553466902253548081226618397096970699 - 0.34356074972251246413856574391455856847*I -I -0.34356074972251246413856574391455856847 - 1.4553466902253548081226618397096970699*I]
[1 -1.4553466902253548081226618397096970699 - 0.34356074972251246413856574391455856847*I I 0.34356074972251246413856574391455856847 - 1.4553466902253548081226618397096970699*I]
[1 -1.4553466902253548081226618397096970699 + 0.34356074972251246413856574391455856847*I -I 0.34356074972251246413856574391455856847 + 1.4553466902253548081226618397096970699*I]
1280.0000000000000000000000000000000000 - 6.728922305550388939 E-36*I
[1, x, 1/2*x^2 + 1/2, 1/4*x^3 + 1/4*x^2 + 1/4*x + 1/4]
1280
[2 8]
[5 1]
[2 9]
[17 1]
2176
2176/9
[1, x, 1/5*x^2 + 2/5, 1/5*x^3 + 2/5*x]
[2 6]
34
544
[2 5]
[17 1]
[1 I 2.1013033925215678467731335152161665233 + 1.1897377641407581357639680612798653140*I -1.1897377641407581357639680612798653140 + 2.1013033925215678467731335152161665233*I]
[1 -I 2.1013033925215678467731335152161665233 - 1.1897377641407581357639680612798653140*I -1.1897377641407581357639680612798653140 - 2.1013033925215678467731335152161665233*I]
[1 I -2.1013033925215678467731335152161665233 - 1.1897377641407581357639680612798653140*I 1.1897377641407581357639680612798653140 - 2.1013033925215678467731335152161665233*I]
[1 -I -2.1013033925215678467731335152161665233 + 1.1897377641407581357639680612798653140*I 1.1897377641407581357639680612798653140 + 2.1013033925215678467731335152161665233*I]
8703.9999999999999999999999999999999997 + 0.E-34*I
[1, x, x^2, x^3]
[2 8]
[5 1]
320
[2 6]
[5 1]
[2 2]
[17 1]
576
624
[1, x, 1/2*x^2 + 1/2, 1/4*x^3 + 1/4*x^2 - 1/4*x - 1/4]
3392
[2 6]
[53 1]
eulerphi(x): Euler's totient function of x.
2
1
1
2
[1, x, 1/19*x^2 + 2/19, 1/95*x^3 + 21/95*x]
[2 4]
[17 1]
6656
[2 9]
[13 1]
[2 1]
[5 2]
[13 1]
[5 1]
[19 1]
289
650
361
34
*** unknown function or error in formal parameters: expand((x^2-17)^2)
^------------------
expand: unknown identifier
factor(x,{lim}): factorization of x. lim is optional and can be set whenever x
is of (possibly recursive) rational type. If lim is set return partial
factorization, using primes up to lim (up to primelimit if lim=0)
[1 -0.30024259022012041915890982074952138854 + 0.62481053384382658687960444744285144400*I I -0.62481053384382658687960444744285144400 - 0.30024259022012041915890982074952138854*I]
[1 -0.30024259022012041915890982074952138854 - 0.62481053384382658687960444744285144399*I -I -0.62481053384382658687960444744285144399 + 0.30024259022012041915890982074952138854*I]
[1 1.3002425902201204191589098207495213885 - 0.62481053384382658687960444744285144400*I I 0.62481053384382658687960444744285144400 + 1.3002425902201204191589098207495213885*I]
[1 1.3002425902201204191589098207495213885 + 0.62481053384382658687960444744285144399*I -I 0.62481053384382658687960444744285144399 - 1.3002425902201204191589098207495213885*I]
271.99999999999999999999999999999999999 - 3.877349896605722789 E-36*I
4
256
625
881
[881 1]
[1, x, 1/7*x^2 + 3/7, 1/7*x^3 + 3/7*x]
43520
[2 9]
[5 1]
[17 1]
17
289
256
545
[5 1]
[109 1]
[1, x, 1/8*x^2 + 1/2*x - 3/8, 1/40*x^3 - 11/40*x + 1/2]
[2 4]
[5 1]
[109 1]
[2 1]
[5 2]
[13 1]
[73 1]
[1, x, 1/6*x^2 - 1/3, 1/12*x^3 + 1/3*x]
[2 4]
[73 1]
645120
[2 11]
[3 2]
[5 1]
[7 1]
[2 3]
[5 1]
[7 1]
280
100
2746368
[2 11]
[3 2]
[149 1]
[2 1]
[149 1]
[1, x, 1/16*x^2 + 1/2*x + 3/8, 1/352*x^3 - 21/176*x + 1/2]
[2 1]
[113 1]
169
384
484
79/400
[79 1]
256
292
1168
[2 4]
[73 1]
[2 2]
[73 1]