一些初等函数：

lilianjie

:=IntegerRing() ;Z;
6 G8 ]) I8 Y4 j& t1 I% Fn := -1666666666234567890;
& v' ~' `# y  o$ o> n;
6 R, n" P* p4 }4 p- R7 X4 i/ f
> n:Hex;                           转16
* Q" U& p' c% Q- g" dIntegerToString(n, 2);        转2
; E7 N( A* }  |1 {) SIntegerToString(n, 10);       转10
8 B  r. B0 p% N% R4 m& Z! r: fIntegerToString(n, 16);        转16
IntegerToString(n, 36);         转36IntegerToString(n) ;
IntegerToString(-0x17213080A7E55CD2);转串Zero(Z);
Identity(Z);                  
Representative(Z);         环代表元
' z6 X* T2 B% r4 CEltseq(n);                        取整
Eltseq(-0x17213080A7E55CD2) ;Denominator(n);Denominator(12/13);Denominator(222222/111);
) P- T1 q9 {+ d* M
, j1 J$ m1 m% T  A6 Nm := elt< Z |  -0x17213080A7E55CD2>;m;         在虚实2次域中进制砖换不变
8 W( l' ^5 p4 Z7 u' uk := Z ! elt< QuadraticField(3) | -1666666666234567890, 0>;
; U+ w4 i( v0 O2 ]> k;
) @3 y7 b4 |+ R6 b! g1 n1 i9 Dn eq k;
# ]& b$ W3 N; j7 h! Ukk := Z ! elt< QuadraticField(3) | -0x17213080A7E55CD2, 0>;
> kk;
" r! g% u" |: P& Bkk eq k;

k := Z ! elt< QuadraticField(13) | -1666666666234567890, 0>;
> k;
n eq k;
8 b" q- K9 s$ j- ?  n' e5 ekk := Z ! elt< QuadraticField(13) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;
7 c/ A: k  Q  e& Q
Eltseq(kk) ;Eltseq(-1/14);
2 W! W- O7 t% j" Z
# k+ ~9 {; b0 i! D/ _1 l% d
9 I+ ?# U: F8 h" @& F2 B4 g7 v
. G4 D) U6 w( {" Z
k := Z ! elt< QuadraticField(-3) | -1666666666234567890, 0>;
> k;
n eq k;
# H3 E  B& M3 U4 Lkk := Z ! elt< QuadraticField(-3) | -0x17213080A7E55CD2, 0>;
> kk;
$ L  ]8 _3 O$ F' I; P4 r( kkk eq k;
5 }/ Q# ]: x2 m# w
7 J1 u! t' |# h3 G6 S$ |k := Z ! elt< QuadraticField(-13) | -1666666666234567890, 0>;
> k;
n eq k;
kk := Z ! elt< QuadraticField(-13) | -0x17213080A7E55CD2, 0>;
# K$ l" h) f  j# {! p& T/ ~! w> kk;
kk eq k;
4 ^, s( |) ~3 F% t' e) P6 t0 l' j
Eltseq(kk) ;Eltseq(-1/14);
5 q2 r/ ^( {: ~
$ y4 A' z' ~$ T: J

& E5 q" J9 N' \; t# F
5 r8 l$ r- ]# B5 B6 R# W

  X) R  _* y' e4 W; v7 p
$ W+ E! T$ D4 T2 T/ r( G
3 X1 S0 ?+ e5 G
" |4 o0 [6 F" P
* E+ S0 Z$ e' E3 k+ ?4 j+ n1 Z5 m=============




Integer Ring
-1666666666234567890
-0x17213080A7E55CD2
5 H2 d/ B- @* Z) ~-1011100100001001100001000000010100111111001010101110011010010
" X2 V. Y7 o7 o8 Z: R6 V/ c-1666666666234567890
0 |$ ]+ c; f- \* p( y-17213080A7E55CD2
5 Q1 t. ^" q9 y7 K+ F6 T: ]-CNUO0WGPY9CI
; U" @. n8 N1 V  y0 h-1666666666234567890
-1666666666234567890
0
% u; Q2 R. E6 _. w, T6 s& U: F6 u! m1
0
[ -1666666666234567890 ]
& W' F/ ?) l+ i& m! h[ -1666666666234567890 ]
8 t, V% ~9 d( t0 n1
13
8 _7 r6 \9 `8 j, o/ `1

-1666666666234567890
* F4 A/ {) ]8 ]$ E1 otrue
-1666666666234567890
% G+ U) d) S; {, A! Ttrue
. W# f( d4 t5 s- W7 s* T6 K-1666666666234567890
! |# x4 [( R9 _4 R+ _9 ntrue
-1666666666234567890
true
[ -1666666666234567890 ]
[ -1/14 ]
/ T, m4 I+ M8 }5 n* T% A
( d3 W- U1 O# Y, \" @) B
8 s" ^& _) t5 b; V1 I& p% [, X2 _

7 v; j, T, _- Y, o: C' j; ?
& H5 V! z2 Z% [7 ]4 N$ _# \7 ]# L5 z
0 b' r1 f& i% O5 V& c( P  Y
-1666666666234567890
-1666666666234567890
9 {5 M% I4 J. W+ p  O" Ktrue
-1666666666234567890
true
4 _/ x9 P  X' b! G-1666666666234567890
, L- P5 U1 H8 R- Q" Y# ?/ }6 n- ]true
( e8 p% }2 M; \8 q# j-1666666666234567890
9 B4 r8 a( V3 b6 otrue
[ -1666666666234567890 ]
9 K" W' g8 L9 c% ]) {) p[ -1/14 ]
  y% D, h6 O$ U0 ?( p2 A3 F

lilianjie1

Z:=IntegerRing() ;Z;   
+ O+ X/ [9 m7 W* b  ]5 q7 K& @# E" p. U4 RI12:=ideal< Z | 13 >;
I12;
2 I; X% ?0 Q+ qZZ:=IntegerRing(60) ;ZZ;   
IZZ15:=ideal< ZZ | 31 >;
IZZ15;
/ d1 Q, A) ?) X$ u9 NResidueClassField(I12);
' p; ^- u$ [/ j2 B6 P8 V# h* L( l7 NResidueClassField(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> ;
( N* D7 V3 P" [: z$ p9 @2 Aloc< 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
9 _& v9 ~3 V) y# \ext< ZZ | > ;
/ N8 S, W! c" z3 N* W0 ]# s% R
ext< Z, 2 | > ;超越扩张到多元多项式

4 e" v4 Q* f/ _- E- y2 wext< Z, 3 | > Completion(Z, I12) ;
6 a( W# l4 y& h5 p; ^
) }! O! _" ?) V3 ^! n& L
comp<Z |I12  >;
* m! t# \& r. t) m/ ]& f    素理想零理想完备化，和P进环联系起来
Completion(Z, 0) ;
comp<Z |0  >;
& l& C/ U* T0 R) @8 H
Integer Ring
! }8 d7 K$ |5 m- k+ fIdeal of Integer Ring generated by 13
- L6 j$ J  ?( j; VResidue class ring of integers modulo 60
Residue class ring of integers modulo 60
8 h9 O6 X  K) Z3 r% S- J8 P, ~7 jFinite field of size 13
$ u9 H* {" L' i  kMapping from: RngInt: Z to GF(13)
modulo 13
+ o7 F( ~! e& K0 O" I& [" e
>> ResidueClassField(IZZ15);
                    ^
Runtime error in 'ResidueClassField': Bad argument types
Argument types given: RngIntRes

% P0 Q# ?! f" D8 N3 }, W( w) ?Valuation ring of Rational Field with generator 19
Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 19
/ i, Y0 f0 R8 T) }: x" r4 u2 nValuation ring of Rational Field with generator 17
  K$ X9 S; ]! y+ l$ T7 I# fMapping from: RngInt: Z to Valuation ring of Rational Field with generator 17
Valuation ring of Rational Field with generator 131
8 {& U' L5 V% zMapping from: RngInt: Z to Valuation ring of Rational Field with generator 131
Univariate Polynomial Ring over Integer Ring
' T5 F' j. j8 U! ^4 GUnivariate Polynomial Ring over IntegerRing(60)
5 a2 |' e# }1 ~9 c: ^
# x1 c% B( Z& n) P# i! |! `>> ext< Z, 2 | > ;
      ^
4 Z1 I2 a1 D( ARuntime error: This constructer is no longer supported
1 @" z. m$ |" A; q* H
. T! r# R* B+ j) i
>> ext< Z, 3 | >
7 Z" m5 T! p$ [7 p      ^
4 }6 \4 a; ^* ~; j6 u1 {9 R9 KRuntime error: This constructer is no longer supported
1 S6 N0 _/ z  T9 u/ D( r4 r
; u, ?; X+ A  [, u13-adic ring
Mapping from: RngInt: Z to pAdicRing(13)

Completion(
    Z: Integer Ring,
* M- n/ s! d/ y; |" [0 Z0 T" J    P: Ideal of Integer Ring generated by 0

lilianjie1

* b3 S! a! ~/ z9 u6 {* \* _1 V
" g# h$ [. u( @0 M3 nZ:=IntegerRing() ;Z;   
I12:=ideal< Z | 12 >;
: Q8 Y- H4 S* PI12;
+ p  D/ ?) ^' t3 PZZ:=IntegerRing(15) ;ZZ;   
8 a! z  H+ K7 jIZZ15:=ideal< Z | 15 >;
4 M% F$ c& F6 I0 ?: L% S" dIZZ15;
I12 eq IZZ15;
+ j# V' c9 G5 }8 T4 h" sQ1:=quo< Z | 12 >;Q1;
  A9 n3 {1 K, s; M5 aZZZ:=IntegerRing(5) ;ZZ;   
+ ~( l4 s. T6 }& x% i3 Q5 c! uIZZZ5:=ideal< Z | 5 >;
IZZZ5;
9 b' b' ~2 M: S5 D7 U* G
: h# B+ w" o  Y: e) b( u7 b9 }I12 *  IZZ15;            理想和/积/并/交，
, E4 R: j9 Q( @# k' Q- U" X1 Q) W理想和是理想对应两（可多个）元素加，
+ N" j* b5 b6 _# u, e3 N3 q  I3 Z理想积是两理想（可多个）对应元素积，
理想并就两（可多个）理想元素并，就不一定还是理想，
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
- E- u: b+ v% yI12 +  IZZ15;
5 ]" `2 j% }/ C* ]; CI12 meet  IZZ15;

( K% D' X3 L7 Q- V* O) h5 {I12 * IZZZ5;
6 T* w3 S4 q' r. @3 Q% tI12 + IZZZ5;
* R* Z& Q$ s1 K" c( jI12 meet IZZZ5;
' B! H/ J! f8 ?8 b& A1 t/ II12 / IZZZ5;
IZZZ5/ I12 ;
Z * IZZZ5;
( @  p& X' O( CI12 + IZZZ5;
1 u  q5 z9 J2 R5 W  j" B6 S9 y9 w  IIZZ15 meet IZZZ5;
IZZ15 / IZZZ5;Z meet IZZZ5;
I12 meet IZZZ5;
$ y9 R$ f& g1 j& G5 bIZZ15 meet IZZZ5;
3 x& F" g, e+ D! f8 ~5 p* [; ]# c$ KIZZ15 / IZZZ5;
2 i9 p7 [3 @4 t! Q& O* X
! a0 s9 X4 C7 `. n; A% ]0 CI12  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;
Integer Ring
# z# n" Y* \- R7 D. z2 n! uIdeal of Integer Ring generated by 12
0 t0 g( N8 e& `$ ?' oResidue class ring of integers modulo 15
7 f8 Y1 J' g5 h$ x4 V1 b6 J9 @. DIdeal of Integer Ring generated by 15
false
6 _% |4 B( z) j# i' _Residue class ring of integers modulo 12
% b0 H* T# s, o( ]1 M  {5 _, r7 X+ _Residue class ring of integers modulo 15
9 Y" |0 z) \6 N% hIdeal of Integer Ring generated by 5
Ideal of Integer Ring generated by 180
; s5 E- a- P( X: P0 {3 L: |Ideal of Integer Ring generated by 3
Ideal of Integer Ring generated by 60
Ideal of Integer Ring generated by 60
Integer Ring
7 l  q' o9 r, W  r. @- j( i+ `Ideal of Integer Ring generated by 60

; ^% c2 y5 @7 o* y2 e, L" H>> I12 / IZZZ5;
/ y* i0 i; u$ T" E' p- `       ^
Runtime error in '/': Argument 2 must divide argument 1.

, u; P" x# h" p7 O; n9 L' I
>> IZZZ5/ I12 ;
! ]( Y8 G( s$ }& F        ^
* D( k1 w/ ~3 y8 O) y7 DRuntime error in '/': Argument 2 must divide argument 1.

Ideal of Integer Ring generated by 5
Integer Ring
Ideal of Integer Ring generated by 15
* y$ x0 t( b9 t" K! Z" c3 z; NIdeal of Integer Ring generated by 3
" ~& o- H9 d: V9 B5 VMapping from: Ideal of Integer Ring generated by 3 to RngInt: Z
Ideal of Integer Ring generated by 5
8 m) M0 ?/ D, ]3 u& q3 pIdeal of Integer Ring generated by 60
Ideal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
& W% i% g+ N2 D" x% W, h% C7 U( rMapping from: Ideal of Integer Ring generated by 3 to RngInt: Z
" h* o( Y$ _# G1 q
7 Y: I2 z! f6 k, r3 K4 |false
( u8 T: E; F* A+ ^# V7 R0 H0 i% s! Wtrue
true
* |0 N4 F& s8 @8 q1 h* B6 f. afalse

lilianjie

Z:=IntegerRing() ;Z;   

+ a& D0 E* {: {7 @4 \. R( S) s7 BR:=IntegerRing(12) ;R;   
S:=IntegerRing(13) ;S;   


PrimeRing(R) ;
1 o6 F/ S: @+ |7 m: v, pCentre(R) ;
9 Y% D  U% w+ Q0 `3 I! {3 @
Characteristic(R) ;
# R ;阶----元素数
1 I. T2 R* @) i3 ~( _7 A4 HIsPID(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) ;
" V: \& {$ V7 p6 l' R1 V, J" M4 QHas**(R) ;
. l; g) l+ r3 j1 e: t/ {/ z5 l
4 L1 m$ |: f7 zIsPID(S) ;
0 q0 |0 ]& \7 ]/ H, O8 QIsDomain(S) ;
Has**(S) ;
  ?+ T! h/ Y4 N: O, oR eq S ;
R ne S ;

3 c, _- U( f1 O2 `' @5 M& J- s4 T) @Parent(R!123) arent(S!123) ;
4 U# a1 `; O  U$ Z! _. }Category(R!234) ;Category(S!234) ;

0 i  L. n: w# O0 e+ Wa:=Random(R) ;a;b:=Random(S) ;b;
; U: n+ f: f" L; O0 i3 V/ RRepresentative(R) ;
6 b3 I5 D; \1 C. B% A: Y. IRepresentative(S) ;
& _) Y. w( U0 v& ^! v
- N7 s5 I( ~- ?& u# O(R!a) in R ;
0 {& }' U: E0 c- B(S!b) notin S ;
6 A* W5 v) U  t5 N$ I5 ^IsUnit(a) ;                是单位吗
IsIdempotent(a) ;是幂等元吗
: J" n% t3 a. y1 S* gIsNilpotent(b) ;是幂零元吗
IsZeroDivisor(a) ;可除零吗
IsIrreducible(Z!b) ; 可约吗IsPrime(Z!a) ;
3 b& j+ y' S0 \
Z!a gt Z!b ;
Z!a ge Z!b ;
Z!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) ;
( n& W/ d3 p: {/ T3 u1 w. f1 TMinimum(R) ;

1 W1 f- R6 l: U) R" u

Integer Ring
9 F5 R( t4 v3 M& fResidue class ring of integers modulo 12
' c, k$ b4 H3 ]! R! `( g0 cResidue class ring of integers modulo 13
4 j( E* ]( R8 O* Y  U' {7 rResidue class ring of integers modulo 12
( A" [% r. x0 I% y+ wResidue class ring of integers modulo 12
  g& B0 X# G. K7 N& }% h1 p12
8 p9 C; b6 g' u9 Z, s12
false
false
true
5 @9 l6 v5 o3 U" I: etrue
' ^; y0 k9 y3 p) ptrue
true
false
true
# @& z6 O! t  {: O+ A/ z" ~  fResidue class ring of integers modulo 12
$ Y1 d3 X9 q) F$ T& DResidue class ring of integers modulo 13
/ U* S# k  _/ }, b* JRngIntResElt
RngIntResElt
! ?4 ?) t0 K& E3 B9
12
, }, C! g7 x, `& P0
0
3 \) l0 z1 G4 K# Wtrue
/ ~! d( a0 P0 i5 |9 Bfalse
' p5 |( [% E$ {5 V1 I3 g: Zfalse
" L! A( l; `' p1 m6 f* mtrue
1 e2 d0 I. g$ `; G0 T- n! T; S. n$ c! jfalse
0 e6 `! L- h( Gtrue
false
false
- V5 G9 F6 Q3 s4 j/ hfalse
& K3 \$ o1 n% k2 w; Y! l4 e( N, F# nfalse
true
true
12
1
3 t8 E; I- C6 }( N5 X* Z
1 f3 k: |  o5 A>> Maximum(S) ;
          ^
9 O: p9 h( ^1 R  d. B$ W5 A( T3 ^Runtime error in 'Maximum': Bad argument types
9 k& c: e' ~# A/ RArgument types given: RngIntRes

: C9 F5 J! |! e3 Q6 ^9 t- c5 d9
+ I8 ~" E8 @# q
>> Minimum(R) ;
          ^
Runtime error in 'Minimum': Bad argument types
  h( \- w# \! \( w+ u5 s7 CArgument types given: RngIntRes

lilianjie

Z:=IntegerRing(12) ;Z;   
UnitGroup(Z);
8 P' Z) c$ y3 v" n' A5 t* q0 UMultiplicativeGroup(Z);
Category(Z) ;
5 \) }: ?4 W8 x! E% s! n) jPrimeRing(Z);
AdditiveGroup(Z) ;

  U3 }- ^1 X- E# f7 `; }Z:=IntegerRing(13) ;Z;   
UnitGroup(Z);
MultiplicativeGroup(Z);
% V* ~$ w! m  c" d; H4 ?! k: J; E" jCategory(Z) ;
& Y0 x7 D* D) Q& d5 b) m8 H9 G% UPrimeRing(Z);
AdditiveGroup(Z) ;



; Q4 K) m) I/ pResidue class ring of integers modulo 12
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
Relations:
    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
7 t5 ^" Y. s& E8 f6 G2 ^Relations:    2*$.1 = 0
    2*$.2 = 0
7 ]) P5 B, n4 k1 jRngIntRes
6 l0 _8 t: {, |, IResidue class ring of integers modulo 12
' Z9 P9 z) O: g2 J# l1 WAbelian Group isomorphic to Z/12
Defined on 1 generator
$ ~" A6 U+ L: M9 }" h% hRelations:
    12*$.1 = 0
' p' y9 _) ]! S5 x4 B' zResidue class ring of integers modulo 13
+ O9 w2 C" K5 J- F0 d! y$ o! \0 aAbelian Group isomorphic to Z/12
# u* W. ]. z) ]% nDefined 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
7 ~9 c0 V5 E/ _/ H: cRngIntRes
Residue class ring of integers modulo 13
Abelian Group isomorphic to Z/13
. S2 P3 g! T4 D5 P% g5 M( uDefined on 1 generator
Relations:
    13*$.1 = 0

lilianjie

+ L' K  |6 g2 e( C3 c
Z:=IntegerRing(5) ;Z;           模5等价类环n := 1666666666234567890;
> n;
( N3 G# Z- M* i0 z* [$ d: Jn1:=Z!1111111111111111111111;n1;
% C' c+ ?% F) y+ ^n2:=Z!11333331111111111111111;n2;
7 M+ @+ k0 X- r5 Y% y) V/ X

K:=Z!n1+Z!n2;K;

. K3 `; y6 b2 B2 X- o4 i/ B! rIsField(Z);      是域吗Characteristic(Z);环特征
: ^  e) q; ^$ y0 oIsFinite(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。。。。
2 d' r! w0 u; \/ b* J1 f3 c2 IIsPID(Z) ;主理想整环吗
/ u& I' j9 Q% R9 i0 Y2 j) A% D
IsUFD(Z) ;唯一分解吗
3 `4 ?, p- C6 J5 M& `/ Q! r0 N( MIsDivisionRing(Z) ;除环吗
; a: N$ D7 z- fIsEuclideanRing(Z) ;欧环吗
IsPrincipalIdealRing(Z) ;主理想整环吗
! h7 E$ C" V! z8 h* [: J0 G5 t6 WIsDomain(Z) ;整环吗FieldOfFractions(Z);分式域
' B1 @2 w5 y7 OUnitGroup(Z);单位群
% [; Z) u4 O" q$ w8 |; VMultiplicativeGroup(Z);乘群
  t! X( O: w0 ?: ?1 _( }9 f6 f/ rCategory(Z) ;范畴Parent(Z) ;父环
; ^* [5 H3 f( ]# ~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;
- I' T8 N  @) d' j) U) Q5 X% HClassGroup(ZZ) ;
+ d9 Z1 ?( O. z! [5 a
===========
+ ]6 _* d' n% c% o9 D
Residue class ring of integers modulo 5
1666666666234567890
8 j2 l3 K5 L/ U0 E. a4 x% X1
. x! \5 c) q! j; v. Q7 e( Y, g1
' s% |2 p' N$ S  j+ L* ~2
1 q0 z. k) N8 J% k6 `2 I% ^true
0 M# `  g' i- S8 y1 x1 `5
8 L) m! s- r$ l( }0 }! x# y/ Vtrue 5
" D7 Q6 a1 e# O, T5 ]  X! h* R- ztrue
false
true
9 s8 L) {( U# s9 I6 _( [" Ztrue
true
. m& l+ _3 ^# {+ R! R9 D1 itrue
true
true
4 H4 z6 a5 b5 s+ Y: _% }true
Residue class ring of integers modulo 5
Abelian Group isomorphic to Z/4
1 \/ D: @. ?/ H0 u, ~/ |; [Defined on 1 generator
Relations:
    4*$.1 = 0
  z9 y3 |7 }3 A& M* EAbelian Group isomorphic to Z/4
Defined on 1 generator
( T6 G0 R2 Y& O3 ?* ]2 ]Relations:
* Q  E  z$ L5 z% o6 M9 @& m2 t* a    4*$.1 = 0
RngIntRes
Power Structure of RngIntRes
) R% K8 P2 d( G& kResidue class ring of integers modulo 5
Residue class ring of integers modulo 5
. S, N# q( w$ }9 JAbelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
    5*$.1 = 0

>> ClassGroup(Z) ;
             ^
5 ]5 s+ c0 d( J) G  tRuntime error in 'ClassGroup': Bad argument types
, {- W, M9 a3 t( e, W2 gArgument types given: RngIntRes
7 N$ u* Q+ Z; z. @* x: S
Integer Ring
  f# F2 T4 m$ R. ]  Y2 E: j7 FAbelian Group of order 1

lilianjie

ss:=12345678111;ss;
s:=0x12345678111;ss;
2 S4 A: J9 |% D9 C( E. w8 `7 F* [
) b4 P8 X. _, |; i4 Isss:=Factorization(ss);sss;
sss1:=Factorisation(s);sss1;
FactorizationToInteger(sss);
5 A: i% `: N4 X& N8 @3 ]1 {) DFactorisationToInteger(sss1) ;
3 }! o$ c+ ]# xFacint(sss1);因子分解和还原ssss:=Intseq(ss, 2);ssss;
SequenceToInteger(ssss, 2);
+ L' V! B+ C! b5 Y2 yssss:=Intseq(ss, 17);ssss;
SequenceToInteger(ssss, 17);
ssss1:=Intseq(s, 17);ssss1;
1 ^$ p0 m/ g* I) Q8 t8 o) WSequenceToInteger(ssss1, 17);转成2和17进制

2 q  L5 y4 g( e" A; D12345678111
12345678111
3 k: w4 a$ u; f- d$ a4 j[ <3, 1>, <13, 1>, <31, 1>, <1447, 1>, <7057, 1> ]
[ <3, 1>, <83, 1>, <34129, 1>, <147209, 1> ]
  V  ~! ]  L: P+ \4 _  N12345678111
1250999894289
$ L6 X  h) A6 J+ B1250999894289
[ 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 ]
0 {* Q3 P3 \/ ^12345678111
9 X7 f+ b8 t, r0 H  F+ O* Q[ 8, 6, 6, 4, 0, 8, 1, 13, 1 ]
12345678111
[ 14, 6, 7, 11, 9, 15, 11, 5, 9, 10 ]
8 U# u, a$ p: ^1250999894289

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