一些初等函数：

lilianjie

:=IntegerRing() ;Z;
4 X0 R( H$ v, a" M5 f+ b& `n := -1666666666234567890;
> n;
2 b: U" {( h5 `
$ z& Y- |  J+ W0 n+ W> n:Hex;                           转16
IntegerToString(n, 2);        转2
IntegerToString(n, 10);       转10
3 Y4 ~# q* o3 m7 g% f9 LIntegerToString(n, 16);        转16
IntegerToString(n, 36);         转36IntegerToString(n) ;
IntegerToString(-0x17213080A7E55CD2);转串Zero(Z);
6 q# b; H0 L: }: U  i; MIdentity(Z);                  
Representative(Z);         环代表元
Eltseq(n);                        取整
Eltseq(-0x17213080A7E55CD2) ;Denominator(n);Denominator(12/13);Denominator(222222/111);
8 c. G5 T6 Z, J! Z8 g' l! u$ }
m := elt< Z |  -0x17213080A7E55CD2>;m;         在虚实2次域中进制砖换不变
) k1 s, G: d! [; r: vk := Z ! elt< QuadraticField(3) | -1666666666234567890, 0>;
$ U9 \+ l. U& e* n' x" N9 t; z> k;
+ y" W4 k& x; a; H# P# xn eq k;
3 V/ t* n) M( G- C: Ukk := Z ! elt< QuadraticField(3) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;
% C' x' w4 B( q/ x
3 s2 p2 f4 V) o( a1 R4 Yk := Z ! elt< QuadraticField(13) | -1666666666234567890, 0>;
> k;
6 @8 L9 @1 g. g/ e9 L) }! _n eq k;
kk := Z ! elt< QuadraticField(13) | -0x17213080A7E55CD2, 0>;
> kk;
' z- G6 j& l. X( wkk eq k;

6 e8 N3 Q5 B6 Z# t! ~/ X" y: t7 @7 SEltseq(kk) ;Eltseq(-1/14);

: t' q: f& ^; Y( V3 s. l6 o( t

9 T9 A% N" X8 U1 k! {4 z' u
k := Z ! elt< QuadraticField(-3) | -1666666666234567890, 0>;
' D4 K) J) S- N> k;
n eq k;
kk := Z ! elt< QuadraticField(-3) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;

2 ?* F1 h/ i# xk := Z ! elt< QuadraticField(-13) | -1666666666234567890, 0>;
> k;
8 z7 Q) l5 L$ C6 g' Y' H% \n eq k;
kk := Z ! elt< QuadraticField(-13) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;

0 Z/ U- j, c/ k7 v' U* z9 G9 R/ jEltseq(kk) ;Eltseq(-1/14);


1 c' S0 n0 f9 K5 Q  y, E4 I


$ j" j  B2 t. p' e" k. b& i




; q0 f- ~6 p* d+ J$ l=============

( i: C* q' x- ?% I' G5 g: ^& Z


/ G$ `. k/ Z  b) ?4 ?) R8 cInteger Ring
-1666666666234567890
-0x17213080A7E55CD2
-1011100100001001100001000000010100111111001010101110011010010
-1666666666234567890
& E/ p- u7 b! e* i* k4 E-17213080A7E55CD2
-CNUO0WGPY9CI
2 S# N5 S+ g! k! y-1666666666234567890
( j7 J6 {! H* P) X" F/ B' T; l-1666666666234567890
: s1 K" F- Y' C0 L- }& @( ]. X0
$ N6 a0 b+ S, v$ O3 q1
* a7 m6 A- S2 T4 P! l* X6 k0
! m9 z4 H- V# @% ][ -1666666666234567890 ]
6 c  k+ J/ f& G' |9 q[ -1666666666234567890 ]
' r+ u+ H% l/ G) O+ @2 N1
13
% P& G6 I7 K0 h; N1
0 ^4 @1 Y- A$ f0 ~1 B2 ]. ]2 z
-1666666666234567890
4 b; F# x# h3 W7 C$ ptrue
-1666666666234567890
true
6 O5 l0 x* d8 j2 Y-1666666666234567890
; \& j# Y$ P, _4 O5 }: q, Y5 Etrue
-1666666666234567890
" c* S! C- p; Y4 m5 Ytrue
, F3 y: K& ]2 w( r  R8 F$ L7 v[ -1666666666234567890 ]
& G# C% \# c0 p[ -1/14 ]
' r4 s4 \6 `9 @1 a$ C; h; J7 e
; \' g# h+ V$ U' ~+ U

: i9 K0 z5 X2 L9 C3 H3 I8 I



+ n( l( Q  B1 L( S; u6 p9 d# o-1666666666234567890
-1666666666234567890
( r$ h) q$ _$ i; v" m# w) A7 mtrue
-1666666666234567890
true
  \- r" e) m. e-1666666666234567890
0 T( O+ z) I1 N1 dtrue
-1666666666234567890
- h7 _. C' h( r8 {* [true
[ -1666666666234567890 ]
[ -1/14 ]

lilianjie1

Z:=IntegerRing() ;Z;   
. ^4 u7 ~& v  R/ f$ FI12:=ideal< Z | 13 >;
$ [) ~0 @# \0 q* F2 V9 dI12;
ZZ:=IntegerRing(60) ;ZZ;   
) j( V3 a3 e# t' e6 c& D% LIZZ15:=ideal< ZZ | 31 >;
5 j# g% _9 c' v% }$ |IZZ15;
2 }( a+ L+ R& {. h. v4 BResidueClassField(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> ;
4 Y0 l( d5 u: Bloc< Z | 17> ;
loc< Z | 131> ;局部化：一个素理想到原环元素的映射
0 b% D7 a2 B6 |" @$ J$ Vext< Z | > ;超越扩张到一元多项式
0 {. \1 B  N( j9 `ext< ZZ | > ;
% U: e5 [6 r, t9 D
$ ~' V* I5 k0 G1 Sext< Z, 2 | > ;超越扩张到多元多项式

6 k+ ~. V$ \/ d4 ]" L7 x* uext< Z, 3 | > Completion(Z, I12) ;


# z9 C& Z% c2 Y+ vcomp<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  >;
* r0 z5 \& J0 ]; w! ~$ V2 _
5 V7 |3 a; o- X0 kInteger Ring
Ideal of Integer Ring generated by 13
Residue class ring of integers modulo 60
$ U- @. }3 `  l7 X) }9 s9 hResidue class ring of integers modulo 60
8 u+ B; J) M  r3 t! y0 N/ iFinite field of size 13
7 Q; j8 A. A# R0 S- v! F7 HMapping from: RngInt: Z to GF(13)
: _2 T, U5 y2 R( K7 emodulo 13
4 D# w, q6 ^* Q9 H3 i
# Z2 V6 S8 ~4 h) z7 U>> ResidueClassField(IZZ15);
                    ^
Runtime error in 'ResidueClassField': Bad argument types
Argument types given: RngIntRes
! e- z8 M4 k- j+ w$ p3 z
Valuation ring of Rational Field with generator 19
Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 19
+ W& c6 |% u3 }1 \* d, `Valuation ring of Rational Field with generator 17
  z  e+ d! Y- F# S# W4 u3 E% A  a& kMapping from: RngInt: Z to Valuation ring of Rational Field with generator 17
9 Z4 F5 z/ x0 ]6 F0 @7 pValuation ring of Rational Field with generator 131
! Y  q8 W# u* E- E  cMapping from: RngInt: Z to Valuation ring of Rational Field with generator 131
3 e' u7 p7 x; K6 [Univariate Polynomial Ring over Integer Ring
Univariate Polynomial Ring over IntegerRing(60)
5 h$ g0 Y+ R- m
>> ext< Z, 2 | > ;
! G6 y, x1 J% ]3 s      ^
( d5 z& j1 O" Z$ i2 g- F' t- ORuntime error: This constructer is no longer supported


>> ext< Z, 3 | >
4 @9 |: v, B5 l, A4 m. n      ^
Runtime error: This constructer is no longer supported
# u" Z5 f  I, o) R" f( [% g
% a' n- O" P3 r8 Q$ E; k' f) Z# f- |13-adic ring
5 J* f3 V% ^0 L9 u9 pMapping from: RngInt: Z to pAdicRing(13)

2 c4 L" d9 B( n/ I, B. ~* FCompletion(
    Z: Integer Ring,
    P: Ideal of Integer Ring generated by 0

lilianjie1

Z:=IntegerRing() ;Z;   
I12:=ideal< Z | 12 >;
: w9 M4 J$ A% v: c8 rI12;
9 {; Y& ?' a( ]( r. g; b$ D' B+ c% KZZ:=IntegerRing(15) ;ZZ;   
IZZ15:=ideal< Z | 15 >;
6 A7 B( m: G$ r5 ?, _! Z3 b0 lIZZ15;
I12 eq IZZ15;
4 K. z* d( O1 U* j" }( p  I% LQ1:=quo< Z | 12 >;Q1;
9 C8 D! W1 p# C5 ~8 Y. v- M0 ~ZZZ:=IntegerRing(5) ;ZZ;   
% L* i5 V- q+ I5 XIZZZ5:=ideal< Z | 5 >;
IZZZ5;
. s, y: M/ V- e* l5 C. S4 e
I12 *  IZZ15;            理想和/积/并/交，
理想和是理想对应两（可多个）元素加，
# k- D7 T) R; B. }8 Q理想积是两理想（可多个）对应元素积，
9 H# Y( e2 S! O, E( ~4 W9 w9 e3 ~理想并就两（可多个）理想元素并，就不一定还是理想，
' T# i: P+ R! L" a! c0 y7 ~. B+ z理想交是理想（可多个）元素交，理想交一定还是理想，
, R/ }, I9 Q. N- D
1 y8 s2 s- o5 y- J2 C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
0 f3 f( o! H$ L, O( ]* F: Z$ kI12 +  IZZ15;
I12 meet  IZZ15;
+ v& r, k) [+ h- g8 b
I12 * IZZZ5;
# J4 g! ^7 c* b5 j  S3 PI12 + IZZZ5;
" |9 c& g: U) p( a5 R1 |9 EI12 meet IZZZ5;
I12 / IZZZ5;
( |0 T+ l, \! K2 k; P) m( EIZZZ5/ I12 ;
Z * IZZZ5;
8 [' u" ]1 O" D( e# [I12 + IZZZ5;
: d# {/ b% J1 w) D; zIZZ15 meet IZZZ5;
2 O* B6 a; b0 W6 T# z1 vIZZ15 / IZZZ5;Z meet IZZZ5;
6 G) K, e" C, _) y* j' ^6 oI12 meet IZZZ5;
4 t7 b( T" I9 K# QIZZ15 meet IZZZ5;
IZZ15 / IZZZ5;

$ e4 m7 Q6 v$ h; L! z* {I12  subset  IZZZ5;运算后的各种理想互相是否包含IZZ15  subset   IZZZ5;
IZZ15 subset IZZZ5;
IZZZ5 subset IZZ15;
3 n5 ~- e9 F' |  o& A4 N" f+ eInteger Ring
6 l2 a8 P1 x% F7 U4 H  FIdeal of Integer Ring generated by 12
% n$ j) p0 j7 Q9 `: c3 T* L* e) J8 N9 ^Residue class ring of integers modulo 15
Ideal of Integer Ring generated by 15
4 Z( L  ~# `6 W  ^/ ^3 G' u6 Pfalse
2 x( L6 r9 a, I* rResidue class ring of integers modulo 12
1 H( z, u+ @5 IResidue class ring of integers modulo 15
. v8 @! s: O' \! V: [& g9 k: QIdeal of Integer Ring generated by 5
Ideal of Integer Ring generated by 180
Ideal of Integer Ring generated by 3
Ideal of Integer Ring generated by 60
Ideal of Integer Ring generated by 60
Integer Ring
( l; R' B9 N  [. P% o! HIdeal of Integer Ring generated by 60

/ @  ?- Q# u  N# I>> I12 / IZZZ5;
! k: b' X. N0 T) @2 ^       ^
# X  M( R+ o8 m) U* I  lRuntime error in '/': Argument 2 must divide argument 1.
7 T% U( [& t5 ^+ M
5 x. L" O2 L3 ^: [9 r, D* X6 t; N- N/ Z
! c' Z2 _$ ?' G2 H0 i' {: W$ ?>> IZZZ5/ I12 ;
9 t0 o' m' y. D! M        ^
0 t3 e& K, K2 W6 d& m7 ERuntime error in '/': Argument 2 must divide argument 1.
4 e2 S6 I" z. N  c' l4 u% ]" J7 v
" S) r0 g) M4 Y8 RIdeal of Integer Ring generated by 5
Integer Ring
: w% y7 C+ r3 @2 K. p! KIdeal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
Mapping 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
/ ]4 h* o9 r# Q  H9 a3 }/ ]Ideal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
Mapping from: Ideal of Integer Ring generated by 3 to RngInt: Z

( q+ U# [" K7 ~false
5 v7 t; m; I8 Y7 ?true
true
4 V8 |7 _6 k  h% x3 p* Ofalse

lilianjie

! r: x! o. a' BZ:=IntegerRing() ;Z;   

; M+ m6 n: D6 f. qR:=IntegerRing(12) ;R;   
+ i/ T+ E7 S7 zS:=IntegerRing(13) ;S;   
2 r- A8 x; U- p/ Q, t
; p3 I/ M0 f: C
0 {: Q( J, f# nPrimeRing(R) ;
Centre(R) ;

( F  ~7 \. `' X% d4 d. GCharacteristic(R) ;
9 d# q5 t2 P$ y0 x" n# [( M9 T) o  \# 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) ;
Has**(R) ;
: b- S/ y0 V! [* L+ Z
IsPID(S) ;
# s3 F! I" z0 f& r, |  W# NIsDomain(S) ;
* Y4 S# O! r  j+ t* @, e& j1 HHas**(S) ;
R eq S ;
R ne S ;

Parent(R!123) arent(S!123) ;
Category(R!234) ;Category(S!234) ;
, Y% T8 p" r+ n" S* u$ a% c
! |8 [/ m( B6 z' d/ Ta:=Random(R) ;a;b:=Random(S) ;b;
4 ^1 D( C6 P/ n/ ~1 \: P6 G3 s  yRepresentative(R) ;
Representative(S) ;
3 \& }" P) ?& o5 ~  ~8 l
(R!a) in R ;
(S!b) notin S ;
$ f" c: ~6 O# ?& YIsUnit(a) ;                是单位吗
IsIdempotent(a) ;是幂等元吗
( h' j& _4 a1 n$ a8 r% y# K4 gIsNilpotent(b) ;是幂零元吗
8 H( o3 }5 x* a7 I! x) M1 E2 VIsZeroDivisor(a) ;可除零吗
$ ]9 H7 @# y& q' Y2 `3 W6 ZIsIrreducible(Z!b) ; 可约吗IsPrime(Z!a) ;
; {5 C4 V2 c9 r
Z!a gt Z!b ;
Z!a ge Z!b ;
$ l2 a7 [: B! m+ K8 p, qZ!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) ;

8 Y5 j& E) p! r& i. E! t0 x/ }Maximum(S) ;
5 O0 @5 g$ p% U+ `) cMinimum(Z!a, Z!b) ;
Minimum(R) ;
. e; A) W" W" K4 X1 t

' d  V  r. b  O& @
8 A& R/ ^  O; ]$ F) D5 iInteger Ring
Residue class ring of integers modulo 12
Residue class ring of integers modulo 13
Residue class ring of integers modulo 12
Residue class ring of integers modulo 12
7 f, u; l8 g. W* _12
12
: [3 l1 Y1 N2 H2 I' {& A9 ifalse
false
true
+ h1 o- o/ [' q+ ?. Btrue
* ^# O1 r6 v$ q& K2 Strue
( K1 M3 S( Y  t$ }: ktrue
false
% K' i5 V" O5 q* @1 h& Rtrue
Residue class ring of integers modulo 12
3 N/ ]5 i7 h5 _' y" @Residue class ring of integers modulo 13
3 x4 z- x) ]% F# r+ S6 uRngIntResElt
' t- ]7 \* g5 L, {2 l3 nRngIntResElt
+ o1 N; Q% S0 O9
12
0
0
true
false
6 p/ r7 ]: n4 P* L. o9 U5 \false
true
0 u* N$ Y6 N+ y0 ~false
' g- d- I& O1 _  {+ H. l# N" mtrue
  h3 g' |) f7 n5 G1 Q# p# ^7 Afalse
# K+ O, O, `. H3 T: u- ^+ Yfalse
false
0 u0 H* S  w9 s6 n8 Nfalse
$ @8 C" @; K. h, ltrue
true
7 D; m+ C; c8 y. i0 b& o12
8 ^" Z) b4 d# L4 [# T* E  Q* a+ q$ G1
( I" X1 t" |3 |
>> Maximum(S) ;
          ^
Runtime error in 'Maximum': Bad argument types
Argument types given: RngIntRes

9

# T2 Q! B" F9 D+ w9 x5 [! u: ~  J>> Minimum(R) ;
          ^
9 P% T. X4 A) W* x2 iRuntime error in 'Minimum': Bad argument types
: a3 d. n  R3 i3 @Argument types given: RngIntRes

lilianjie

Z:=IntegerRing(12) ;Z;   
8 G* w. Y" c8 F6 a9 A0 f UnitGroup(Z);
MultiplicativeGroup(Z);
; g; L6 I) |! i% P9 G& LCategory(Z) ;
/ w" x' [8 n* g3 A9 NPrimeRing(Z);
2 m: g( b1 }) z+ M: _6 PAdditiveGroup(Z) ;
9 b7 A* E5 `* }0 Y9 [$ ~' C. B
: N3 \5 T, }& l8 @. HZ:=IntegerRing(13) ;Z;   
UnitGroup(Z);
MultiplicativeGroup(Z);
Category(Z) ;
0 Z+ P1 i% w, {- [  b( A- L# c& GPrimeRing(Z);
AdditiveGroup(Z) ;


9 |% O4 [) {% c3 X7 E$ W
Residue class ring of integers modulo 12
Abelian Group isomorphic to Z/2 + Z/2
9 s" P8 r" Q' [* O: p0 Z" l% QDefined on 2 generators
Relations:
5 ~, F; W4 u4 r  F    2*$.1 = 0
    2*$.2 = 0
Abelian 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
Relations:    2*$.1 = 0
    2*$.2 = 0
/ M6 o5 ~# m$ m6 k. URngIntRes
: j. z# q5 R! m+ rResidue class ring of integers modulo 12
Abelian Group isomorphic to Z/12
Defined on 1 generator
Relations:
' M' N  _4 d( L# X/ B+ f' F6 d    12*$.1 = 0
Residue class ring of integers modulo 13
& r* S* p( g  l- E" IAbelian Group isomorphic to Z/12
Defined on 1 generator
Relations:
    12*$.1 = 0
Abelian Group isomorphic to Z/12     素数环的乘群同构Z13-1=Z12Defined on 1 generator
Relations:
    12*$.1 = 0
, y& t; a3 I# n6 d/ I) @RngIntRes
Residue class ring of integers modulo 13
! t' k# o$ B, J( FAbelian Group isomorphic to Z/13
4 n1 H* p, C0 KDefined on 1 generator
Relations:
    13*$.1 = 0

lilianjie

Z:=IntegerRing(5) ;Z;           模5等价类环n := 1666666666234567890;
> n;
) V; P' j) o8 N2 G/ Rn1:=Z!1111111111111111111111;n1;
( E- Y6 R* C9 w9 \n2:=Z!11333331111111111111111;n2;

5 D, S5 _* ?% T3 O1 C2 J
6 u4 {% P) m1 @( RK:=Z!n1+Z!n2;K;

: \5 q1 Z6 `( F4 N: c. hIsField(Z);      是域吗Characteristic(Z);环特征
0 s6 J' ]" O( r9 `. ^* h% RIsFinite(Z);有限环吗
IsCommutative(Z);可换吗
IsOrdered(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

IsUFD(Z) ;唯一分解吗
) o) N* b) U, J" D' HIsDivisionRing(Z) ;除环吗
IsEuclideanRing(Z) ;欧环吗
) Y9 ]6 s5 {% fIsPrincipalIdealRing(Z) ;主理想整环吗
IsDomain(Z) ;整环吗FieldOfFractions(Z);分式域
" O$ ~% t3 Y2 C% V1 VUnitGroup(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
2 W9 x3 `0 H7 ^, \' |8 Z6 aAdditiveGroup(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;
ClassGroup(ZZ) ;

, f; J! F! \6 {% P===========
8 d8 B9 x) d2 n2 S' m4 Y
  a! ^9 ^6 ]+ b; t+ pResidue class ring of integers modulo 5
, R! \+ v; v3 Q2 U# Q1666666666234567890
1
1
2
3 y0 Y1 ]) ?8 \5 Ntrue
5
# a6 X% _: e: K1 Z- ]true 5
! J+ h6 @0 ~# p0 k7 }! rtrue
0 q( b# C5 i( L: F0 W( zfalse
true
/ F9 S$ U# H( W; b+ H9 w% \true
' v5 |- @/ T' {  Ftrue
true
true
( ]8 N. J" s5 b5 ^- ]% ttrue
  ^+ h9 J* U, t5 u; Itrue
" K7 _+ J1 ^2 KResidue class ring of integers modulo 5
4 R& M% T% N# \- VAbelian Group isomorphic to Z/4
Defined on 1 generator
: g, H. f5 I  z. \Relations:
    4*$.1 = 0
Abelian Group isomorphic to Z/4
, u5 w- k5 G7 Q" [, \, w# I& v; cDefined on 1 generator
& `6 J9 i. z- q% V4 b2 K. ERelations:
& j8 W2 ~  K; h# O    4*$.1 = 0
RngIntRes
Power Structure of RngIntRes
Residue class ring of integers modulo 5
Residue class ring of integers modulo 5
; Q' t8 p* z1 mAbelian Group isomorphic to Z/5
Defined on 1 generator
6 q1 d( ?: U) A. _: Y7 yRelations:
" X* L% @, s9 t, I# k+ g& ?! T. |; q    5*$.1 = 0

>> ClassGroup(Z) ;
             ^
8 O: d  g) q4 ?" P# eRuntime error in 'ClassGroup': Bad argument types
Argument types given: RngIntRes

Integer Ring
Abelian Group of order 1

lilianjie

ss:=12345678111;ss;
- ^) f8 R# s/ b1 ^9 D, h- m: ]s:=0x12345678111;ss;

4 {3 A; x. y0 b- Msss:=Factorization(ss);sss;
sss1:=Factorisation(s);sss1;
& K" F# m$ b2 a: UFactorizationToInteger(sss);
# `# i- i. P1 z. \5 ?FactorisationToInteger(sss1) ;
Facint(sss1);因子分解和还原ssss:=Intseq(ss, 2);ssss;
; ]7 T% P8 R* R& s, o: MSequenceToInteger(ssss, 2);
ssss:=Intseq(ss, 17);ssss;
0 p" y3 b8 U! M1 g: s+ QSequenceToInteger(ssss, 17);
ssss1:=Intseq(s, 17);ssss1;
SequenceToInteger(ssss1, 17);转成2和17进制
5 L( k% w/ \% }% _8 H) H
5 S. y; C3 r( e* S) W12345678111
12345678111
9 G, ]( N" J, b  L. J[ <3, 1>, <13, 1>, <31, 1>, <1447, 1>, <7057, 1> ]
1 B4 a: s) i( O0 u* L3 t- p' F8 m( v[ <3, 1>, <83, 1>, <34129, 1>, <147209, 1> ]
0 a8 h' f0 M9 f2 y/ c12345678111
1250999894289
1250999894289
[ 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 ]
8 g% b& e% P7 q$ N( E/ r12345678111
6 Y7 P( d, G7 N, \, s& Y; ~5 \[ 8, 6, 6, 4, 0, 8, 1, 13, 1 ]
, ~8 f5 }5 V6 ^- z12345678111
4 @# h5 e1 f1 [0 W# t[ 14, 6, 7, 11, 9, 15, 11, 5, 9, 10 ]
/ n9 a, r! A; O( |' w  H# p4 p1250999894289

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