一些初等函数：

lilianjie

:=IntegerRing() ;Z;
n := -1666666666234567890;
> n;
3 G: Y  {& x# f5 f. {4 Y; \
1 g/ T7 \7 Q8 M0 ]> n:Hex;                           转16
2 k* }# x/ m. N# d0 I3 \IntegerToString(n, 2);        转2
IntegerToString(n, 10);       转10
IntegerToString(n, 16);        转16
IntegerToString(n, 36);         转36IntegerToString(n) ;
& I; ?9 r7 H4 y+ y: ?0 H1 SIntegerToString(-0x17213080A7E55CD2);转串Zero(Z);
Identity(Z);                  
Representative(Z);         环代表元
1 [' g# _4 d; n4 r5 D9 k+ nEltseq(n);                        取整
Eltseq(-0x17213080A7E55CD2) ;Denominator(n);Denominator(12/13);Denominator(222222/111);
9 a) i2 T6 k, p" ^0 m: ~( b2 ^
m := elt< Z |  -0x17213080A7E55CD2>;m;         在虚实2次域中进制砖换不变
$ i& c, t% l, F5 t& [. a0 R$ {* fk := Z ! elt< QuadraticField(3) | -1666666666234567890, 0>;
3 m3 B5 F+ Q5 x7 V  |> k;
; k7 u* ]$ I8 \n eq k;
kk := Z ! elt< QuadraticField(3) | -0x17213080A7E55CD2, 0>;
> kk;
- x" m5 q! T( s* c# n$ tkk eq k;

! l8 }5 J! @5 Y5 @! i+ xk := Z ! elt< QuadraticField(13) | -1666666666234567890, 0>;
( N6 B8 w* Q  z+ E4 [2 S, j+ h> k;
n eq k;
& y( w/ \/ U! g8 {$ {kk := Z ! elt< QuadraticField(13) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;

Eltseq(kk) ;Eltseq(-1/14);
6 X4 [3 H) |' Y% U- [5 d! u! Z2 J
4 F6 h* S. m8 p- q, C/ S
, V7 V1 C( T" v5 B+ q% {5 X3 Q6 N7 a

k := Z ! elt< QuadraticField(-3) | -1666666666234567890, 0>;
8 K+ e9 ~3 v! Y- A( b" `+ o. h> k;
n eq k;
kk := Z ! elt< QuadraticField(-3) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;

, r5 Q4 p8 ^. Ck := Z ! elt< QuadraticField(-13) | -1666666666234567890, 0>;
> k;
  S  U  R$ J! L$ E. On eq k;
kk := Z ! elt< QuadraticField(-13) | -0x17213080A7E55CD2, 0>;
> kk;
! m) j/ n+ V+ o" j& h; Ykk eq k;

Eltseq(kk) ;Eltseq(-1/14);
+ K1 [# }2 ~& b4 s9 G! |. t

& W  T; v: h% Y! B7 X! p

; L. ?9 e! C3 p% ?5 o


2 _7 j- @0 N# V6 ?% P
6 A- _! p! D) v  _6 y3 E; _: D; T

=============
3 X7 q, N% P4 q* ]7 ^



9 ]4 y  M. U9 J' [) iInteger Ring
-1666666666234567890
. c5 `$ K0 d' z) ~2 E2 ~' @$ R6 v& V-0x17213080A7E55CD2
-1011100100001001100001000000010100111111001010101110011010010
-1666666666234567890
-17213080A7E55CD2
-CNUO0WGPY9CI
-1666666666234567890
-1666666666234567890
0
; E  C) R/ r8 z/ W. t1 i7 ~0 D1
0
9 _& b/ S) o3 G3 `8 a( j' Z[ -1666666666234567890 ]
/ s% ]; d0 T( ^# q& y: J[ -1666666666234567890 ]
1
& q4 Q5 ^3 O% J4 B: ]( F/ h13
: q5 H  c+ |) ]# D: p1
5 x) A2 x- q: f0 z: c) {; z" g
-1666666666234567890
3 r; `, Z4 g3 {# Htrue
-1666666666234567890
. [, M  s9 y* j8 ]& \true
-1666666666234567890
true
-1666666666234567890
* L$ i" z! A5 l# O% ]true
* ~( }* p( g* g, Y7 Z4 p( B[ -1666666666234567890 ]
: F8 o$ d$ f; m* {9 V[ -1/14 ]

# J8 N  H5 J" ?: O


4 L8 {+ V% A" L/ T& j
* f6 Y+ ?6 K4 m% Z- P; Q

  E; O" M2 M4 }7 a-1666666666234567890
-1666666666234567890
" V4 R# R3 r8 d9 B* n: O' k' dtrue
-1666666666234567890
true
6 P" `2 p5 ]6 c  Q9 ^-1666666666234567890
$ S  ^9 l$ p" @$ l: Utrue
" f2 L" U5 J( b" N-1666666666234567890
true
[ -1666666666234567890 ]
/ W7 m; p0 J6 [8 K: n  a5 E4 c[ -1/14 ]

) ~$ W# G6 X  Q

lilianjie1

Z:=IntegerRing() ;Z;   
, E. i4 ?) G5 g* Q% v4 z; }; mI12:=ideal< Z | 13 >;
I12;
ZZ:=IntegerRing(60) ;ZZ;   
IZZ15:=ideal< ZZ | 31 >;
# p" }) q% h5 ]1 ?1 YIZZ15;
$ a# L2 x! O9 B9 v/ G6 O+ fResidueClassField(I12);
ResidueClassField(IZZ15);环和极大理想的商构成域---剩余类域，剩余类环中的素数都是极大理想
loc< Z | 19> ;
loc< Z | 17> ;
loc< Z | 131> ;局部化：一个素理想到原环元素的映射
ext< Z | > ;超越扩张到一元多项式
8 w9 T4 r2 W% X( M$ B& q1 ]ext< ZZ | > ;
' e/ i- w& F$ U% h0 O4 L3 o
0 Y9 W2 w6 W, v: m  r6 Y6 ?  text< Z, 2 | > ;超越扩张到多元多项式

ext< Z, 3 | > Completion(Z, I12) ;


comp<Z |I12  >;
    素理想零理想完备化，和P进环联系起来
Completion(Z, 0) ;
comp<Z |0  >;

Integer Ring
Ideal of Integer Ring generated by 13
5 A8 d! W2 W# E- \Residue class ring of integers modulo 60
* ]  g* s3 T. u2 FResidue class ring of integers modulo 60
: x3 T# c- S+ V- a* p6 {6 DFinite field of size 13
Mapping from: RngInt: Z to GF(13)
% ^; |8 u& m+ z6 r7 b) gmodulo 13
8 c7 T) W& [/ [/ w$ N4 U6 G
>> ResidueClassField(IZZ15);
                    ^
% }9 O* f3 q. O8 N- ~Runtime error in 'ResidueClassField': Bad argument types
+ b3 U. _8 L$ W& L+ ZArgument types given: RngIntRes

Valuation ring of Rational Field with generator 19
' C3 \% O0 W: ZMapping from: RngInt: Z to Valuation ring of Rational Field with generator 19
/ k# s: x8 ?: w& U4 C4 W4 FValuation ring of Rational Field with generator 17
Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 17
Valuation ring of Rational Field with generator 131
% }, _# W  g3 V- D/ QMapping from: RngInt: Z to Valuation ring of Rational Field with generator 131
Univariate Polynomial Ring over Integer Ring
Univariate Polynomial Ring over IntegerRing(60)

>> ext< Z, 2 | > ;
$ s" X2 s* n. h& c      ^
# b$ ?- A$ z' r& m& A, tRuntime error: This constructer is no longer supported

1 X0 g- ?- a3 i
>> ext< Z, 3 | >
* p: F! g' |4 K( O      ^
Runtime error: This constructer is no longer supported
5 l6 c2 F* j6 z- c1 j/ Z7 \' e  }/ T
13-adic ring
! u/ b: ~1 \" t% K* V% v3 FMapping from: RngInt: Z to pAdicRing(13)

( J5 C( {. `# Z' c0 v. M' G3 }2 qCompletion(
    Z: Integer Ring,
; z& F! g" a; A- K7 D    P: Ideal of Integer Ring generated by 0
1 Z9 F5 L' k; a1 @, U

lilianjie1

  j- m, a! I" F
Z:=IntegerRing() ;Z;   
3 l1 h$ Y" f) ?5 z& ~! L$ G0 _I12:=ideal< Z | 12 >;
4 R0 B2 a, |% a2 N- g* C) {I12;
+ ~( y" }) }+ p* ~' M3 b% N$ ^ZZ:=IntegerRing(15) ;ZZ;   
IZZ15:=ideal< Z | 15 >;
IZZ15;
3 z# h. y( l+ ^, |$ j5 ZI12 eq IZZ15;
! B1 {* I5 f" R6 [" C4 b5 AQ1:=quo< Z | 12 >;Q1;
ZZZ:=IntegerRing(5) ;ZZ;   
IZZZ5:=ideal< Z | 5 >;
IZZZ5;
5 L! n1 V, W9 F* ^( c! V0 K
& o8 N+ K# ]. HI12 *  IZZ15;            理想和/积/并/交，
$ m# J" p+ u7 j' t6 H理想和是理想对应两（可多个）元素加，
理想积是两理想（可多个）对应元素积，
% B/ d1 a( o2 ^2 \- X4 v  y9 y理想并就两（可多个）理想元素并，就不一定还是理想，
8 ?& m: o, p+ h) q/ y) C2 s理想交是理想（可多个）元素交，理想交一定还是理想，

理想积是理想交的真子集，极大理想交是理想------J根
理想商就理想间同态：是必须能整除
I12 +  IZZ15;
I12 meet  IZZ15;
# ]$ {  |  _6 H' C
I12 * IZZZ5;
( h8 }5 o* Y6 e* fI12 + IZZZ5;
0 H# d. P& t  G. U) ~. hI12 meet IZZZ5;
I12 / IZZZ5;
IZZZ5/ I12 ;
3 ?2 A% f$ g( @9 i+ BZ * IZZZ5;
: |) Z5 H7 n* L& P) y0 HI12 + IZZZ5;
IZZ15 meet IZZZ5;
+ `: @3 G! h0 |/ W7 b2 VIZZ15 / IZZZ5;Z meet IZZZ5;
- k% o9 B, b/ w# UI12 meet IZZZ5;
: }/ j& n- r. {IZZ15 meet IZZZ5;
; {- C2 f! t* v5 B7 W9 O0 }9 ~; PIZZ15 / IZZZ5;
8 s0 L2 j, j+ N) |
0 x* R5 P9 Q, G! x6 w- `8 b; D! oI12  subset  IZZZ5;运算后的各种理想互相是否包含IZZ15  subset   IZZZ5;
IZZ15 subset IZZZ5;
) y# ?; y7 Z5 U9 W$ @IZZZ5 subset IZZ15;
Integer Ring
Ideal of Integer Ring generated by 12
Residue class ring of integers modulo 15
Ideal of Integer Ring generated by 15
( g" Z* `) O) \0 |" O8 {7 `false
! K8 H6 D' r3 s* f$ ]* MResidue class ring of integers modulo 12
Residue class ring of integers modulo 15
9 @- Q) W& ^7 d1 I) Y6 oIdeal of Integer Ring generated by 5
. `5 b& A* d& ~: n) s' |6 ^$ FIdeal of Integer Ring generated by 180
Ideal of Integer Ring generated by 3
0 A8 n( Z4 K* {( ~4 VIdeal of Integer Ring generated by 60
Ideal of Integer Ring generated by 60
% Q0 Q/ L! P. w0 |* b4 L. G' FInteger Ring
Ideal of Integer Ring generated by 60

>> I12 / IZZZ5;
       ^
$ ~2 ?( c; f2 t. ~4 ]Runtime error in '/': Argument 2 must divide argument 1.


5 o& ^' f9 ?3 f$ E- g>> IZZZ5/ I12 ;
        ^
Runtime error in '/': Argument 2 must divide argument 1.

Ideal of Integer Ring generated by 5
Integer Ring
Ideal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
3 @/ P9 e- T7 v5 A; @4 |0 sMapping from: Ideal of Integer Ring generated by 3 to RngInt: Z
Ideal of Integer Ring generated by 5
Ideal of Integer Ring generated by 60
3 `# j( g) u/ M; y* mIdeal of Integer Ring generated by 15
* o( ~$ P! t% D& H* {; T" zIdeal of Integer Ring generated by 3
Mapping from: Ideal of Integer Ring generated by 3 to RngInt: Z

false
2 F8 g) T, g; z5 H1 }" m- itrue
8 `- g0 w( U8 e+ I6 c0 E7 etrue
false

lilianjie

. l/ _/ B5 k, U! a7 w
$ o4 _9 D9 c7 s/ d% OZ:=IntegerRing() ;Z;   
4 C2 \9 V  K# {) \7 m7 j
R:=IntegerRing(12) ;R;   
/ n/ }- _0 q4 S8 Z5 `S:=IntegerRing(13) ;S;   
/ ]3 v8 _, p9 W
8 v7 C" i2 ]' m8 l- Y2 Z
) s& M0 a0 v+ L0 _5 oPrimeRing(R) ;
! U& r0 O& ?" z2 @/ s, g/ |Centre(R) ;
: x% b: `" X6 ]$ D  A* U: A& ~
- Y6 C+ E) b! U0 UCharacteristic(R) ;
7 k8 ?1 Q$ {7 ~" t  a2 ^2 a; t# R ;阶----元素数
IsPID(R) ;非素数不是整环不是极大理想整环，但都有极大理想公因子IsDomain(R) ;
/ i- o7 i: u9 g3 e  f' a% u; vHas**(R) ;

3 ]( E& ^: o$ d& V) {& AIsPID(S) ;
IsDomain(S) ;
6 [$ C8 u0 [# O" {4 E) T! |) M1 OHas**(S) ;
8 R$ ~1 a6 J! A9 c' r/ n" ~R eq S ;
; _- }( ^& ^8 _: e# K- ]. q4 SR ne S ;
) K0 b4 F+ X8 U3 G/ d
Parent(R!123) arent(S!123) ;
Category(R!234) ;Category(S!234) ;

; M3 k+ E3 G, [4 |; xa:=Random(R) ;a;b:=Random(S) ;b;
Representative(R) ;
! ~; a! k& M+ N6 N+ Z$ C% VRepresentative(S) ;

. `# Z* q) k4 l- m/ ^- t. C# \(R!a) in R ;
4 P  Q+ A2 {% h+ i  V(S!b) notin S ;
IsUnit(a) ;                是单位吗
4 Q: j( E. S9 @" L& X  _0 u: BIsIdempotent(a) ;是幂等元吗
2 f7 t0 _! t/ s+ WIsNilpotent(b) ;是幂零元吗
# N, c. P% K- `IsZeroDivisor(a) ;可除零吗
IsIrreducible(Z!b) ; 可约吗IsPrime(Z!a) ;
* F7 `: K! B" ~* e
& J( V9 J4 ~  j/ wZ!a gt Z!b ;
Z!a ge Z!b ;
; g# x& k9 D- N8 A) b3 a- x/ jZ!a lt Z!b ;
Z!a le Z!b ;只有同类环才可比较元素大小，Maximum(Z!a, Z!b) ;
Minimum(Z) ;

Maximum(S) ;
Minimum(Z!a, Z!b) ;
4 n8 Q" A! ?: p  c* V1 {: aMinimum(R) ;
0 L4 P6 l" T" d7 b5 L: `0 x. s
# C7 y6 [; c8 F9 ?, W0 r

Integer Ring
8 J5 k! z) o# J6 P  TResidue class ring of integers modulo 12
+ j, @+ U6 }! F; rResidue class ring of integers modulo 13
3 {4 a: R; y- |; H4 aResidue class ring of integers modulo 12
& W7 p7 D* m2 Z5 ^# M0 e1 v! t8 X8 oResidue class ring of integers modulo 12
! z& @3 x; @& H5 P0 R( I12
12
. r$ c4 t! M' m' _  [3 @false
' ?$ B* C3 F) b9 K+ Y* @false
true
true
true
true
false
( p; f/ x- D$ b+ ?0 R; @3 Dtrue
Residue class ring of integers modulo 12
Residue class ring of integers modulo 13
RngIntResElt
4 ?( q, b' b7 IRngIntResElt
7 N& b8 s0 Y! t$ l1 v3 E, e* F9
12
0
0 G) y4 R' o+ l( `, A8 i% Q0
+ v5 |2 K! A4 Y: ]- u9 u  A2 strue
' q6 T5 J' L1 F  {, w% i5 K1 Nfalse
false
  Q2 j$ T6 u5 S0 |' T+ L& Htrue
false
true
false
false
8 J" P6 o% s3 B0 q, Mfalse
) i9 z( c% `7 efalse
- o9 P. `2 N) e5 V6 \* p/ Utrue
true
12
1
- H5 a8 J& E) H7 `: r
>> Maximum(S) ;
! Y# A, Y8 w2 r# p          ^
Runtime error in 'Maximum': Bad argument types
# r* S; o5 d8 |( `+ u+ vArgument types given: RngIntRes

9

  y3 g5 S9 e+ ]/ ]- K>> Minimum(R) ;
          ^
Runtime error in 'Minimum': Bad argument types
( r* l% `+ Z# {' a/ uArgument types given: RngIntRes

lilianjie

Z:=IntegerRing(12) ;Z;   
UnitGroup(Z);
" p0 V% s, y3 {5 j, ^, ?3 _MultiplicativeGroup(Z);
7 `3 L! e5 {& U3 `% H6 I/ D% ZCategory(Z) ;
PrimeRing(Z);
AdditiveGroup(Z) ;

+ f. V: }: n) i3 \; ^/ tZ:=IntegerRing(13) ;Z;   
UnitGroup(Z);
1 y3 k4 e4 u4 \, I  VMultiplicativeGroup(Z);
/ y" \, L; [( ?7 d1 nCategory(Z) ;
' k& U) B- q7 g0 V/ WPrimeRing(Z);
AdditiveGroup(Z) ;

* p! C$ b* J2 u$ w" s

Residue class ring of integers modulo 12
Abelian Group isomorphic to Z/2 + Z/2
6 r" I% G: T  p& k& k5 V1 NDefined on 2 generators
Relations:
    2*$.1 = 0
& Z- f* {% r  e$ p/ k    2*$.2 = 0
: b1 L( l: e; P5 T& G. O! Y' PAbelian Group isomorphic to Z/2 + Z/2非素数环的乘群同构两个小群的直积（1*11    5*7）Defined on 2 generators
4 D$ \. @* A! q) }4 H" RRelations:    2*$.1 = 0
$ U) E9 A, Y# v( m$ y1 y    2*$.2 = 0
/ N' c6 c3 a5 f& A2 D; Z/ [RngIntRes
% p) W" v$ [/ [8 X, EResidue class ring of integers modulo 12
2 V4 ]6 t5 N; o; L7 tAbelian Group isomorphic to Z/12
Defined on 1 generator
Relations:
8 E4 o( j5 Q+ @: s( p& R    12*$.1 = 0
) _- Q9 _" E# E; Z/ C' L/ i! \8 t4 RResidue class ring of integers modulo 13
7 _. M( i1 F# m6 |* I4 A+ tAbelian Group isomorphic to Z/12
- t1 u  ~* M1 Z% }3 t2 T; S; PDefined on 1 generator
: i: Z4 ~) S& j  d: K0 rRelations:
  ^6 b& d# b7 y    12*$.1 = 0
Abelian Group isomorphic to Z/12     素数环的乘群同构Z13-1=Z12Defined on 1 generator
Relations:
& z6 w" B" w8 n    12*$.1 = 0
' V9 n$ i8 ^' A! IRngIntRes
' X- c( \+ J6 j7 t5 BResidue class ring of integers modulo 13
- v0 N4 y3 Y' P/ r, y0 F4 C0 IAbelian Group isomorphic to Z/13
Defined on 1 generator
! v4 f; Z3 ?3 n) pRelations:
    13*$.1 = 0

lilianjie

Z:=IntegerRing(5) ;Z;           模5等价类环n := 1666666666234567890;
> n;
' S7 _. j% L; v, T  ~, {6 @6 ln1:=Z!1111111111111111111111;n1;
n2:=Z!11333331111111111111111;n2;
; i$ ~2 N2 w) _' q3 s# k+ l
9 ~5 r( u* W( u3 M3 o
K:=Z!n1+Z!n2;K;
5 m3 i2 o4 b4 M- G) z- O; c
IsField(Z);      是域吗Characteristic(Z);环特征
IsFinite(Z);有限环吗
& \% h& e9 v  e2 Q4 o4 l; uIsCommutative(Z);可换吗
; ~0 r+ g- r8 d  GIsOrdered(Z);有序吗-------应有不过这函数没有这功能IsEuclideanDomain(Z);欧整环吗------欧环还有非整的。。。。
IsPID(Z) ;主理想整环吗
3 j* A6 N6 b1 k. w) I% R( |
IsUFD(Z) ;唯一分解吗
IsDivisionRing(Z) ;除环吗
IsEuclideanRing(Z) ;欧环吗
4 k' a2 n0 j; c, ~" {( E3 `IsPrincipalIdealRing(Z) ;主理想整环吗
IsDomain(Z) ;整环吗FieldOfFractions(Z);分式域
; w; l4 j4 |) M" b9 `UnitGroup(Z);单位群
MultiplicativeGroup(Z);乘群
Category(Z) ;范畴Parent(Z) ;父环
PrimeRing(Z);素环单环和本原环不同Center(Z) ;中心
AdditiveGroup(Z) ;加群-----就第行一特点ClassGroup(Z) ;类群----------只有Z才有------难懂理想类群更难懂

ZZ:=IntegerRing() ;ZZ;
  }1 ]7 j: ?6 _3 LClassGroup(ZZ) ;

* H' L3 l  H0 \===========

Residue class ring of integers modulo 5
1666666666234567890
1
; K7 W' i% |4 w# M0 t6 N1
% ?' b! ~# n6 `" N' Z7 x5 Y8 P2
true
5
true 5
3 p9 c6 v* \4 n* {7 j& S/ dtrue
false
' J3 k! U& S: htrue
1 F9 f0 t8 W3 F, Ntrue
# Z: c5 a; F9 @+ ?true
true
true
# I9 H# M( J& c, Ltrue
true
Residue class ring of integers modulo 5
Abelian Group isomorphic to Z/4
, c: K9 e$ D6 t1 @; I* U" ^Defined on 1 generator
Relations:
! d9 B' d6 j  t  u& r* {    4*$.1 = 0
5 w6 H3 \2 e8 D5 }Abelian Group isomorphic to Z/4
Defined on 1 generator
Relations:
    4*$.1 = 0
7 `' M6 z$ h" P) S+ \% }RngIntRes
% S2 ^! M* _$ o- v& {Power Structure of RngIntRes
Residue class ring of integers modulo 5
+ {# j1 i5 a% h$ ]Residue class ring of integers modulo 5
Abelian Group isomorphic to Z/5
* J! a# b+ L- wDefined on 1 generator
8 `$ L, F: {4 G! W6 v: |* N2 {  ^Relations:
    5*$.1 = 0

3 v  K% v8 L( @1 T8 a>> ClassGroup(Z) ;
             ^
Runtime error in 'ClassGroup': Bad argument types
Argument types given: RngIntRes
3 B6 {1 J1 B) S, ^; c9 W( k" Z9 s
Integer Ring
8 ~: y- T  e7 {; I) uAbelian Group of order 1

lilianjie

ss:=12345678111;ss;
! \; @" A+ T6 A2 `+ _9 `+ l4 gs:=0x12345678111;ss;
8 o2 u( g! M3 k6 z# _: T' ?
sss:=Factorization(ss);sss;
sss1:=Factorisation(s);sss1;
5 M3 u+ ?1 B! ]7 ?6 ]: d( s, pFactorizationToInteger(sss);
/ Z  v# M" j: z( p0 O; PFactorisationToInteger(sss1) ;
Facint(sss1);因子分解和还原ssss:=Intseq(ss, 2);ssss;
SequenceToInteger(ssss, 2);
2 k4 G4 H8 Z- J! E- M: r- E; X) lssss:=Intseq(ss, 17);ssss;
# I+ h  v& W9 g# Z7 zSequenceToInteger(ssss, 17);
. H, b5 o2 B+ a$ j" U5 J) @ssss1:=Intseq(s, 17);ssss1;
SequenceToInteger(ssss1, 17);转成2和17进制
, I4 ]/ l* h+ `* z' \( P! `' K: D
; f8 }7 ?# T7 l5 F1 m12345678111
) J# J* p/ A. }9 Y; z12345678111
[ <3, 1>, <13, 1>, <31, 1>, <1447, 1>, <7057, 1> ]
[ <3, 1>, <83, 1>, <34129, 1>, <147209, 1> ]
3 g" H. p; ^, V/ K12345678111
1250999894289
8 k9 @/ ~2 N' D, u8 s$ F1250999894289
[ 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1,
1, 1, 1, 0, 1, 1, 0, 1 ]
' c4 H" l2 y  L$ }8 x12345678111
[ 8, 6, 6, 4, 0, 8, 1, 13, 1 ]
( \+ X* J7 P2 ?, e( Y: a12345678111
[ 14, 6, 7, 11, 9, 15, 11, 5, 9, 10 ]
1250999894289

孤寂冷逍遥