本帖最后由 lilianjie 于 2012-1-4 17:54 编辑 4 S5 o& B- Q2 M4 u/ p6 }4 N1 K. n5 h1 s+ r! H/ Z
Q5:=QuadraticField(-5) ; @- z: l C0 Y7 S
Q5; 2 M; u3 ]2 t; [7 c! O; F7 p . h8 @5 M+ F E1 [2 r2 @Q<w> :=PolynomialRing(Q5);Q;* z. n' L: ?5 B3 f ?& P
EquationOrder(Q5); % x9 e, H4 g" g( D t" wM:=MaximalOrder(Q5) ;" r6 y* T5 e$ o n8 P* T
M;& v( C. O0 |0 G2 s) D
NumberField(M);+ D o9 s8 J5 m' W* x$ S0 _
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; & t. r9 W, r( c- a0 P/ \IsQuadratic(Q5);0 q' L. K1 x, N0 i5 W M" u: h1 ]4 y
IsQuadratic(S1); % o$ T( E) T& m& l1 s: i. s3 tIsQuadratic(S4);) s- v. O8 Q% \9 V) D: z: |
IsQuadratic(S25);3 |8 @' H0 F: c4 U4 Z; Z& g9 z
IsQuadratic(S625888888); " a0 W% c6 |- [7 f! w/ T! O' RFactorization(w^2+5); 0 X' W7 u# S( `8 Z7 ?; BDiscriminant(Q5) ;7 N2 ?/ v) n% H! Q3 o/ I7 A+ {; G
FundamentalUnit(Q5) ; " o2 q, R( b! Y6 x- \: r5 IFundamentalUnit(M);& Z# G: F j+ B5 h7 j
Conductor(Q5) ;6 u h/ d2 `' Z+ v: o. Z
% U5 n* X1 Q- i! W+ dName(M, -5); . Y/ u+ q$ L7 a8 S4 SConductor(M); * n% j# F; C& X6 a# AClassGroup(Q5) ; " B( O/ r, r% R1 x6 eClassGroup(M); ( W# h8 c2 ^8 M: zClassNumber(Q5) ;9 ?8 s& ]# ]+ @- \( U
ClassNumber(M) ; 4 N- g- \8 `7 I8 P3 G' O M0 z0 JPicardGroup(M) ; ! b7 o8 K6 m: U! ?5 ~% UPicardNumber(M) ; % t) f2 e7 u# t$ D & ^( t6 E" c9 _9 i! e5 EQuadraticClassGroupTwoPart(Q5);# r5 {% f7 Q, ^; h) Y! L1 Z1 w. ]$ \
QuadraticClassGroupTwoPart(M); ! M* a- f5 M' F: x- |6 gNormEquation(Q5, -5) ;8 r; J+ P; V3 c; w* G7 j
NormEquation(M, -5) ;' n3 D% m( p5 u* \+ V
Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field 4 p% i6 x- O8 c6 YUnivariate Polynomial Ring in w over Q5 $ e: f/ R% I( Q7 UEquation Order of conductor 1 in Q5. K2 ~+ g$ R; E2 J. w- ]/ t
Maximal Equation Order of Q5 7 T/ b6 k4 K3 K( Y0 _1 e# OQuadratic Field with defining polynomial $.1^2 + 5 over the Rational Field9 Y `/ `! o6 L1 r9 B
Order of conductor 625888888 in Q5 ; k7 j% O( x& \8 h/ M0 W1 etrue Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field ( N( F3 B# }3 F1 D5 P' F+ ytrue Maximal Equation Order of Q5 + S" V0 u* L) _) a, E2 n/ {true Order of conductor 1 in Q5( y; Q: ]8 O% s+ T3 r
true Order of conductor 1 in Q5; w7 B( S$ S( f2 q
true Order of conductor 1 in Q5 4 v! Z) M5 t5 h6 o[" i+ c- X8 S$ ?1 o9 R# x
<w - Q5.1, 1>,& v7 V1 @& {: T- {, O) |2 b
<w + Q5.1, 1>6 I0 u) b: U, E# m j
]: G0 N* ]# w% _$ L
-207 t, U- p% A! q! ]
! K) v2 G9 U7 w$ u# d, A. L$ Y6 p
>> FundamentalUnit(Q5) ;6 i% J9 n8 ?) @! [) y
^ : N W' N) [4 {6 m5 _Runtime error in 'FundamentalUnit': Field must have positive discriminant# b8 }+ d( ^( P1 U3 j! T4 g. T
2 w: ^# |; o! K7 g ]' v: \# g2 j3 Q6 x/ L
>> FundamentalUnit(M);4 S; D# D) a- G' L) E" D
^ & B6 Y9 `; \" M/ ]# e6 _7 U1 cRuntime error in 'FundamentalUnit': Field must have positive discriminant 4 b; @& e% c" ]: o# N% F 0 P7 f5 e& K9 s* @" U5 I20* p1 F7 M" B" ?) C/ H3 s
8 r0 p" O# F9 z>> Name(M, -5);6 \! u# `# e! Z' [7 E
^) C8 P! s' i9 a$ D* i$ a
Runtime error in 'Name': Argument 2 (-5) should be in the range [1 .. 1] ( w" N! Z9 h2 C9 p6 ^+ L x' p) L/ }! R( D5 w
12 y7 u6 g" c5 h1 z3 f
Abelian Group isomorphic to Z/2 , U3 r6 u$ q# xDefined on 1 generator8 a' K% A: k; @. {/ k
Relations:* @; ~8 z' v( j* S- n8 u
2*$.1 = 0( @- o* P, [$ m) e
Mapping from: Abelian Group isomorphic to Z/26 O* F2 B8 z6 @! }1 j
Defined on 1 generator ! q6 h- x4 _# a! v$ [ yRelations:7 t* P, j# {; D5 t
2*$.1 = 0 to Set of ideals of M3 h9 f% e5 q7 |3 B
Abelian Group isomorphic to Z/2, ?, W0 K* Q+ G( Z- l8 ^9 s: N
Defined on 1 generator 2 h% z n3 V2 S# i+ s8 |Relations: 9 L- s4 q) E- u* e0 y6 ` 2*$.1 = 04 b% m T) z3 t! q. r% B
Mapping from: Abelian Group isomorphic to Z/2+ E9 E: l6 `" s2 b1 a6 }3 c
Defined on 1 generator+ J- q7 ^$ `( D0 i
Relations:7 A6 _$ L- V+ c1 Y
2*$.1 = 0 to Set of ideals of M0 U! g! A4 o( u0 c* E
2 ! m; o' v! H& {6 S23 ]) H1 Q3 C' g9 b
Abelian Group isomorphic to Z/2 / i! H! A$ @3 \! s {- }( xDefined on 1 generator* l+ Y9 k" ?( |, B# C
Relations:, V/ d2 {6 ^. _ }% S$ Z5 _
2*$.1 = 0 . `' v4 j4 Q" k6 x4 kMapping from: Abelian Group isomorphic to Z/2 + ?5 O. f4 g9 V. U' W% }Defined on 1 generator 4 p2 v) g9 P: z6 G+ K& }4 cRelations:4 l, X' \2 n2 c( W% M, E6 O2 O! B3 X
2*$.1 = 0 to Set of ideals of M given by a rule [no inverse]4 k' K" F3 G9 l+ F/ \% W6 E. y' c+ N
2 9 B" \$ [6 i; ]4 NAbelian Group isomorphic to Z/29 @+ S/ J9 @+ b9 y
Defined on 1 generator $ d/ \0 H- l: }; w* y. S2 A4 KRelations:) [$ y+ I+ }( y" t4 Y. N+ m
2*$.1 = 0 2 ?" g ], j6 G) u h7 \8 B# \- ?Mapping from: Abelian Group isomorphic to Z/2 ! s& k+ T% A. U; m! U1 F5 H2 DDefined on 1 generator( \1 b9 b/ u0 G `. x
Relations:; J6 C! R, O8 z' M2 ~2 P4 z8 e! f* ]
2*$.1 = 0 to Binary quadratic forms of discriminant -20 given by a rule [no 0 H, ^$ B: U9 Q7 S% J7 d& Winverse] : F$ h; v2 e1 a4 q; E" {Abelian Group isomorphic to Z/2 0 |0 i7 C! W) `* O. cDefined on 1 generator8 f$ ]% g. ?$ w- l, p
Relations:; \7 k9 _/ [/ ?. z( O* E
2*$.1 = 0# n4 u/ M8 b. q" |5 ]/ T
Mapping from: Abelian Group isomorphic to Z/2 1 s- o& q" W- S$ C- H$ p: M& @Defined on 1 generator * [2 Q4 _2 F; X* {Relations:& W' `1 E" {. [: J
2*$.1 = 0 to Binary quadratic forms of discriminant -20 given by a rule [no ' k: o9 `3 C/ k- [, f8 y* X
inverse]. P6 x& H; e- `) b( R
false* u( w2 o* x# f e+ x+ M4 \
false8 w; e/ m: d! \3 M
============== ; A3 y( S! Y/ U9 G( z$ C1 y. p9 _( s
' [8 H% G% U. x4 T' k: n9 BQ5:=QuadraticField(-50) ; 9 X- u6 Q- M/ v' u) ?6 |; tQ5;, n7 u# M) M2 L
1 ~6 O$ @: a: |. D4 g* EQ<w> :=PolynomialRing(Q5);Q;9 @) J/ H% E! {1 l3 w9 K
EquationOrder(Q5);, e! u4 D% W ]7 A
M:=MaximalOrder(Q5) ; 8 I- F2 i' P' E7 AM; $ G1 @% N) K! N; z ~0 V" a0 S& dNumberField(M);) u; K& y+ J2 d; A
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;. |2 R7 h4 a4 O
IsQuadratic(Q5); / F6 C. m) E& R1 B' hIsQuadratic(S1); : ^2 p# l4 o% G* UIsQuadratic(S4); ; ^ |: E0 D, Q2 t* B4 vIsQuadratic(S25);2 K* p1 `4 E' H/ q+ }+ H7 t: }
IsQuadratic(S625888888);; d4 y8 ^% \+ G' j' X8 U
Factorization(w^2+50); . M J0 k% X) \, Q* O
Discriminant(Q5) ;2 A# P! n. `1 W+ b! g3 n) [
FundamentalUnit(Q5) ; : W/ Z7 ~; _. Q6 M+ P5 IFundamentalUnit(M); 3 G7 R8 T/ t8 J; ^Conductor(Q5) ;& I! y6 I3 S, t q
# r" k/ u1 ~9 p4 M6 XName(M, -50);0 u9 P& b% Y0 j: n% T. d% ]7 A0 w- U
Conductor(M);2 I* q2 V/ \! U
ClassGroup(Q5) ; . D" b7 P* Y9 Y% oClassGroup(M); ' S1 S( E' `% d0 \ClassNumber(Q5) ;. l p# m; p$ `& C% V9 j( l/ u
ClassNumber(M) ; ' C) B# F+ {$ d( A. PPicardGroup(M) ; " f- C7 R2 P+ Q1 kPicardNumber(M) ;. s! c- h7 L6 M, v3 k
' ~: Q8 J" g. V5 HQuadraticClassGroupTwoPart(Q5); 9 _) e& ~$ L8 z2 _QuadraticClassGroupTwoPart(M); / r8 o: H/ d- M4 a( E1 NNormEquation(Q5, -50) ; 0 g, e7 e e3 \3 T1 e7 i( vNormEquation(M, -50) ; ' A. i5 p1 { j6 N* E , {0 T8 @. ?5 `Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field* d7 R4 V. n7 M. | z8 p* Z$ w1 ^4 Q
Univariate Polynomial Ring in w over Q5 ) H" S4 {3 w, h5 V& JEquation Order of conductor 1 in Q5! U" A" x; v; a
Maximal Equation Order of Q5 ' e; X# \+ O8 [Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field F* X# U) k" E8 I! B$ S+ \Order of conductor 625888888 in Q5 E" ?5 R+ z; e! P& J2 r u4 {
true Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field H0 z9 |7 ` L. U( v9 S9 l! |true Maximal Equation Order of Q59 W7 c8 D0 m8 x, w* w- E+ g* O6 S
true Order of conductor 1 in Q5 7 \ M6 ^- y, _% H' f7 dtrue Order of conductor 1 in Q5 ! j& v: e1 v; G! v; ftrue Order of conductor 1 in Q5 & o9 D5 z, ^7 K, \7 o[9 ~& p1 u- A) d$ N- L
<w - 5*Q5.1, 1>, 3 Y5 V* B X$ t <w + 5*Q5.1, 1>8 k! ?* c! ^0 X. d" m* }4 \; [0 T
]; |2 H5 J/ {2 w5 \& N2 T8 o
-8 * ^& `9 _8 Y8 h, L / e$ S% G* E/ x- {# x1 c>> FundamentalUnit(Q5) ;3 F; D4 i' Y7 L: V8 I
^ ; y1 a% W; e* {9 j9 A6 j3 nRuntime error in 'FundamentalUnit': Field must have positive discriminant2 A, g# q2 Z9 Q* ]; X' d2 R% ~
6 }% |7 m2 V! T9 E. [3 h, R0 v3 ~4 Z( S3 ?1 ~0 A
>> FundamentalUnit(M); ' @- B4 R1 k' m ^5 S( T" u1 c. W! P5 h/ C
Runtime error in 'FundamentalUnit': Field must have positive discriminant# V! Q0 o/ n6 S/ I
5 i) `$ v/ _5 X3 r- p, e8 6 P3 g) ?2 m, O3 R7 I 9 D1 z/ g8 w7 |+ a# d4 O2 h>> Name(M, -50); # ]; Z% h/ D9 v& p6 q. Z ^. i+ n' Q( ?; B3 |, S5 x, D4 z
Runtime error in 'Name': Argument 2 (-50) should be in the range [1 .. 1]& ]' m# Z; j; \
% Y3 \1 H$ Z* I( Y/ }6 v
1 7 W5 J# D5 g; ]- p5 z' a# J$ @Abelian Group of order 14 l' n9 O% e' h" L Q: @
Mapping from: Abelian Group of order 1 to Set of ideals of M ' A# P4 i. _) v' w: J- j, sAbelian Group of order 1. E& u* k2 [* `0 n/ q# u/ ~
Mapping from: Abelian Group of order 1 to Set of ideals of M 2 p& i1 ~6 ?6 f. ?1) b8 L5 F& g6 K, i+ Q+ N
14 J/ g9 `( I8 \4 M2 f) N$ \
Abelian Group of order 1 , i2 ?2 J8 a8 s" Q# G% hMapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no9 Z4 f2 E7 |. d9 ]
inverse] 3 ~$ H* w. H% O3 d9 x( E* w1) B% C4 L7 j; l8 S3 n `7 I7 h) c
Abelian Group of order 1 ( c) _" ~. k' ]: oMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant3 X6 M% f# R- Y$ {+ y: h% l& h
-8 given by a rule [no inverse] f, [" p: G+ W8 I6 [
Abelian Group of order 1 / f4 S9 ~8 {% o1 s1 R% o% U6 iMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant5 Q4 F3 k- S: { ^
-8 given by a rule [no inverse] / N9 W) `8 P* N8 ?+ P) G c- G/ `8 l. efalse0 I! J$ \5 M1 D) T
false 1 a, G8 o4 X4 E' e( H3 x! N) q
! q) ?# Z. c# ?2 z: y* mQuadraticClassGroupTwoPart(Q5); 1 R0 Z- M2 z6 G2 k. o$ eQuadraticClassGroupTwoPart(M); 8 [: i+ P1 g: b! b* m. DNormEquation(Q5, -1) ; ) y, V8 M) X" G; J" H$ s" x# NNormEquation(M, -1) ;8 q) d6 o. r; a
: Q, ^. c' g( i7 @3 pQuadratic Field with defining polynomial $.1^2 + 1 over the Rational Field$ U1 a$ @. [6 P! @$ o$ ~
Univariate Polynomial Ring in w over Q5" f+ `& L8 q; a. N- W
Equation Order of conductor 1 in Q5 6 l/ J$ S6 s* j( V9 Z# EMaximal Equation Order of Q5 6 h$ `+ @7 g3 [/ N: F: P. hQuadratic Field with defining polynomial $.1^2 + 1 over the Rational Field 1 v. _! [3 A3 B9 c8 IOrder of conductor 625888888 in Q5 & y+ _0 u- k4 a' X `- ptrue Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field' o z- A) N H- l6 G G, e) E
true Maximal Equation Order of Q5! `& F# p9 Z1 [
true Order of conductor 1 in Q5 5 g6 ^- F6 E4 Itrue Order of conductor 1 in Q5/ N! ^* R3 X$ x$ y
true Order of conductor 1 in Q59 |6 ~0 {7 W7 S
[ 5 { w( R1 g0 ~ <w - Q5.1, 1>,4 T2 J3 g: q7 a" _- f
<w + Q5.1, 1>, d) @) S! f+ D: H0 F& F
]6 q7 n" z2 E) ?, R0 a6 B: `
-4* H& }- u4 v" o1 s2 ?5 @
2 s% J. M9 X" r% U6 d. c" o% {) ^>> FundamentalUnit(Q5) ; / ?# A( H3 ~' U* k3 X ^ / \* t% }# Q, m$ ^Runtime error in 'FundamentalUnit': Field must have positive discriminant , H* @: h; w+ _8 m* q9 l9 S( g; G: E+ {% F
8 r' [* l5 P+ U/ z6 \>> FundamentalUnit(M); / B9 e, |6 b" t# { ^ 6 X& L" i% C- W7 eRuntime error in 'FundamentalUnit': Field must have positive discriminant0 s) A# y. F. `. ~
; j( B! y$ `* W1 C7 y4 $ a( n' X3 X `: \* A3 k 9 }, I7 |3 p- q/ Y. z2 G>> Name(M, -1); 7 _) {( k( ~! k4 x$ C! f* b8 s) a9 w2 a ^+ E5 L) Q+ G% o- O$ D$ y5 W- W
Runtime error in 'Name': Argument 2 (-1) should be in the range [1 .. 1] $ [5 j1 p9 {" S8 L7 {( ^* j |$ u$ r. W* K x1 }7 F* C) Z4 l3 R& i
1% A9 o2 q1 ^$ ]. r) P2 m
Abelian Group of order 1" j0 _ k0 I% {, Y0 ?/ r
Mapping from: Abelian Group of order 1 to Set of ideals of M* U7 o+ N1 J6 s- u' w2 B
Abelian Group of order 13 `, y9 K7 [3 ]8 \
Mapping from: Abelian Group of order 1 to Set of ideals of M7 f4 ^8 ^4 q' c3 T1 o X
1 : H. K% P# b5 c3 ~' Q7 `5 F/ T9 o1 ) U2 x8 P: I+ _% C7 [+ S" lAbelian Group of order 1, ^. G% a% U( n) \6 A. J
Mapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no 5 F5 w: P$ L' B Binverse]6 A0 }: J. R7 A0 D: f" I5 r8 o
1 : D3 J2 Z G2 z4 v+ \+ ]Abelian Group of order 1 2 ^6 E5 k! }* Z+ r5 ~) ~Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant* @2 V! A+ {4 ], l
-4 given by a rule [no inverse] ! d2 E5 i6 X6 q% j) B( H. L+ I, GAbelian Group of order 12 Q: l1 V, L1 }4 T- e4 ?2 o8 K3 [
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant8 c" m% \" i6 T2 h
-4 given by a rule [no inverse]+ j, r2 d! a+ R
false* }7 H5 }2 J! {
false/ }' I8 ?8 P% V0 ]
===============& X" m2 W! v! n1 d/ l9 ~
$ R3 Q8 @, G4 c4 d( a. \5 u
Q5:=QuadraticField(-3) ;' k0 M# ]) P2 q }7 e9 f
Q5;. j: U L- T# [) h% \
" J9 x: X0 K! {* y# h
Q<w> :=PolynomialRing(Q5);Q; {' T- G, N$ C& DEquationOrder(Q5); ( w) C/ S$ b* {) k* aM:=MaximalOrder(Q5) ;& h& Y. n7 | ~! f2 {! ^
M;# }% I8 S6 } H' Z6 i W# E' F
NumberField(M);; `/ E! {; X: }5 R# ^
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; 0 j. _2 n9 o, m) SIsQuadratic(Q5);. h3 ^* T a2 ~
IsQuadratic(S1);( e. s! s6 S- |
IsQuadratic(S4); $ n. C6 T o! F0 H0 U" s5 P) k5 F+ LIsQuadratic(S25); 3 V; z8 I' R; ZIsQuadratic(S625888888); ~' I" f4 c" Q9 o; Q
Factorization(w^2+3); 5 x6 g1 h7 }5 `1 K$ Y1 qDiscriminant(Q5) ; 9 z0 m, T, \! m- f- r* O& V8 t* QFundamentalUnit(Q5) ;! H8 B3 c* ?/ q' N
FundamentalUnit(M);) O( K; a, R. A
Conductor(Q5) ; " k/ k) }4 `$ I* r. C1 `8 S5 f# E/ V$ O$ i6 A. H5 f
Name(M, -3);6 ]0 E p+ L( k, N9 J3 i
Conductor(M); , ^; O( r. D: i' A. zClassGroup(Q5) ; 9 P$ N; w0 v; r
ClassGroup(M); ' W* T& ?/ `/ L5 s, }4 YClassNumber(Q5) ; 0 } H* V3 ~0 A4 x% TClassNumber(M) ; ! t2 x9 ^( s9 ~; P) S( ^! PPicardGroup(M) ; : z7 ~" w, h" l, V. F: {PicardNumber(M) ; 3 R9 ?% p( K3 N( K+ [ # v. {% G0 V$ g( w0 MQuadraticClassGroupTwoPart(Q5);( H2 q8 o+ L# D
QuadraticClassGroupTwoPart(M);& s& U/ p' S5 W
NormEquation(Q5, -3) ;3 h. m! D r4 W: D h
NormEquation(M, -3) ;& D- I8 t0 U6 Z+ q* w( a J
& e. g% I/ y# D+ M: S; T/ k$ I2 c
Quadratic Field with defining polynomial $.1^2 + 3 over the Rational Field ' x k0 v7 D8 P/ H& J7 ]& dUnivariate Polynomial Ring in w over Q5 ( R# `+ i3 V: L) k& o( SEquation Order of conductor 2 in Q5" L9 t& `" \( X# `/ z9 |9 m
Maximal Order of Q5 ; T3 L/ @3 U( R% \7 E" m) Y* _Quadratic Field with defining polynomial $.1^2 + 3 over the Rational Field 6 L7 N) O$ j& C1 u! R1 q! B8 ?0 Z$ HOrder of conductor 625888888 in Q5 , ^; p0 I2 d3 h8 A5 g8 T9 v! jtrue Quadratic Field with defining polynomial $.1^2 + 3 over the Rational Field " i+ W# y/ m/ r6 [true Maximal Order of Q5 7 j$ F- z/ L+ }# mtrue Order of conductor 16 in Q5" }% M; V7 t1 [7 C0 }0 o2 W
true Order of conductor 625 in Q5 $ t! ]' f5 U0 L( btrue Order of conductor 391736900121876544 in Q53 ~4 d7 [' Q9 m: B% |2 N
[ , G% Q! }# y) Y6 ] <w - Q5.1, 1>, I. O" F5 M& {, Y- [ <w + Q5.1, 1> 4 C* b3 T+ Z- {* u- T) h) W- n]+ I1 j& F9 b: `, W- b
-3 : p& A+ j6 o. F- |1 w6 O m% B! D4 d' i% o( e- Z7 k; q$ J
>> FundamentalUnit(Q5) ;8 f& M. q, j: h) R
^ + Q7 q% E" h& a7 k" l! H5 GRuntime error in 'FundamentalUnit': Field must have positive discriminant 7 m& f! j5 l% C# T$ [- z' L( J* d ~# T* O( w8 V. G
1 ?. P% ~. m. _# L% Y" S" }>> FundamentalUnit(M); 9 [, j! q8 z7 K [! J/ f ^' t7 w D( w) t4 p$ n
Runtime error in 'FundamentalUnit': Field must have positive discriminant 9 U R k7 ]/ j 8 M0 b; \/ h' o! W J/ }36 M, c( c" @/ E( j1 e
# \, u8 Q8 e$ e2 [
>> Name(M, -3); - r# X9 E( x; R5 |# b# j2 O ^ $ l/ n1 s% Y4 |, R2 t, `3 z" A# ZRuntime error in 'Name': Argument 2 (-3) should be in the range [1 .. 1]5 p% q4 Z% [9 m9 V3 n* @: v5 R7 J
) T3 \. L9 d) }- [' v, D2 @
1: p1 o$ n# T1 d3 a9 ^
Abelian Group of order 1 ' K, k! D3 f3 H3 F7 l. {. qMapping from: Abelian Group of order 1 to Set of ideals of M 1 t$ r" _' h5 C1 H% Z: }Abelian Group of order 1 5 E, A- I+ m- @2 P+ xMapping from: Abelian Group of order 1 to Set of ideals of M K9 t' g( i& N8 {. \1 1 `/ g2 V4 f2 {9 U1 @1 y, m1 6 n8 y2 j8 h8 P8 a% \! lAbelian Group of order 1 3 j! E+ H9 A9 v5 Y/ YMapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no! k4 N% q: v! w& g! u/ e5 z2 A1 f
inverse]8 I) u, s7 P- n! q0 M9 A7 ]" T0 P2 R
1 6 C2 C; W& ?( _) {Abelian Group of order 10 c/ _* ?& Q5 ?5 F/ T+ z4 U
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant $ o& g. Q% x0 r7 t; J-3 given by a rule [no inverse] ( J( L( P' @! u+ `Abelian Group of order 1 % Y4 b2 y& e+ d, yMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant7 K7 L% W7 e/ q' S9 e
-3 given by a rule [no inverse] / g7 T( T. i6 `, Ffalse ( T( f3 y h R6 [. C7 T( g9 S, c/ gfalse
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发表于 2012-1-4 17:41
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