$ H8 R7 a$ t& h, b" _QuadraticClassGroupTwoPart(Q5);4 B' S) i' q4 ?; X! ]# P. a# E$ |
QuadraticClassGroupTwoPart(M); ) P$ n2 D5 s+ q7 x0 y- tNormEquation(Q5, -5) ; 9 ]! s2 `3 [' {7 f+ s0 ONormEquation(M, -5) ; # p- N2 |/ v2 k) o! q8 ^Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field 8 @ c* g) c# ^- V0 nUnivariate Polynomial Ring in w over Q5 n: O5 m" V7 c1 W/ P5 q$ Z# f( vEquation Order of conductor 1 in Q5 & p' k7 H t3 J: S% \7 s- SMaximal Equation Order of Q5! p) k1 T! I7 z( t) \
Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field ! Q- z; U9 ~9 m+ R, kOrder of conductor 625888888 in Q54 t! J5 ]( [8 P- p- C4 \
true Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field2 ~; P e( ?( T: S+ t' ~2 F& ~0 u
true Maximal Equation Order of Q5 2 ?# a( }7 g6 E/ l C+ btrue Order of conductor 1 in Q5 - X7 s K& |! a4 Btrue Order of conductor 1 in Q5 , ]* {7 C8 U. ^7 `' ltrue Order of conductor 1 in Q5: r2 ?- t5 k& a$ {+ K- Y% \
[ / a5 ^* W* Z$ f# Z& v; j0 F2 c <w - Q5.1, 1>,: o5 I0 {; K1 [: z& w ^
<w + Q5.1, 1>; K4 t$ Y! @. k! _) C' G$ x
] 7 D7 U$ O& s" M' f. Y- i- E9 m7 g* |-20" J, g! m3 \. i, f# M" O' y
& N% A0 b$ x1 v>> FundamentalUnit(Q5) ;3 ]1 R( \/ X! V6 {- j- h
^+ \9 N* g/ r: h/ t$ O3 P
Runtime error in 'FundamentalUnit': Field must have positive discriminant ! |# b+ D ?8 \3 G; @- f 0 S5 p8 }5 q7 `) X+ Z7 T8 } $ m# [" J6 }- s7 w* T: `>> FundamentalUnit(M); : K# a' `' W% X( ?6 W" V, g ^ & p, Q9 N4 T. k2 }! p- K. X$ ]Runtime error in 'FundamentalUnit': Field must have positive discriminant * V) g: l6 |) F$ K T2 V2 Y& i$ D1 s6 ~7 ?" B/ i
208 x! N9 z1 F9 w9 S" r
% q1 x! p+ `# W" s
>> Name(M, -5);# J' N( l0 M4 a' [! D! }* {
^, x. X/ X0 d1 }0 `
Runtime error in 'Name': Argument 2 (-5) should be in the range [1 .. 1], ?* v) C! d( m7 _
3 O3 U5 S2 Y( s3 Q. o0 g( a& o2 E: s1 $ [, H. ^; S. Z% `* d. oAbelian Group isomorphic to Z/2& p' Z1 S- X3 \- t4 j8 i9 L
Defined on 1 generator( ]& b$ n5 m' D4 y
Relations:: X5 v" x& K9 T
2*$.1 = 0 ; Z \5 S" S3 XMapping from: Abelian Group isomorphic to Z/26 Z; U. V/ |( o o: m4 h, |- X
Defined on 1 generator- }, N0 g8 x' G/ ~8 j3 B
Relations: : _' P5 |7 a, f" Q! h0 a3 C1 A d0 w 2*$.1 = 0 to Set of ideals of M % ?( E/ Q+ O! m9 g& l9 m% N# I# iAbelian Group isomorphic to Z/2" a8 g& Q& \% K( E5 p
Defined on 1 generator " f) S+ V, f- @ l/ U# K$ @+ K& X9 nRelations:$ Z" X' }& s7 A0 ?
2*$.1 = 0* |$ N1 W8 B y* v0 O) S
Mapping from: Abelian Group isomorphic to Z/2 _4 f. k- N/ @/ j ?Defined on 1 generator' P: P$ Q0 o, g3 Y5 e+ g% G1 m
Relations:5 |/ ~$ Z2 m! j6 j
2*$.1 = 0 to Set of ideals of M7 m5 S* i; b+ M7 K. ^
2 6 i( j |8 k( ?; i3 [27 w. n, P8 u% j7 ]. V% l
Abelian Group isomorphic to Z/2 # `$ V) ` \- n9 T; q3 |Defined on 1 generator! [ s+ U& K3 p" a4 I/ l
Relations:( F0 w, U. K8 Y% z2 F% y% H* U5 l! }
2*$.1 = 0 ( T4 m+ e$ `. J9 HMapping from: Abelian Group isomorphic to Z/2 5 y+ o/ @; C3 Y" N; u7 n1 cDefined on 1 generator : ?& c9 _& K+ ?1 sRelations: " `7 [! s6 c$ I6 j* q 2*$.1 = 0 to Set of ideals of M given by a rule [no inverse] 6 q5 V% H4 W* W$ H5 o2 J2# H" e* X! k: z+ M a* g( C2 O
Abelian Group isomorphic to Z/2+ y- v7 y' P0 Q5 h1 ?! g
Defined on 1 generator# _" o% }$ _" X; h! ?; p9 h0 Z5 v; j4 H
Relations:/ h, E1 I: s' e/ P% g
2*$.1 = 0 7 i2 \6 x; {) W) V' HMapping from: Abelian Group isomorphic to Z/28 V1 g2 ]( V$ `1 w- f
Defined on 1 generator$ I1 y/ x$ U$ k; `% J4 j
Relations: " C1 q ?! B+ L" @* N" S5 M 2*$.1 = 0 to Binary quadratic forms of discriminant -20 given by a rule [no 9 Y1 D) d& H* g) y1 t0 yinverse] 5 u; b+ R1 A5 G: J: jAbelian Group isomorphic to Z/2% c3 p9 h2 |6 u' y& q
Defined on 1 generator 8 h- x% L) I- TRelations:' o+ r5 @, @$ x6 A6 w8 x4 i
2*$.1 = 0; R7 c- [6 S8 ], O' X
Mapping from: Abelian Group isomorphic to Z/2 ( X5 O; ]0 j. L. B" }1 \$ c* wDefined on 1 generator 9 I7 y0 X* a* ~8 n3 ]0 ?7 T( L! hRelations:. p- t- B4 Y3 R( I
2*$.1 = 0 to Binary quadratic forms of discriminant -20 given by a rule [no . h# r8 e2 ~3 O/ C" C
inverse]0 T, S4 D7 b+ `; |, Y
false - p! x4 O/ D. vfalse , [3 Z1 i0 ~( u' h2 P0 W============== % O) Q- u. g# I# R + z# s5 ~7 p7 b% f % b0 R9 o5 W. }8 a! c C0 eQ5:=QuadraticField(-50) ;% H$ S6 G j& I3 `1 V& G
Q5;' w% D2 x! `8 X- {- p$ W2 ]! p
- x+ D! B! I, K. J# ]1 yQ<w> :=PolynomialRing(Q5);Q; * d. |4 Y8 `5 A2 C$ bEquationOrder(Q5);- ?8 T# S8 X7 I7 y5 ^" n9 U7 m
M:=MaximalOrder(Q5) ; # s1 }: w. T* \4 \: @% _M; / {* ~+ S3 C# X r6 NNumberField(M); 9 j$ t9 r! P9 wS1:=sub< M | 1 >;S2:=sub< M | 2 >;S3:=sub< M | 3 >;S4:=sub< M | 4 >;S5:=sub< M | 5 >;S25:=sub< M | 25 >;S625888888:=sub< M | 625888888 >;S625888888;: O' R3 p4 `* m, ^: ?
IsQuadratic(Q5);4 k/ u0 Y, a( J7 m
IsQuadratic(S1); J3 j+ x2 M) @' g, q# bIsQuadratic(S4); ) i2 F3 n5 v% r% O. yIsQuadratic(S25);8 l4 ]6 M& i. K- O
IsQuadratic(S625888888);$ N$ Z+ f/ y' t: r
Factorization(w^2+50); V, |- S: Y! `, N$ |0 dDiscriminant(Q5) ; ) K( Q3 w$ X$ F4 |FundamentalUnit(Q5) ; 0 B6 V/ L5 x) l5 y @7 N CFundamentalUnit(M);% b. C$ L. a0 n' g L1 b
Conductor(Q5) ; 6 i! R7 J& c- d: I+ M1 C0 c/ y" ]/ w% o" M9 w! l. n. V! Q& j
Name(M, -50); " u8 P; \' `, }) sConductor(M);( u: M, s2 {$ z/ i9 r( Q9 t
ClassGroup(Q5) ; * K' F6 `# V4 d* W9 S' U8 s; o4 yClassGroup(M);$ G; Z2 L4 z; H& I; g$ F
ClassNumber(Q5) ;; G- u- y7 h' R" k1 ?
ClassNumber(M) ;( g* ?$ x( q2 w+ n
PicardGroup(M) ;4 J1 f4 S$ W7 {9 r" M
PicardNumber(M) ;, e; T8 D9 X# @( n- k# Y, ?, p
& k+ }& m2 X( T9 ^8 O! q, i+ c1 Y
QuadraticClassGroupTwoPart(Q5);# o* U) {3 B" Z% l1 R m
QuadraticClassGroupTwoPart(M);' k! S% X7 D" c
NormEquation(Q5, -50) ;: C9 }5 _* a7 S' [3 q( N$ s
NormEquation(M, -50) ; ( i5 C" _/ x# w1 |3 l' C$ G6 t( c" c4 Q0 H# n
Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field: Y" G8 s- m; S8 [
Univariate Polynomial Ring in w over Q5 ( c# `6 F$ m5 J+ Y; T ^% MEquation Order of conductor 1 in Q51 m5 A3 G7 ^, K
Maximal Equation Order of Q5 , a+ t6 w' A9 E9 c) Q" hQuadratic Field with defining polynomial $.1^2 + 2 over the Rational Field' Y* B" S- R/ j Q+ K5 D6 ~: ~
Order of conductor 625888888 in Q5" T! y3 E, z. z* N
true Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field ' ~* e, U) g0 Q6 ?true Maximal Equation Order of Q52 W2 g" Y$ g/ r3 d+ c5 K8 ^. ^
true Order of conductor 1 in Q5. J" m' u1 W. N5 p
true Order of conductor 1 in Q5 8 m- X' K4 h- l; u- Gtrue Order of conductor 1 in Q5- z# Q% ^9 ^$ ~9 U2 v2 C2 L* n
[$ y) \& l! ^( l Y$ `! G8 k
<w - 5*Q5.1, 1>, }' S# E4 \ \* R; G u6 d <w + 5*Q5.1, 1>3 W- L" p4 F5 X( [4 B @
]- [( G5 c- ~9 T- u5 v, X1 T
-8 3 c# i0 ~* d, E: f4 E+ K" I( D V% R' S
>> FundamentalUnit(Q5) ;# }8 O' B2 M0 v2 u9 W W6 O8 K7 y
^7 d0 ?/ A+ B& x! {0 B6 k; ~
Runtime error in 'FundamentalUnit': Field must have positive discriminant5 b: w9 S$ P( R- }0 O7 B
" w/ E, T O; A* s6 a, u8 T
, S' }$ R% ~& {% D. {
>> FundamentalUnit(M);) ] f1 g* X% Y" r9 f8 Z6 j
^7 i* z/ ]* |, a# ], O
Runtime error in 'FundamentalUnit': Field must have positive discriminant # i. C0 Z5 a7 e. o" @$ T; s 8 n: Y- \( h! X4 H5 J8 7 D7 D+ E1 }1 S' O9 v# O0 H7 l9 d9 w' l" P* e) W
>> Name(M, -50);. a; I, s6 N. }/ \8 i
^7 s4 |$ P) N9 T) ]* y
Runtime error in 'Name': Argument 2 (-50) should be in the range [1 .. 1]" F; b8 K1 R; Z: @2 H" G
- `8 u2 h% b1 ]0 H6 w# k1 $ P% S' T" z/ aAbelian Group of order 1 / n8 W) v" C& eMapping from: Abelian Group of order 1 to Set of ideals of M7 L% m+ q7 x |
Abelian Group of order 1, J }8 H2 ~' X! N; X1 R$ w
Mapping from: Abelian Group of order 1 to Set of ideals of M- k' X W, Q) J$ h
19 |( D5 F# g1 G! a1 a
1: d7 r# g( e+ `3 v
Abelian Group of order 1, G/ h" J( k0 F @1 T: \6 x
Mapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no : q* ], R1 t; A4 @% yinverse] # G. i& E$ M) f% i4 G( \; B1 * e1 D2 o( m l9 s6 Y- xAbelian Group of order 12 W1 R8 m3 ?7 T M. x/ E+ }
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant " j7 r6 `/ T, f-8 given by a rule [no inverse]: }9 q: i& N9 c5 B
Abelian Group of order 1 $ [" a/ N6 _4 S! N$ ]8 UMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant # J* n. X2 O8 `' q* K-8 given by a rule [no inverse]* b/ ?2 @3 [% F; E" {( f: }
false" |/ P5 p( [, }2 R5 h; b' j1 d
false ; J; E' }: p( @" O0 m
看看-1.-3的两种： ; E5 G. A* Y0 u. B1 _1 m. x' h/ g/ m' E8 G `
Q5:=QuadraticField(-1) ; 9 N) q* ?, d0 s6 V4 f1 E$ i7 @Q5; " l `0 p' m5 ~+ t 3 Y6 _/ D" A J6 W! V& j5 _: JQ<w> :=PolynomialRing(Q5);Q; $ |- K& G# Q8 G1 \' j. u) UEquationOrder(Q5);3 v, ]' ?0 }- ]8 W- q! H0 }
M:=MaximalOrder(Q5) ; 2 s1 J2 }& @6 a) S' {0 f6 zM;& O) A- s- v9 Z) P
NumberField(M);$ F6 d- r: n* G/ h q( O7 W. T5 a0 ~
S1:=sub< M | 1 >;S2:=sub< M | 2 >;S3:=sub< M | 3 >;S4:=sub< M | 4 >;S5:=sub< M | 5 >;S25:=sub< M | 25 >;S625888888:=sub< M | 625888888 >;S625888888;/ l2 U! h, l+ T: g- m) r4 b
IsQuadratic(Q5); ! H6 ~+ Z& r8 x' C4 }IsQuadratic(S1); , V8 D) [2 ~5 ^" b2 @IsQuadratic(S4);) X, r9 v9 U5 j1 k; e7 a$ b
IsQuadratic(S25); ! o8 x7 ~" r* S' f$ j% cIsQuadratic(S625888888); K" ?3 H* }8 x2 Q) EFactorization(w^2+1); * T1 u* u# |( w$ R/ H( Z% ~
Discriminant(Q5) ;+ k0 n: g' [! {* f {$ l
FundamentalUnit(Q5) ; / E% x5 ]" u' U; _& A2 |FundamentalUnit(M); % Q4 v5 _# d5 U* \Conductor(Q5) ; 1 r0 f* [9 S! P& }: @8 d x' d. J% J7 P p; _2 [& p. d
Name(M, -1); p! R% ? x+ }8 K! cConductor(M); v: v/ ?# ]7 L) q4 {3 p: u. I
ClassGroup(Q5) ; & v) f$ p+ D0 I+ lClassGroup(M); 1 R3 w+ U/ w. A# MClassNumber(Q5) ;: c0 B# G' a/ q; w, D9 }
ClassNumber(M) ; ' l9 z0 y$ R) I; GPicardGroup(M) ; 7 N, p% @6 b3 G7 S- bPicardNumber(M) ; 9 C. u! I' B, i& m+ D, b$ y% E8 c( A- }9 T8 N" F! C' W
QuadraticClassGroupTwoPart(Q5); ! z* }- }, b5 I/ s% dQuadraticClassGroupTwoPart(M);# ]' f$ I5 ~* h3 S8 ?
NormEquation(Q5, -1) ;. r: k: l0 V8 ^7 a+ O5 |
NormEquation(M, -1) ;& ~) W# |( d5 T) `, @
& p( |7 @+ m0 R# Q
Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field $ u+ l) }4 w! D$ nUnivariate Polynomial Ring in w over Q5, }# x2 m% }4 H5 j! _0 Q- `
Equation Order of conductor 1 in Q5 ! g% i% x* K4 e5 p5 P" j8 \Maximal Equation Order of Q5; v+ @+ m8 p2 ^3 g5 Q6 O' B' C2 q
Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field * I) H2 T4 L7 d: t- l% z5 K' w# mOrder of conductor 625888888 in Q52 p4 K$ A/ s* o
true Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field 3 x# F) m+ D3 J0 S% L/ mtrue Maximal Equation Order of Q5 m% u# S. u) L7 w0 \0 P W; ~* itrue Order of conductor 1 in Q5 9 X3 X! O$ T( q. f; ]6 M+ qtrue Order of conductor 1 in Q5 : H/ C! ?' o" Q* b: U; n/ Z, Ptrue Order of conductor 1 in Q5 3 X0 r: g! S+ Q0 _% G" T[ + p' b# l3 Q- `9 Z7 v <w - Q5.1, 1>, $ E, H1 T7 g8 m/ ^3 u <w + Q5.1, 1> * V/ x D/ f1 {. s4 X) N]6 M1 w+ |2 B8 x. {. v# t
-4 Q+ o; H; c: i
1 i8 ?: X; E! X; k3 D
>> FundamentalUnit(Q5) ;5 \. K9 |& ^$ l' a& T7 I
^0 R% A, D; [: E; m8 C5 |: \8 a
Runtime error in 'FundamentalUnit': Field must have positive discriminant * ^2 I% \, n, K& R: y( f 8 t6 [2 \" g% s5 I 8 D* b( j# r* p" d: b>> FundamentalUnit(M); 3 M; r- L9 |( e, s# m ^" F% _- N! Y" ?& Y- X
Runtime error in 'FundamentalUnit': Field must have positive discriminant5 R9 ~# R: g: c p: u
" s' W) a: p0 @2 A; s43 }* G4 y/ }& o+ e. _1 a+ e( h
0 ?; N& D$ R2 ]
>> Name(M, -1);: m9 Z1 R6 ^2 ^+ x$ s; L. w
^ 9 T7 i/ X9 }- H$ ]Runtime error in 'Name': Argument 2 (-1) should be in the range [1 .. 1] a+ P, I! ^4 N* P5 Z4 V& I : Z. ]! |7 [' u$ g) R- m }) d3 R1 2 ^' w* V& B# e$ e( z4 YAbelian Group of order 1" R( f6 r% z4 _8 o) S+ ]
Mapping from: Abelian Group of order 1 to Set of ideals of M % l1 s8 f, N2 z S! `) FAbelian Group of order 1. {' A1 q( _! m: O
Mapping from: Abelian Group of order 1 to Set of ideals of M7 P9 c* w# R1 [& W+ _; Z
14 m, N6 f, \2 a. t' S8 _# A- i8 j2 @
1 ' L% I, R7 f! N* g" zAbelian Group of order 1 0 U5 z4 W g) X1 l6 TMapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no * l. A0 h( |6 i3 i, Y0 W$ minverse]& M/ U2 v. ~, V+ u- d( K
1# d* z; l* T9 y& o$ ?. ]3 _# U4 r
Abelian Group of order 1 - c6 ^6 K3 K2 W9 n6 l! ]Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant ' A5 P' e l6 @& N/ o2 N1 w-4 given by a rule [no inverse]+ ?# K6 p% P0 {
Abelian Group of order 1 : t5 { N, S2 u/ p0 UMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant* p3 H1 B9 m- v' Z+ b
-4 given by a rule [no inverse] $ r0 Q) |3 n/ a1 o/ ?0 _false : A; O- o" w+ W6 i; \false $ B" h( t, O0 z/ o: U! s1 L===============3 t7 _8 N. r- Z0 K* F
0 u' I& D( a: Y0 N* A1 ?! E
Q5:=QuadraticField(-3) ;. o) O5 `, x0 c$ |0 @ n* q7 Y
Q5; ) y: T5 [9 g: G' |6 _2 s* C% n ! N; K% X( U4 E# c: E* gQ<w> :=PolynomialRing(Q5);Q; 3 J6 L# ]+ Q, i1 C& wEquationOrder(Q5); : J& ?' U, c2 PM:=MaximalOrder(Q5) ;: e& {3 v4 V7 V8 o; X" ?5 V
M; " L- h# V7 v6 h* n: S; Y1 JNumberField(M); ) p) m+ T8 v" o( g3 i3 H' GS1:=sub< M | 1 >;S2:=sub< M | 2 >;S3:=sub< M | 3 >;S4:=sub< M | 4 >;S5:=sub< M | 5 >;S25:=sub< M | 25 >;S625888888:=sub< M | 625888888 >;S625888888; ' n$ C: H% O) _9 O- G7 l6 Z3 i: AIsQuadratic(Q5);( x+ b7 L7 T. X; o1 G, _
IsQuadratic(S1);# v- K F* m3 ?: h! i w' {
IsQuadratic(S4); 7 c8 N2 q: `, w7 ^* B7 J) G% [IsQuadratic(S25);% Y0 Q4 r: V' j U
IsQuadratic(S625888888);8 l* H3 f3 i" k! q2 t0 w% Y7 A, A
Factorization(w^2+3); $ I9 |- s$ W4 k1 nDiscriminant(Q5) ;+ e w. y3 K4 x, U% e) w- G9 c
FundamentalUnit(Q5) ;) T; Z$ F( \5 P' b. A4 p
FundamentalUnit(M); ' X+ K& z& {* }8 r5 A9 V" {$ d$ ?Conductor(Q5) ;, c. R+ I; m4 C3 c
! T/ a2 o& y' K+ B4 u, i3 zName(M, -3);" d" j' w& r( H
Conductor(M); 9 ?1 X {1 W% N3 X J( y. g7 [ClassGroup(Q5) ; & p2 Y; @. a& d( \; vClassGroup(M);. A/ X; }! q) y* W( N8 C
ClassNumber(Q5) ;% n) K& I k( D) s9 D2 U
ClassNumber(M) ;9 J3 i5 w/ E4 t
PicardGroup(M) ; % n: V+ a7 T; ?3 v5 i% J( q/ tPicardNumber(M) ;' ?% W* N5 d' C1 f$ m: S* u' ?
! h* z$ O$ Y* T, w; ~
QuadraticClassGroupTwoPart(Q5);1 V& o1 k8 g& X0 r! ?! W
QuadraticClassGroupTwoPart(M); , f6 n: G# c1 R" M/ @/ A* JNormEquation(Q5, -3) ; 9 ?0 x' g( Z) I+ P% C' eNormEquation(M, -3) ;( L3 `, C3 C! S& \: F z! |1 M
2 T0 r7 L0 Y* c% h% gQuadratic Field with defining polynomial $.1^2 + 3 over the Rational Field: i5 \$ t5 s5 K3 v$ K
Univariate Polynomial Ring in w over Q54 |* ^: }+ C6 ^* A# U0 |+ R
Equation Order of conductor 2 in Q5 $ J: p, n- y% Y( aMaximal Order of Q5 " |. N" j) ]* _9 |( ~6 bQuadratic Field with defining polynomial $.1^2 + 3 over the Rational Field# }1 _ a' l2 N7 E2 A; j v5 `
Order of conductor 625888888 in Q50 N- M Q4 _* s {7 n% A% |- Y& u
true Quadratic Field with defining polynomial $.1^2 + 3 over the Rational Field 8 d) {+ a+ N7 F$ ?! Ptrue Maximal Order of Q5. C. q* I* L' i' | Z# R
true Order of conductor 16 in Q5 : c6 L) L+ d& Htrue Order of conductor 625 in Q5 & _; y( b' m$ O P! f: I( ?8 D+ P! Utrue Order of conductor 391736900121876544 in Q56 \0 ^+ n/ [6 z9 T7 P/ y
[ ! u4 _1 S O" M4 ]: r <w - Q5.1, 1>, ! R4 D) j) ^$ P9 R5 n6 x$ d <w + Q5.1, 1> : b: F: M5 @% f2 k9 b. c. B]3 ?" J# F/ x# q$ A, Q
-3- f1 l+ v# N' M7 b( L" T" m4 ^, d
& g( B% E( g2 i/ C. L
>> FundamentalUnit(Q5) ; % G. O# r/ [* f: I$ j7 T ^ / b0 j' Q+ V6 o: ERuntime error in 'FundamentalUnit': Field must have positive discriminant+ I9 B- X; W8 V
- }8 Q7 l0 W* m' Z" ]) T2 s9 l2 }% `1 s$ E- e& ^
>> FundamentalUnit(M); 7 A) U! Q J+ e T1 e |6 h ^& ~9 t/ b3 Y2 q4 Q4 V7 j0 ^ R
Runtime error in 'FundamentalUnit': Field must have positive discriminant: T1 x1 h% E5 L3 W, n; y
3 S) u5 x4 E/ ]: B
3 8 M( f) i6 O" C2 Q5 l$ {* a+ r6 z2 t9 l4 J- @( j
>> Name(M, -3); 9 n/ R. }/ U2 ^/ w' D6 W ^ ! m. e1 { Y2 N+ v" DRuntime error in 'Name': Argument 2 (-3) should be in the range [1 .. 1]; ~/ w# K, I/ u( b$ n! |4 @
0 }2 Q: g& M# n
1 ; G: q+ }: Y+ u% |) sAbelian Group of order 1 % j" E$ M$ j& B7 sMapping from: Abelian Group of order 1 to Set of ideals of M % o2 U) \* U. ?1 b. t8 x7 hAbelian Group of order 1 % N, W; z0 Y* |6 jMapping from: Abelian Group of order 1 to Set of ideals of M* |; b! Q6 l8 a# A$ K8 G' h
1 2 x# o- A5 \% s# q% I' {5 M1, V$ E! \+ ?* q
Abelian Group of order 1- [/ b: A& g: H
Mapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no5 \6 J! Q# R5 b& Z$ k$ P* \
inverse] " {2 t% o8 E4 F+ Y1, W }% g3 x+ L7 d% U# W
Abelian Group of order 1" ]/ p2 H. T" \/ D
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant% p {+ v6 i h- U1 V, M' a+ \& u
-3 given by a rule [no inverse] + V Y. |, w$ I) fAbelian Group of order 1! x2 R* T- {% d- V# S
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant; k6 l) X/ P: |% s4 ?8 f
-3 given by a rule [no inverse] ! _. m4 B0 G. T/ ?false " s# L/ q% x7 l7 F f% wfalse
, m3 N8 q7 W! |Cyclotomic Field of order 5 and degree 45 y! v' w6 ~, b
$.1^4 + $.1^3 + $.1^2 + $.1 + 1. N' o8 ~ |1 h% n: j- D
Cyclotomic Field of order 6 and degree 26 O+ J# E" I, A4 m2 ?
$.1^2 - $.1 + 1& H# l. ^, i) Z* ? O
Cyclotomic Field of order 7 and degree 6 g% ^2 p- N: ^ B" e6 d$ F- o$.1^6 + $.1^5 + $.1^4 + $.1^3 + $.1^2 + $.1 + 1 7 N4 c% E6 ?" i Q* o6 YRational Field % k7 j4 U, g% w2 o9 K( [Rational Field7 @9 \, h Z4 Q( I
Rational Field & T3 P7 E# P$ }* qRational Field 0 W+ M+ R0 v5 S2 Q" Z% ] V1 ]9 Dzeta_11: q. R" Z& t# q. W% {( f6 D
zeta_1119 ~! y* H* c$ f7 G; ^3 i- e# A
1237 z ?' N7 U' t1 O
71 I/ c1 ^# Z8 i& W
7$ H- A1 l$ x4 n: t. i" Q: Z* S* {- C
Permutation group acting on a set of cardinality 6+ E4 c+ ~& j7 x
Order = 6 = 2 * 3 1 V# T% n7 Y" Q9 s; @0 v r7 R6 c3 o (1, 2)(3, 5)(4, 6) 9 a0 Z5 T5 |6 U (1, 3, 6, 2, 5, 4)* L' R" b# @3 G! ]2 |) Q
Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to Set of all automorphisms of - m" ^- |6 {4 X4 R
CC/ K4 U+ T Z! g
Composition of Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to GrpPerm: $, 3 ^6 M4 l9 z5 @3 N ZDegree 6, Order 2 * 3 and 4 Z1 x% F4 i4 g" }Mapping from: GrpPerm: $, Degree 6, Order 2 * 3 to Set of all automorphisms of 9 N B' C) H' I/ T3 R
CC
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发表于 2012-1-4 17:41
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