% ?1 C' D1 n/ A* o/ DQ5:=QuadraticField(5) ;7 I4 w }! k; J+ }7 M9 T
Q5; ( {/ E( @" d; M% UQ<w> :=PolynomialRing(Q5);Q;7 {1 A4 D0 ?/ A2 M0 X
V* q/ H% k- z; \& B0 M
EquationOrder(Q5);3 g3 m+ Z3 y' N9 b9 }1 k
M:=MaximalOrder(Q5) ;* b8 U0 F% X4 a& N
M;- m0 _0 I- B8 A4 m: g( \ K
NumberField(M); 2 m; v1 N- R/ fS1:=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+ u$ S2 R2 [
IsQuadratic(Q5);IsQuadratic(S1);IsQuadratic(S4);IsQuadratic(S25);IsQuadratic(S625888888);3 L9 ^& a5 V! m" g; u0 l. I9 Z
Factorization(w^2-3); , l1 T3 C* p& v% @$ `, o9 @Discriminant(Q5) ;& _. Q' c" D+ z
FundamentalUnit(Q5) ;! h& H; L! M$ x* F
FundamentalUnit(M);8 f- G' r/ L: M4 o. X) O
Conductor(Q5) ;+ k; r3 k8 a$ X8 k# e3 S6 a
Name(Q5, 1);5 I- m; p, R1 N
Name(M, 1); . B! ~0 R" w3 L6 U! b2 nConductor(M);* i7 H1 ?! y5 u8 }' H: f6 f5 x
ClassGroup(Q5) ; ! x4 x2 h* |# m3 e# x) Y+ U$ g# {ClassGroup(M);4 u4 y% I f5 Q) F# S) ?4 R
ClassNumber(Q5) ;( S1 w3 C, O \
ClassNumber(M) ; 9 J& f/ s% {2 n$ T* ? 8 [1 n% k$ I! q/ q! [+ P& N6 wPicardGroup(M) ;' ~9 \; A! [6 }) S+ a
PicardNumber(M) ;' D ] T, M3 y' I, v) U8 w Q
- \$ }3 }1 \. g& N+ N
# c, r- d3 p! D1 _
QuadraticClassGroupTwoPart(Q5);+ p+ x7 a& i0 |/ n0 @+ O) m8 O- L
QuadraticClassGroupTwoPart(M);( j0 C' {5 l) \1 u6 h/ Q. _; m
! l9 D0 y8 R0 q5 z
. s: ^! M$ ^6 M3 V sNormEquation(Q5, 5) ; & W8 H3 ^* x( f& T \$ l0 u0 cNormEquation(M, 5) ; & w- H+ b/ E& A% F7 g) e. k . _ f+ L( V; w- j8 u' v- J ! i- k- ^: i. e7 l( H$ OQuadratic Field with defining polynomial $.1^2 - 5 over the Rational Field 0 [+ P: h9 u# ^" D- ~Univariate Polynomial Ring in w over Q5) T! F/ \/ T( X. n
Equation Order of conductor 2 in Q50 R) e" c! i6 J" n
Maximal Order of Q5 / i# e4 C' z9 PQuadratic Field with defining polynomial $.1^2 - 5 over the Rational Field1 Q6 W% _8 t" i1 A1 R6 A/ }/ Y* |
Order of conductor 625888888 in Q5, C5 A2 W/ |* r1 u9 l+ @; F9 v
true Quadratic Field with defining polynomial $.1^2 - 5 over the Rational Field+ R9 T/ G6 q: X; f }
true Maximal Order of Q5 : Q! X$ J' c" Z7 F: x; vtrue Order of conductor 16 in Q5 ) C# [# D) E2 x# d: Etrue Order of conductor 625 in Q5# F, c3 d. ]# h# T9 i
true Order of conductor 391736900121876544 in Q5 , r: o: `0 C- H% N q2 Z& v[1 J8 x" C4 S2 W) w0 m# r, N, m
<w^2 - 3, 1>* ^2 m( @! m+ u$ S9 G2 o
] " @% w3 r V. q* }: d' Y) I1 |5 1 _% ]5 k+ `6 i1/2*(-Q5.1 + 1) T( l* ]6 a8 R: P# B& U6 ~. U6 U
-$.2 + 1+ T$ M6 r2 {. N
5$ I& v4 N! I! T+ I( [
Q5.1 1 n% D7 A, x& y& [* J1 J$.2 ( \0 b$ u0 |7 W0 M8 X19 U% o$ i$ L0 q) K& x/ b. k5 i5 I# L
Abelian Group of order 1, b3 a8 m8 s) J" @: i3 y
Mapping from: Abelian Group of order 1 to Set of ideals of M " T/ d9 n( k5 T, u. k( VAbelian Group of order 1 - x9 ], a& G) x2 D, {Mapping from: Abelian Group of order 1 to Set of ideals of M ; B0 j/ G* O, Y" V5 }9 V9 l17 N# W) ?! l3 R
18 w; e7 G) e- o1 S+ I
Abelian Group of order 1 1 J% @1 ~8 _4 Y4 b+ fMapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no; S7 N* B, Y; H( {3 v
inverse] 1 y- [0 @8 N+ x; I1 4 \6 x. G. I. b& PAbelian Group of order 1- G# M3 U: r8 d1 H5 Q' ?5 R( Z) E v6 G$ w
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant# P* P4 b: Q5 L5 z& d
5 given by a rule [no inverse]8 I* M. q& x/ S {# M8 H( ^
Abelian Group of order 1* V3 B1 R' c( Y3 O4 b; R2 j
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant ; {+ j3 e8 T# y- P5 given by a rule [no inverse]1 X$ K! f; o6 [1 X# ~
true [ 1/2*(Q5.1 + 5) ] ' Y& h9 o# @, \true [ -2*$.2 + 1 ] $ v9 W4 ]- W" J* c + _5 T. Y0 X7 ^3 F0 z0 d1 E9 z6 _) Q9 J- k" ?8 H
" Q! j! | i) o8 L . p6 Z7 x4 U* _ 7 }& Y, M+ F' p& u- _9 s3 q! C* {% D1 r, }$ g
$ q$ u0 d; \7 j% _) V" q! j 1 z+ f4 J0 L$ y: j k5 I; A* ?0 m 6 F0 l: u! i1 y0 m& T/ S - }: s( h% N: K7 e4 _+ \ $ {7 \/ T0 ?- c) O============== ! E: n5 U9 A! Y7 A3 h9 y( J* s 3 T$ B$ ?( A3 U, B- |+ oQ5:=QuadraticField(50) ;6 O) t1 _6 \1 v$ e% V" w
Q5;. s& L8 o3 ^: c7 U1 J
1 J/ H( N4 m* z1 p- Q6 h
Q<w> :=PolynomialRing(Q5);Q; + m* i! I' }8 ?) REquationOrder(Q5);# ~/ \! y% f. W
M:=MaximalOrder(Q5) ;, s' u5 c1 v) ?1 U* n) G' f
M;9 R0 U h: U- W+ F' u# M) ~
NumberField(M); / }! L* U* T& f. `4 C+ Y* RS1:=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; + Y2 D/ F" n/ e* lIsQuadratic(Q5);% P0 i; u* D8 q' r9 q
IsQuadratic(S1); 4 p. c2 m, S8 N5 @IsQuadratic(S4); ' h4 R7 @- }0 t g! N) GIsQuadratic(S25);" _, v- d' c2 n7 J
IsQuadratic(S625888888);6 l7 F7 Y! e9 c* Z
Factorization(w^2-50); $ {2 N6 R! a# l. @$ A( h% c
Discriminant(Q5) ;' q+ _ _# S7 A0 `! m' M0 k
FundamentalUnit(Q5) ;+ ]2 i0 b5 Z. ?$ n
FundamentalUnit(M); & L" f6 ?! [; t( r% EConductor(Q5) ; 9 @4 x( i$ \ |+ w: L2 A, N2 i K # c' M" |" @# z% M7 n4 \! T' [+ P5 u- ]! \Name(M, 50);: p% q/ x& U+ S5 W' [
Conductor(M); ! f0 p6 X" `" u6 J$ K% @/ iClassGroup(Q5) ; 3 s: r/ N1 j7 n* bClassGroup(M); c2 b# Q: Q, l1 ]2 M
ClassNumber(Q5) ; F4 b( x1 B; j( V' J, E
ClassNumber(M) ;2 M/ J9 h7 q, L2 f
PicardGroup(M) ; $ e2 K$ O5 R. m3 z; x3 X2 {PicardNumber(M) ;% I" a2 D6 _ l
( n" }$ X5 r1 |. PQuadraticClassGroupTwoPart(Q5);$ y' a! ?; n2 I q/ j$ A
QuadraticClassGroupTwoPart(M); * c3 r) y, n; z: q9 qNormEquation(Q5, 50) ; 7 ~) t) q" q& WNormEquation(M, 50) ; 0 K2 I y7 ?; H: o1 N; q$ Q5 l2 `5 Y3 n9 K6 G$ T
Quadratic Field with defining polynomial $.1^2 - 2 over the Rational Field 9 m5 H& I V/ G% J( J! V$ hUnivariate Polynomial Ring in w over Q5& i! q, z% G+ Y
Equation Order of conductor 1 in Q5 0 \" e, C& C: {, t. yMaximal Equation Order of Q5 F/ x( k" _6 w! |+ ]& S& ZQuadratic Field with defining polynomial $.1^2 - 2 over the Rational Field7 e/ \, i/ F l; x& O
Order of conductor 625888888 in Q53 I) E$ B5 g( e
true Quadratic Field with defining polynomial $.1^2 - 2 over the Rational Field + D1 M5 j" M6 \( R3 S) q1 n: G! j" rtrue Maximal Equation Order of Q5 . \1 [) w( D1 G: b, H2 |9 Itrue Order of conductor 1 in Q5 ! ?2 n' A! X# O% qtrue Order of conductor 1 in Q5 0 `' J3 q) ]$ i; A7 @& w7 q8 w% E- otrue Order of conductor 1 in Q54 S0 f( k" W4 k! J8 q
[5 D y1 b' ]) y5 ]6 s7 v
<w - 5*Q5.1, 1>, 4 \/ j) S; r+ X" U7 ~3 C <w + 5*Q5.1, 1>+ `1 q5 E7 e) g9 n+ ^& H
] 1 F' _" V8 p8 @$ H, E/ J1 L85 G$ w/ S: q% a! G2 ^. e m
Q5.1 + 1 : j+ q" C% c% T. Y: }9 j9 w( F$.2 + 1 - u- X+ `1 V. Z; P; c$ ^83 t: _ T! @5 w( r
. A8 W4 Y' X8 ^! t) `$ P>> Name(M, 50); ! }$ h, N+ b& Z) \. q ^- ]! D1 P& ^" Q0 F+ ?$ v' _* b6 u" n
Runtime error in 'Name': Argument 2 (50) should be in the range [1 .. 1]2 C$ s. E9 Y4 D, B! j) b$ P- J
0 \" k# o8 R2 m5 V- j1 " t2 S' `5 E3 P2 vAbelian Group of order 1! `; m& Q% J8 d8 f4 J
Mapping from: Abelian Group of order 1 to Set of ideals of M# \2 X4 d: p8 y, j4 F7 D3 F9 e
Abelian Group of order 1 / {( q3 W/ t ^) E% O% V+ `Mapping from: Abelian Group of order 1 to Set of ideals of M) O* A, U+ k$ r1 V
1; U+ h9 F. ~3 f. Z
17 t/ k2 P1 g2 ?8 R6 r& C
Abelian Group of order 1 2 e$ l, q7 ]' M5 `+ K0 HMapping from: Abelian Group of order 1 to Set of ideals of M given by a rule [no1 g* h9 G( N& T& X& ?( p
inverse]9 h, N: a( [; n8 E, W3 u
1 6 j" M. {3 n% NAbelian Group of order 17 K b% r' v0 h3 [
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant 3 T2 J; U9 g/ ]* m* {8 given by a rule [no inverse]7 l6 _- v: |: O U4 D0 A
Abelian Group of order 1) C3 ?! E8 l0 x. P$ M, e4 S6 L$ G
Mapping from: Abelian Group of order 1 to Binary quadratic forms of discriminant; H" E6 o( P# Y+ N9 Z/ a
8 given by a rule [no inverse] - B' H1 H& ?8 w0 a' `4 e2 qtrue [ 5*Q5.1 + 10 ]! j2 s( e( z" f: u2 L# b, f5 l
true [ -5*$.2 ]
IP卡
狗仔卡
发表于 2012-1-4 14:05
转播
淘帖
分享
收藏
支持
反对
微信
提升卡
置顶卡
沉默卡
喧嚣卡
变色卡
抢沙发
显身卡
