! i* r0 h3 N- p T3 ?8 }* \Q5:=QuadraticField(-5) ; 6 [& U( @8 R, s! R. ]- | wQ5;6 L# S; Z* w O
6 s$ M- p% i6 K, C4 C( e; _
Q<w> :=PolynomialRing(Q5);Q;; x+ x4 D6 n. n n4 p+ V
EquationOrder(Q5);7 H/ S S( v s+ I# ^1 h
M:=MaximalOrder(Q5) ;; ~( Q8 \7 s) A
M;8 s2 y- }& V8 H6 h! n/ F& ?& M3 s
NumberField(M);: F& V0 V+ i( x) d4 c# i
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;8 E, u% e, e. w" e: [
IsQuadratic(Q5); " L7 ^9 d6 h, KIsQuadratic(S1);/ M0 b z, v6 ]+ V2 i3 g
IsQuadratic(S4);# e$ ]5 k8 {+ g5 z5 P# ]
IsQuadratic(S25); ' s B% x7 w8 i* @' M/ QIsQuadratic(S625888888);, L0 D: x' q$ i# ^; a2 i
Factorization(w^2+5); + c. m2 ]5 z+ ]
Discriminant(Q5) ;7 I0 d |/ ^8 u7 R
FundamentalUnit(Q5) ;: l9 U, t% k& C6 g
FundamentalUnit(M); @5 W6 R! H9 x$ `2 EConductor(Q5) ;4 Q0 T4 e' N y9 o; b1 Z! x7 I
4 X t1 B8 x% P! I% d r# AName(M, -5); % H- C5 W0 p9 `! ZConductor(M);) q' e. A2 C0 r9 ?! U$ F
ClassGroup(Q5) ; 4 e t3 A: q* G* fClassGroup(M);' E2 N: k/ `! X
ClassNumber(Q5) ; 0 W# }) B* z3 S1 |& K4 N8 l+ s8 WClassNumber(M) ;' B! M \/ ~, f8 \7 L
PicardGroup(M) ;, ?! N$ k$ F/ y* j1 Q9 }
PicardNumber(M) ; / o, B9 V/ |( Y% ^' N- v$ X9 O0 N) } 2 P' V9 j& z" U5 r5 \3 XQuadraticClassGroupTwoPart(Q5); $ W( J/ f. O: X5 t7 s4 i$ FQuadraticClassGroupTwoPart(M);, L7 C5 u+ I4 q3 z0 T
NormEquation(Q5, -5) ; 2 a6 z* J0 k) F1 SNormEquation(M, -5) ;7 ?: Q, i: y: f; }5 o; S0 }
Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field0 T. h% |% }3 S% x: ]1 _0 D% W# f
Univariate Polynomial Ring in w over Q5 ' ^% q! W/ g7 BEquation Order of conductor 1 in Q5# a# |+ Y% F6 H4 y* _; x. d" E
Maximal Equation Order of Q5 - \3 ~ {; P, |0 z2 dQuadratic Field with defining polynomial $.1^2 + 5 over the Rational Field , K$ M0 }' y8 \; fOrder of conductor 625888888 in Q5 , Z# o1 ?" c; `6 e. |! Qtrue Quadratic Field with defining polynomial $.1^2 + 5 over the Rational Field + a' o9 i& R8 d) x9 p7 qtrue Maximal Equation Order of Q5 7 S5 @6 W. |# c% x, ptrue Order of conductor 1 in Q5; I( Q* B5 W( c: `# g0 S
true Order of conductor 1 in Q54 g7 [ A9 N! ]' c
true Order of conductor 1 in Q5 % q" p9 X2 i% c* u0 _/ ?[( Q+ q/ K: {2 o( ~: s% J( D5 K: D
<w - Q5.1, 1>,% A/ }9 t$ ]& Q4 x% v) U) F A/ ?2 l
<w + Q5.1, 1> $ u1 V6 y! ~7 ?9 Z9 k1 e- d] 7 o2 p: w- Z3 @9 m" e, ^-20 r- {8 P- z! K4 T; u3 i+ A* I
+ n* L& M, u5 ?3 }>> FundamentalUnit(Q5) ;4 j0 o8 U1 g7 l6 N0 n4 I# t$ t2 F
^ + q9 q& \/ A5 z) V# x: e" k9 bRuntime error in 'FundamentalUnit': Field must have positive discriminant) h# @4 b- t5 U2 r
& g- G; l6 ?$ w* [$ \2 I L9 e r3 \, ^- P) }+ I& ]" f; `1 B" B
>> FundamentalUnit(M); / t6 e i7 k! y3 U r% h ^: P/ z5 P9 l3 V& b1 d' l8 {. E
Runtime error in 'FundamentalUnit': Field must have positive discriminant $ ], N4 l7 X% M4 L* o 9 T3 |& p& ]' B7 N4 _0 w/ d206 C% \8 X7 N" d* A) L
# s7 l# Q& H, ~7 ?9 m>> Name(M, -5); 1 l- @" c2 J: \: c$ z+ c ^ 4 r$ s. s& g$ z7 _6 O4 JRuntime error in 'Name': Argument 2 (-5) should be in the range [1 .. 1] % Q8 i/ }8 g& h. S( g9 X6 ] ' r6 {1 S4 W! P! `# m% p% D1 6 t$ T( j, D6 L; UAbelian Group isomorphic to Z/2 3 H$ W' g/ G3 c z. LDefined on 1 generator & @5 }: ?: w. P, s9 `! V5 xRelations:+ F G5 X$ {" A' ]4 h
2*$.1 = 0 6 ?- P+ t4 T/ ?% m2 EMapping from: Abelian Group isomorphic to Z/2 + H8 t; s- M2 c2 [Defined on 1 generator5 O: v, m2 s5 X# n& b2 ~; f
Relations: 6 K- s1 f. U& [; E) W 2*$.1 = 0 to Set of ideals of M# D, N/ E: _3 Z. D
Abelian Group isomorphic to Z/2 6 e1 v/ s8 I1 t# I; kDefined on 1 generator8 a8 L9 U7 ^" w5 W% V: C7 ]2 L$ E
Relations: ; h1 p: f+ g5 p; r( U 2*$.1 = 0 - u5 Q4 w. N6 z+ x' sMapping from: Abelian Group isomorphic to Z/2 ' F q W! p' z6 J- j# dDefined on 1 generator% y2 j/ T1 W8 F* n- C
Relations: / n2 J/ [9 F3 O$ v 2*$.1 = 0 to Set of ideals of M. b( Q' S2 N; X) W2 Y
25 o2 u1 @+ [8 F: E
2" r$ G/ l8 f5 V- S# n
Abelian Group isomorphic to Z/2, e7 h: X4 l. B5 u$ M- v/ J6 |
Defined on 1 generator 5 ^, {& ~, g& F4 f: b8 ERelations: * m4 p" [: E K$ i 2*$.1 = 0 U1 B( R# Y' n A
Mapping from: Abelian Group isomorphic to Z/2 " q) s$ M+ W: o6 b4 \5 kDefined on 1 generator8 M, `, q3 C+ q9 A! g0 k1 g, }! g
Relations:8 K3 o+ t$ H( O5 ^
2*$.1 = 0 to Set of ideals of M given by a rule [no inverse]7 D1 L- |3 X, A- V" S3 k
2 ; [0 k! W6 N( A% B( y. r7 d3 O# YAbelian Group isomorphic to Z/2+ Y( ]1 e% P# V4 d7 t
Defined on 1 generator h. ?$ V' ]3 g' c
Relations: 1 I( C. o$ A( P* x4 m+ j: q 2*$.1 = 01 Q! q& a+ Y& j
Mapping from: Abelian Group isomorphic to Z/2 ) E) k& _3 K; CDefined on 1 generator ( `" q7 p; m: F1 m! wRelations:# u" a) s+ B- D" b
2*$.1 = 0 to Binary quadratic forms of discriminant -20 given by a rule [no 4 g$ z2 c+ G6 H; ~, e. t) binverse] / q- Y5 i9 P) \+ M# D2 CAbelian Group isomorphic to Z/2 6 m- B' f, r, F' Q g0 zDefined on 1 generator ; `% J i, q, {- z0 P" T6 L9 w/ ZRelations: & U- @9 [; \. J; T 2*$.1 = 0! j" C' M6 B& X" Y
Mapping from: Abelian Group isomorphic to Z/2& t" @' P6 r2 @! d
Defined on 1 generator: w4 r, c* b+ d6 B$ A) N- Z
Relations: - B& Q; e& I5 k1 C+ a1 c6 [) o 2*$.1 = 0 to Binary quadratic forms of discriminant -20 given by a rule [no ) u4 {& h6 y/ I) B% \6 jinverse]1 [; S3 Q+ K- I+ Y
false0 }; C& ]7 {1 a' k! J/ A) x1 o
false' D1 W- x' w0 u0 z3 B/ o. T
==============( K5 B- V1 g: g2 u- A+ Z% X
" d3 l1 I; w9 x% \ h
, W4 u, V+ O1 _' _2 L# S& m. G G
Q5:=QuadraticField(-50) ;: }5 e5 b9 J# _* u9 }) P
Q5;% S; J1 @: i; O9 P
! @5 N) q9 G6 |4 w2 JQ<w> :=PolynomialRing(Q5);Q; & e7 w! z/ F+ B' u* [- p, {+ zEquationOrder(Q5); 3 K9 N: O+ b/ W+ xM:=MaximalOrder(Q5) ;+ k2 m% E7 b8 L9 x7 q7 }
M;0 I$ s5 e9 j# x4 n- B, S
NumberField(M); ; ?# T0 T0 a/ _8 w, i3 a6 k' AS1:=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;- R3 c- |* S5 G, {1 i
IsQuadratic(Q5); 4 @5 l$ e" S) }IsQuadratic(S1);3 s5 n% F% T+ f# L' c2 v }0 r; E# ^
IsQuadratic(S4); # @! t& f4 S% vIsQuadratic(S25);$ I8 c0 i q& S* r2 H
IsQuadratic(S625888888); * P L' x0 A) O2 Y/ VFactorization(w^2+50); # H6 P+ [6 R) u1 Y# f# b' V
Discriminant(Q5) ;$ d- I8 Q4 T3 [* y4 p
FundamentalUnit(Q5) ;* X% S$ D/ N8 Y: ]9 x) U1 _
FundamentalUnit(M);, s0 c8 P2 {1 s
Conductor(Q5) ;1 |8 v; l6 f; c! ^: b/ G
' e1 L. ^- @ NName(M, -50); 6 a- @$ k! O5 pConductor(M); % i$ i. f( N9 N9 R& xClassGroup(Q5) ; ; a+ X5 Y- S5 `4 ~" Y- EClassGroup(M);+ {, t! s7 A+ z5 F
ClassNumber(Q5) ; % l0 ^- s J8 R b/ ]! X+ UClassNumber(M) ; 2 U& `' ~7 X7 f' ]PicardGroup(M) ; 2 B* Y, |; A4 p0 }8 [% k2 q. kPicardNumber(M) ; 7 {! W' X. a+ @- N8 q5 p# o9 V* F& ~4 Y P! _4 U2 }% ~4 f! p( _
QuadraticClassGroupTwoPart(Q5);2 H: a7 j' a: v6 w2 T/ Y
QuadraticClassGroupTwoPart(M);' r# k2 e$ a( c* Y/ P
NormEquation(Q5, -50) ;0 q& `& _) J( n9 ?% A
NormEquation(M, -50) ;8 A2 v) Y! E4 j6 A
) Y8 ]! J" @% ]) ^7 K2 P9 }7 tQuadratic Field with defining polynomial $.1^2 + 2 over the Rational Field 9 |# k2 x, f. `' q L w/ |Univariate Polynomial Ring in w over Q5 ( a/ p6 E2 Z7 `2 A' X/ E A5 o) HEquation Order of conductor 1 in Q5 - [7 u" a+ P v. \* e$ JMaximal Equation Order of Q5# s1 M/ r9 `% }6 [- L8 R$ v, @9 n
Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field ! L. p! q) { L$ c& B0 z/ p. e POrder of conductor 625888888 in Q51 c9 e3 G! r0 E8 U3 l
true Quadratic Field with defining polynomial $.1^2 + 2 over the Rational Field 6 j; s7 E9 i% `1 S! h8 v" jtrue Maximal Equation Order of Q5/ A% _! k. Z' Z8 [0 s' p
true Order of conductor 1 in Q5 3 ? b8 m) ^6 V: E/ Rtrue Order of conductor 1 in Q5' J, w+ u7 ^5 P! @( ]
true Order of conductor 1 in Q52 p J" Z, a1 |1 R& l4 @
[% M+ l) h1 t5 s1 r5 c4 Y+ T
<w - 5*Q5.1, 1>, / H' [8 s& |+ u+ ?) u9 H F ^ <w + 5*Q5.1, 1> 5 v) Z' g; y, C) ^$ {] * X/ I/ A6 I7 }7 k-83 q( {( t1 f( w2 Z. w: }
. Z+ V5 G# n' D& b3 q
>> FundamentalUnit(Q5) ;$ q! U: j/ p$ F' \! w
^& W# q1 {0 e$ u
Runtime error in 'FundamentalUnit': Field must have positive discriminant 2 F& u0 G3 `9 l( M X6 N: r9 p6 o) X" B# p8 _9 n $ Z+ r+ m7 n( W% ^>> FundamentalUnit(M); - ?. W: z/ y, e7 v ^ . O" [7 E4 X: _6 P4 i! _* K) pRuntime error in 'FundamentalUnit': Field must have positive discriminant 7 k9 B5 v2 G9 W' Y0 U $ u5 A `9 O6 H, v! x8( {4 {! k/ q* J/ c4 Y% R
* \% I3 T( g/ t' a' M. f>> Name(M, -50); & t p' Z. g* r4 f6 p+ j ^& j$ \+ G) Q9 K; S0 @: z0 i. t8 [
Runtime error in 'Name': Argument 2 (-50) should be in the range [1 .. 1]! w4 U% F3 X0 k! h+ ~
/ n+ |& N! B5 R! l; d* P* b1 v7 c; q- S1 P1 DAbelian Group of order 1$ f& }6 A% s4 f, \+ y" `3 v& |5 z
Mapping from: Abelian Group of order 1 to Set of ideals of M8 W B8 w2 w9 S% v5 s
Abelian Group of order 1 |2 i/ a9 X/ H6 SMapping from: Abelian Group of order 1 to Set of ideals of M# Z3 h6 c N+ i
1 , `: F7 v( i/ b3 p1 , Y+ l; O( s. v4 ?" q3 f" VAbelian Group of order 15 d0 ~7 R' z, K/ f% p& b6 t
Mapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no 9 z6 U0 B8 N, N @2 Binverse]: D; X3 Y- y6 U3 O' y: c* y( X) w, e
10 m; u/ t* K9 c
Abelian Group of order 1+ e- y" J! t8 J& H( e
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant . ^$ F! B! m$ c; _/ q-8 given by a rule [no inverse]2 [& h w* G4 [- U! V0 `+ [
Abelian Group of order 15 \- v0 a( | @; k; k
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant4 |! a; `1 i$ \! k/ P4 o
-8 given by a rule [no inverse]7 W0 G6 X1 u3 u; e# t
false$ w, O8 y% f( D/ ~; R* e) l3 j# L6 i( @
false # `) Y1 W' E* C9 u* |
看看-1.-3的两种： & O% A& i, v* i1 g; P1 u7 M 9 \+ W' n2 C0 b) G0 f; M0 nQ5:=QuadraticField(-1) ;5 F* L5 B6 R$ i1 h: \
Q5; 4 f4 t0 R) L: k \3 P , K" { d' f9 h6 eQ<w> :=PolynomialRing(Q5);Q; # N( K) c( ^* O! R0 R; n) a8 aEquationOrder(Q5);& w. s0 _8 x- }; \
M:=MaximalOrder(Q5) ; [2 _) a1 {+ |7 U& c8 Y9 L
M; ! k/ \/ e+ T, g8 b6 G7 _# mNumberField(M); I, T6 j; R: n# @1 c/ J. t7 W( e2 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; . D8 ?" N2 l! W9 D- h4 W- u1 xIsQuadratic(Q5);5 M7 t. b- v" U4 W; g: ^
IsQuadratic(S1);; w. \" U K! G1 V# I* {
IsQuadratic(S4); # [0 b( z' F' e; Y; Y3 LIsQuadratic(S25); + U9 _- _' j; Z9 a9 w' dIsQuadratic(S625888888);6 }- l4 X1 ]9 p* y; v$ U; r7 g
Factorization(w^2+1); 4 {% e0 U6 M1 i; S- c9 ?8 mDiscriminant(Q5) ; & V9 |2 t$ @/ f0 e4 e' lFundamentalUnit(Q5) ; * {+ M2 K8 }( w' }6 T" d% [; \FundamentalUnit(M);9 b( @1 w3 l5 O1 [' O/ y! G
Conductor(Q5) ;4 }4 ?& A% Q( |- g, [9 u4 L, Z- ~, F
/ p }* ^7 S+ i# y ^
Name(M, -1); , R' { r5 i! Y% j. @0 C" x2 uConductor(M);: s/ @. D3 I0 t% W2 o4 V o
ClassGroup(Q5) ; ( o& d2 y d V- P6 p% dClassGroup(M); 3 s5 ^, Y! K4 z. S* xClassNumber(Q5) ;' @9 Q# f/ h( N$ }2 j4 v. C
ClassNumber(M) ; " A! s9 }1 V9 k) R+ |PicardGroup(M) ; ) }* R+ ?$ t8 E4 s9 t7 }PicardNumber(M) ; * u6 i+ [5 y. U! J, n* o. W# B; v" R" f# h
QuadraticClassGroupTwoPart(Q5);( T q2 g/ f. j" O- M( y1 `
QuadraticClassGroupTwoPart(M); ( g8 Z, G: k$ m3 }3 rNormEquation(Q5, -1) ; ; k T' W9 e( C7 bNormEquation(M, -1) ;/ {; w1 ~; L( m. B2 K" y+ H6 E
1 k7 p7 H' y: W! D7 q- C
Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field- M; {2 r }5 R- |
Univariate Polynomial Ring in w over Q57 ]' S" K" ]2 C( ^
Equation Order of conductor 1 in Q5 8 J' v3 _/ j! P D5 `9 W8 x/ CMaximal Equation Order of Q5; t6 t, u. ]2 E1 D0 w. {
Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field1 ?8 T6 ]) W4 o! X) {$ S( s
Order of conductor 625888888 in Q5& }) y: j8 a6 P" O5 A; o2 f2 x( r
true Quadratic Field with defining polynomial $.1^2 + 1 over the Rational Field k$ G& I S: C2 d' q
true Maximal Equation Order of Q5 8 u! S; `' |% g- ]4 j8 d# G" b. A) gtrue Order of conductor 1 in Q5( y: f6 O7 Y7 z R
true Order of conductor 1 in Q5 7 N, p& F! x4 Z! ]+ H! i" wtrue Order of conductor 1 in Q55 s7 n! ~* d- P& V) G5 R; ~3 p
[4 k) e4 l- e: k+ x b% H. g9 F! O
<w - Q5.1, 1>, 0 e+ b" V) v+ H <w + Q5.1, 1>" i# [' L$ G# E: ?# \
]9 k& Y' i5 Q E3 M7 U- O
-4 % o' ?" o; | B( f2 A& L ; D7 d; ] u6 `2 R% R4 c>> FundamentalUnit(Q5) ; : y1 F. X4 D; t: z) }% D p+ a+ Y ^$ ]# d7 ?9 n0 z
Runtime error in 'FundamentalUnit': Field must have positive discriminant# N1 Z: O# c7 r8 w! J: u
3 O e$ R! `9 A2 T' w5 c8 o% R a$ P- H+ ~& o+ g' R>> FundamentalUnit(M); + m2 ?* A! A S& c1 A; B ^ 5 s* `% {9 w( E9 X d7 p7 xRuntime error in 'FundamentalUnit': Field must have positive discriminant- H( |9 S! P8 B6 a8 ]* r4 z
/ p. Z) _ @, \4 J$ H3 b; ?: \6 V 7 V; O. e. z! C, X$ \>> Name(M, -1); , v1 L$ b5 l. d2 R+ W ^* [3 Y. u+ H5 k. P6 o' j2 c& r
Runtime error in 'Name': Argument 2 (-1) should be in the range [1 .. 1]4 x. }0 z7 P. A
1 B4 x3 R9 c% f& K1 v7 Z, K+ H) K1 W16 C2 F2 m" x, b- m7 j$ M3 c% K7 T
Abelian Group of order 16 U9 f- [% U2 d4 d$ o, m* l* a
Mapping from: Abelian Group of order 1 to Set of ideals of M2 H/ a& O2 J- Q& z$ O
Abelian Group of order 1 9 r1 _# L% _' F1 v3 H* [$ p' qMapping from: Abelian Group of order 1 to Set of ideals of M# X* `7 H1 W7 ^: k7 L$ Q |4 C
1! q! a l! f, d0 V2 Z/ D( A) C, F
14 n5 s; s7 N, @; J3 B4 V
Abelian Group of order 1 / T: j8 s3 e4 {* _Mapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no& Q$ L" W3 X8 y: {$ o9 A! `! A
inverse]2 D2 e2 U8 S2 a# r" W
1- {+ Y7 A7 L5 q# C" n. X
Abelian Group of order 1 ' e* S5 k( g5 Q- U1 i5 NMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant % J& ~+ y3 D4 e; d# y. s, A* n-4 given by a rule [no inverse] # z2 Q3 z& h* Y2 t4 |Abelian Group of order 1 : g/ n* g! [7 d6 eMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant8 h( t$ h, q; i- i4 g* F% p; i% ]" A
-4 given by a rule [no inverse]/ T8 I( M, w/ ~: m( i @
false 9 V& i# X* a/ H' ^2 G6 Afalse 2 z( a [/ o7 q8 z) v=============== ' e* ~1 m0 g" H P$ a# F, H7 B! e: L9 J6 U/ g
Q5:=QuadraticField(-3) ; / |% q( V9 T2 Y* M( fQ5; 7 C& N- w5 Z( U/ ^& E" b: o$ Y0 s 9 x1 N& f- v7 ^: c$ HQ<w> :=PolynomialRing(Q5);Q; - h6 ~( p) K5 K! QEquationOrder(Q5);+ R5 }* z: Z+ F# _! ^
M:=MaximalOrder(Q5) ;$ b! ~2 j& A) _0 {4 M* R. k# L
M; 0 J# W0 I7 |# `5 a8 ^NumberField(M);( m1 t* b+ e4 Y _) z! P+ Q
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; # G) z+ R9 J! l0 E6 EIsQuadratic(Q5);; Z1 f4 i! K# p
IsQuadratic(S1);: O; H4 x8 r" Q- k. X) f
IsQuadratic(S4);) s/ x) A+ @* I i4 @
IsQuadratic(S25);6 x9 S1 l, i. M/ ~: Q* b! \% ^7 u
IsQuadratic(S625888888);+ |& J0 L$ n( ]0 l+ Z
Factorization(w^2+3); $ m% B V* v9 b6 yDiscriminant(Q5) ; 2 l4 K! b4 \& [0 y1 N! X& m* xFundamentalUnit(Q5) ; v& i/ x) H$ N) d8 g
FundamentalUnit(M);' d' P H# g W
Conductor(Q5) ;4 v: E. i5 r+ F/ i3 J& {5 ^8 C, T
! K( R) s- Z. D5 o ]
Name(M, -3); 0 C9 D T( s# s- M q5 T5 a8 qConductor(M);0 @3 a! J2 V& O: m# z7 w0 O
ClassGroup(Q5) ; 6 S4 ^$ r) P5 ^& IClassGroup(M);0 Z1 V2 U" n: @1 F( r- j0 T1 m+ k3 s
ClassNumber(Q5) ;8 F- d0 z6 p( R' B! M9 Y
ClassNumber(M) ; - K. l7 z. a. [& D0 ]. x3 T/ mPicardGroup(M) ;3 L* s, c. K1 {1 a7 h
PicardNumber(M) ;, R' C, d1 `" d
( A: F4 t! o1 J$ Y7 f) fQuadraticClassGroupTwoPart(Q5);! m! n$ s8 Z8 d4 }- h9 y0 G
QuadraticClassGroupTwoPart(M);. {* [5 c1 [7 }; h/ M! `5 ^
NormEquation(Q5, -3) ;) l1 U- u8 l+ B7 O) M
NormEquation(M, -3) ; " j0 O$ @& j2 ?" M5 W 8 K9 q4 r' c6 {) C7 K3 p8 Q; MQuadratic Field with defining polynomial $.1^2 + 3 over the Rational Field7 W! Q4 h( u# w! K L2 ?) m9 s
Univariate Polynomial Ring in w over Q54 w `4 Z! q9 D
Equation Order of conductor 2 in Q5 : v' t/ [& n& IMaximal Order of Q5 # j2 L Y# i+ M rQuadratic Field with defining polynomial $.1^2 + 3 over the Rational Field# @; T, G3 f8 z: t4 g7 V, F
Order of conductor 625888888 in Q53 c( w& ^' }; Y3 y0 }
true Quadratic Field with defining polynomial $.1^2 + 3 over the Rational Field * ?! _; ^4 H" n6 w Ftrue Maximal Order of Q5 / h1 G* I$ W3 V# |- e: W! R8 Itrue Order of conductor 16 in Q5 5 f' f# f* c8 z" C1 L. |% Y' J: y: Mtrue Order of conductor 625 in Q5: X b" o3 p n! i0 Q
true Order of conductor 391736900121876544 in Q5+ R6 Y7 t% }3 f
[ " n. Y3 n) u5 U' f& t8 \ <w - Q5.1, 1>, 2 q' u" w# {$ F+ a! b, p <w + Q5.1, 1>6 a0 L% w4 f( y) W
] 6 `3 l2 R1 Q3 Q1 N0 i# b* u-3: y9 f, {& P( z4 s- `+ M
9 N4 d: S) E( T
>> FundamentalUnit(Q5) ; " @8 Z, J) c+ a2 {7 E ^' r; w1 H A* y2 a. x. x. ~- \
Runtime error in 'FundamentalUnit': Field must have positive discriminant( J2 e6 N I, w
1 W& X( c$ d1 b0 B6 W$ ^ H l2 T0 n) \ M3 ]) _
>> FundamentalUnit(M); ; f$ i' o4 [) n4 a/ j# V1 i% _ ^ + k/ u' R7 C: s0 w# m$ S* `7 ]Runtime error in 'FundamentalUnit': Field must have positive discriminant ; I! O4 @9 U, |+ U ! E* H( ^0 C% }2 g* Z3 7 G, U, L, Q% A) r1 ` N, L& K$ y6 t6 A |3 y# r& T
>> Name(M, -3); # Y% I6 l' d4 J/ k7 i' z. ? ^ 1 z- D" m9 l* i6 ARuntime error in 'Name': Argument 2 (-3) should be in the range [1 .. 1], Z! i) o/ T6 D. O1 \9 Y
+ ~. c. ?4 X( J! o8 `
1/ u C# i! W( v
Abelian Group of order 19 x( r4 V! K) ^
Mapping from: Abelian Group of order 1 to Set of ideals of M 6 L7 N, J' K! }$ V5 IAbelian Group of order 1$ m* ^6 k6 `' G( V& Z# C
Mapping from: Abelian Group of order 1 to Set of ideals of M : l. k, s h1 \, \( O2 J9 E2 x. A1 0 {/ y8 D7 L- H) d1 u1 * p: D5 U3 X5 H( |Abelian Group of order 10 ~3 X8 r9 u, F* i# ~+ x
Mapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no& o% |+ z+ {- a. @. t% v* X
inverse] _. H, ]3 `* x
1 ( K% r% O& K2 oAbelian Group of order 1 0 k) g6 M8 D O$ w- l' AMapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant% \$ F x# k+ o: ?% d1 I ?
-3 given by a rule [no inverse]* N4 U3 d/ W% Z/ ~" D6 E
Abelian Group of order 10 @1 n8 C- ~3 a4 x) a) I
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant8 c5 x& q: ?5 g" O
-3 given by a rule [no inverse] O' s7 W& D- n, G- @# Y' K7 d
false: {% C- Y. F E! }6 |
false
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发表于 2012-1-4 17:41
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