一些初等函数：

lilianjie

:=IntegerRing() ;Z;
9 ~) l' o, X' ^8 o6 Sn := -1666666666234567890;
> n;

' C5 H4 Z; `$ f: w% J  N4 O0 Q+ C> n:Hex;                           转16
: e; L! I8 O0 v( q! e* I- LIntegerToString(n, 2);        转2
IntegerToString(n, 10);       转10
5 G; {& y' u2 _0 y; T1 D. M2 xIntegerToString(n, 16);        转16
IntegerToString(n, 36);         转36IntegerToString(n) ;
2 _5 q  b5 s" o" t6 y5 E- @IntegerToString(-0x17213080A7E55CD2);转串Zero(Z);
Identity(Z);                  
Representative(Z);         环代表元
% n. R8 k3 `6 Z: z/ nEltseq(n);                        取整
Eltseq(-0x17213080A7E55CD2) ;Denominator(n);Denominator(12/13);Denominator(222222/111);
+ K! m, J5 J# ]  w* u
5 n& b# f7 ^  a6 Q& T4 G, ^# A" ~m := elt< Z |  -0x17213080A7E55CD2>;m;         在虚实2次域中进制砖换不变
8 `2 \. M+ D' G% Qk := Z ! elt< QuadraticField(3) | -1666666666234567890, 0>;
> k;
n eq k;
kk := Z ! elt< QuadraticField(3) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;
, H! V; Z; b8 B( ^( I' B( z' A
k := Z ! elt< QuadraticField(13) | -1666666666234567890, 0>;
> k;
n eq k;
kk := Z ! elt< QuadraticField(13) | -0x17213080A7E55CD2, 0>;
9 _' ]. [) s8 I> kk;
kk eq k;

Eltseq(kk) ;Eltseq(-1/14);
$ l6 b. J) g% M+ x. r6 x
" s4 c6 U: b" K3 E$ U* G8 f# i


( l) X, I9 i0 M" uk := Z ! elt< QuadraticField(-3) | -1666666666234567890, 0>;
> k;
( n& H  `- D# p- i( a* Zn eq k;
kk := Z ! elt< QuadraticField(-3) | -0x17213080A7E55CD2, 0>;
> kk;
1 L+ o' W& B4 l0 G; @kk eq k;

k := Z ! elt< QuadraticField(-13) | -1666666666234567890, 0>;
" w9 \3 o6 Z% m$ k6 {> k;
n eq k;
+ y: `6 J# u4 ckk := Z ! elt< QuadraticField(-13) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;
. @# O1 j1 ~5 f) G$ W
Eltseq(kk) ;Eltseq(-1/14);
3 [6 z: N& V% {' ~4 R5 y) C
7 ~1 x6 n7 Q! _! Y0 j7 F


+ _7 H& a$ u& z% J4 }3 K
+ K5 m/ p# l  T" O4 i. S
" U- L, H4 H" i
/ o: a3 I6 R( R
6 B4 j5 |7 a- F- A; X
8 h2 e7 o- S+ m! q% e8 A
2 W2 |( y" d+ S$ S& v3 D=============

+ G3 Y$ h$ g. M, c& p  L8 ?


: `9 v0 S$ _0 K6 \7 lInteger Ring
% j4 \# s/ c/ d; j6 J-1666666666234567890
7 j4 |' D1 ?5 J9 J  K6 i-0x17213080A7E55CD2
2 q( d9 F0 L1 C-1011100100001001100001000000010100111111001010101110011010010
3 |; P- E# g# ?& X6 ~4 E  z' g-1666666666234567890
* a* i- D  _7 ]" V-17213080A7E55CD2
: F$ F2 H- l& j/ |) y' N-CNUO0WGPY9CI
1 n  W: F: c4 f- P5 @& N8 w-1666666666234567890
-1666666666234567890
# l% S1 h& P4 ^% U, \: R0
1
0
[ -1666666666234567890 ]
[ -1666666666234567890 ]
# L# I$ k8 Z" c5 e2 A# @, A6 x1
  ]2 n/ C" K# t$ N% k2 S13
* v% o# f4 a1 P6 ]7 I  \8 z1
+ W3 K: T) m" r8 [& ~# [  q# g
-1666666666234567890
true
-1666666666234567890
# b% E1 j, E# a! |  ?true
-1666666666234567890
true
-1666666666234567890
) y* c: ?) M: Rtrue
7 x& j1 T# o6 Y8 }/ ~% Z" O- M[ -1666666666234567890 ]
[ -1/14 ]
$ w# ^7 u, p+ W$ Y* _# D) g
  D9 L2 S6 {2 C" f



- E$ X7 l5 T0 w0 ?3 L( O

3 ^) S7 _, i0 C3 \0 H2 _8 `, ~-1666666666234567890
-1666666666234567890
5 d% B/ V8 p$ K" ftrue
-1666666666234567890
true
-1666666666234567890
4 E: T5 g  K- R3 ctrue
) F+ Q8 A2 z" X) V3 _-1666666666234567890
3 r& j6 p0 d0 J( ]true
6 x1 {2 R1 H; ~; n! L[ -1666666666234567890 ]
% s" o! x+ t. y6 q; u3 d) O* v! z2 ?# }[ -1/14 ]

孤寂冷逍遥

lilianjie

ss:=12345678111;ss;
/ }- K& L* T% _s:=0x12345678111;ss;

6 O% z% P3 ^' }sss:=Factorization(ss);sss;
2 c+ M# o3 {' I6 }6 }sss1:=Factorisation(s);sss1;
FactorizationToInteger(sss);
FactorisationToInteger(sss1) ;
+ S) I7 [4 J3 }; cFacint(sss1);因子分解和还原ssss:=Intseq(ss, 2);ssss;
0 n3 y: P$ X" [9 h: zSequenceToInteger(ssss, 2);
% @8 n0 Q3 ^' ]% Mssss:=Intseq(ss, 17);ssss;
SequenceToInteger(ssss, 17);
! q# w/ u5 k1 I( mssss1:=Intseq(s, 17);ssss1;
SequenceToInteger(ssss1, 17);转成2和17进制
* y& W8 n. ]+ Z' W, Z) R& n
4 U. [& E- H/ M8 D12345678111
12345678111
[ <3, 1>, <13, 1>, <31, 1>, <1447, 1>, <7057, 1> ]
% k& q/ h' x  y5 b; b5 ]# \( W; ~[ <3, 1>, <83, 1>, <34129, 1>, <147209, 1> ]
12345678111
1250999894289
6 s0 ~1 k. b! \" E1250999894289
[ 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,
: b7 ?; ^: T/ q! H! E; v1, 1, 1, 0, 1, 1, 0, 1 ]
12345678111
3 j5 B( D  ^5 }% q[ 8, 6, 6, 4, 0, 8, 1, 13, 1 ]
# M# Z- z9 j* b& I. a12345678111
+ T2 z: b" K& u! t[ 14, 6, 7, 11, 9, 15, 11, 5, 9, 10 ]
1250999894289

lilianjie

Z:=IntegerRing(5) ;Z;           模5等价类环n := 1666666666234567890;
> n;
n1:=Z!1111111111111111111111;n1;
n2:=Z!11333331111111111111111;n2;

, a9 y6 f( |/ n0 v; u1 W
& u  H% W, ?  A9 c9 m  G+ l  BK:=Z!n1+Z!n2;K;
5 r1 O/ L5 d/ L/ }- W
! e+ J0 I' x1 ?& SIsField(Z);      是域吗Characteristic(Z);环特征
IsFinite(Z);有限环吗
/ g+ J4 }+ ^6 n  Y$ f6 OIsCommutative(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
6 y3 H# M5 ~" q
IsUFD(Z) ;唯一分解吗
- I9 q3 V% ]6 d7 D( r5 |IsDivisionRing(Z) ;除环吗
IsEuclideanRing(Z) ;欧环吗
' w1 c- B- ?  S6 gIsPrincipalIdealRing(Z) ;主理想整环吗
IsDomain(Z) ;整环吗FieldOfFractions(Z);分式域
UnitGroup(Z);单位群
MultiplicativeGroup(Z);乘群
2 U& `% Q* q- B# hCategory(Z) ;范畴Parent(Z) ;父环
% S+ k; }, c: {% G5 I0 o* K7 VPrimeRing(Z);素环单环和本原环不同Center(Z) ;中心
: q, J7 M* o8 a# @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;
ClassGroup(ZZ) ;
9 M7 {" H$ A! I* z! M' [$ X: J: X
===========

Residue class ring of integers modulo 5
" O6 f7 \3 p; r9 z# K, X1666666666234567890
1
1
2
5 h. P1 A+ h8 A: l. q5 ]true
5
true 5
$ ?1 ]8 S/ o. a) s, M1 etrue
false
( j" H: C' R6 h6 S: X! Qtrue
true
' B& ]$ @  m9 Q( ^, [true
true
true
) w' F& |: P  J" U! `true
& r% j  C8 {8 F; D! {1 Ytrue
  l) n' v/ d9 l9 P( `1 Q' _; X  |Residue class ring of integers modulo 5
( w7 b$ `$ r( XAbelian Group isomorphic to Z/4
Defined on 1 generator
Relations:
    4*$.1 = 0
) k3 `; ]  U8 W( R: F# p! GAbelian Group isomorphic to Z/4
( C3 t+ n4 S. W& Y' q2 tDefined on 1 generator
Relations:
    4*$.1 = 0
RngIntRes
Power Structure of RngIntRes
Residue class ring of integers modulo 5
Residue class ring of integers modulo 5
Abelian Group isomorphic to Z/5
Defined on 1 generator
* W/ H* |" D- \% V9 n3 jRelations:
9 |5 m2 I7 s4 z) \    5*$.1 = 0

) w( |6 R1 O2 @( w>> ClassGroup(Z) ;
             ^
Runtime error in 'ClassGroup': Bad argument types
Argument types given: RngIntRes
; q; ^  L( `3 i0 w
% t1 |7 D2 Q+ U+ b: e+ M! ]Integer Ring
( D$ |- r" F: I2 [% J9 iAbelian Group of order 1

lilianjie

Z:=IntegerRing(12) ;Z;   
UnitGroup(Z);
MultiplicativeGroup(Z);
Category(Z) ;
PrimeRing(Z);
AdditiveGroup(Z) ;

5 r( W2 ~; l5 S7 V2 LZ:=IntegerRing(13) ;Z;   
4 d5 ^7 n3 R& D) ?9 O$ ]: R1 n0 @6 Z UnitGroup(Z);
MultiplicativeGroup(Z);
9 L$ _( J) G4 @# {' D- T6 B; c. RCategory(Z) ;
PrimeRing(Z);
! d# {( e  h# }; Y/ B" D. UAdditiveGroup(Z) ;



Residue class ring of integers modulo 12
Abelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
0 d3 Y( x- q) u  A+ F; rRelations:
    2*$.1 = 0
& n! F$ ^6 P' l1 E( K    2*$.2 = 0
) k8 Y% t' t( i# UAbelian Group isomorphic to Z/2 + Z/2非素数环的乘群同构两个小群的直积（1*11    5*7）Defined on 2 generators
Relations:    2*$.1 = 0
    2*$.2 = 0
- p6 E. Y+ s3 ?/ o8 YRngIntRes
Residue class ring of integers modulo 12
! \* ~8 e! d3 l8 [$ F4 pAbelian Group isomorphic to Z/12
: f' R* t' |2 TDefined on 1 generator
Relations:
3 U( J& e' l9 C9 R8 I( z3 e# ^0 ~    12*$.1 = 0
' I# T+ w9 v5 c; NResidue class ring of integers modulo 13
9 N7 v9 T% b3 T- iAbelian Group isomorphic to Z/12
: @( t( R$ }# m% p. \( H: GDefined on 1 generator
- v2 {! Y) m# }( B) b- P3 [Relations:
" z. {4 }5 K: v9 J  P    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
: W/ U: U& r9 D0 tRngIntRes
; m% t7 |8 l$ n, b0 V0 T# Y' k  rResidue class ring of integers modulo 13
Abelian Group isomorphic to Z/13
Defined on 1 generator
Relations:
    13*$.1 = 0

lilianjie

3 s: c0 J; I4 M. u6 ]; u9 ~
Z:=IntegerRing() ;Z;   

R:=IntegerRing(12) ;R;   
( A' h& m& T" r. F' fS:=IntegerRing(13) ;S;   

9 q) b% y# b- R  U" G! T1 Y+ \( E
  k& ?2 M7 t1 A1 I6 gPrimeRing(R) ;
Centre(R) ;

$ S# |# n4 |4 F8 G$ DCharacteristic(R) ;
7 Q/ ?8 j% @. k1 E8 c& w) L9 W8 `# R ;阶----元素数
, v& H# X: g1 b: x0 kIsPID(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) ;
1 h/ O; ~& T0 d8 S' F8 s$ S( M. ~
IsPID(S) ;
6 m3 J+ R# A. c  `; EIsDomain(S) ;
4 i) B/ u. {3 u. V: @( eHas**(S) ;
R eq S ;
; g. N% Y4 B3 C8 dR ne S ;

1 R" S+ _6 V0 \4 N( l5 l* cParent(R!123) arent(S!123) ;
5 h, u% D7 z, y0 g- R5 ?Category(R!234) ;Category(S!234) ;

a:=Random(R) ;a;b:=Random(S) ;b;
. Q1 s8 k" E% H# q3 w- N& uRepresentative(R) ;
Representative(S) ;

( H, P7 m) \0 B(R!a) in R ;
/ d2 U* [, S2 E(S!b) notin S ;
IsUnit(a) ;                是单位吗
IsIdempotent(a) ;是幂等元吗
( T4 I8 q- R) n9 z1 t) E, j  |IsNilpotent(b) ;是幂零元吗
/ g4 Q0 P, g, u" t- g# W6 QIsZeroDivisor(a) ;可除零吗
1 Z1 X% `9 c: t# h; R6 ^( NIsIrreducible(Z!b) ; 可约吗IsPrime(Z!a) ;
) u4 }7 j/ t6 d5 t/ {+ ]
Z!a gt Z!b ;
( e$ Y5 m0 s* Y$ }Z!a ge Z!b ;
Z!a lt Z!b ;
& H8 h9 n, K( I* V0 HZ!a le Z!b ;只有同类环才可比较元素大小，Maximum(Z!a, Z!b) ;
Minimum(Z) ;
7 ?$ s) o4 U/ k7 v
2 _7 h6 ?" k% u$ B5 PMaximum(S) ;
8 J1 Q% ~1 P& l# qMinimum(Z!a, Z!b) ;
  s. r" C/ T9 _' p( eMinimum(R) ;
& Q3 {2 a/ F0 w: C* q! Z4 J
+ ?! r5 b8 Z+ x% ^& ^' G

' [. D+ S: A% }$ n2 mInteger Ring
Residue class ring of integers modulo 12
' i( ?- n% ^, S% c6 _( N7 cResidue class ring of integers modulo 13
Residue class ring of integers modulo 12
9 y* }' {' }3 @+ ~+ g' AResidue class ring of integers modulo 12
12
12
false
" r' @6 v$ L7 xfalse
3 L9 X! _. l5 }) J$ xtrue
7 C- T8 X) p0 a( f% e9 G! strue
- R+ i- ^& p( `0 ~$ X: rtrue
- w. P7 N/ j7 y* _! itrue
- J# I4 Y- K+ I% @false
true
Residue class ring of integers modulo 12
Residue class ring of integers modulo 13
RngIntResElt
RngIntResElt
9
12
- w8 L+ y3 E7 i( x* c! l0
- k& x, q2 ~. a6 J8 ?! `% c; s8 H0
true
false
& G+ w- _& G  N0 _5 [% cfalse
  }# F' u6 ^) x, G5 mtrue
) C9 j: ?2 i' J; v* s( ffalse
true
7 D! P8 y! f: ]) s3 I8 P* qfalse
; e3 D8 b9 [  H) i5 sfalse
' C) y$ I# ]* t' j6 ?/ |( Kfalse
3 p: t2 c) t7 Tfalse
true
- Q$ W' A7 x% ktrue
! n% B! b9 p# l) o12
1

>> Maximum(S) ;
          ^
5 Y; @  g) g5 nRuntime error in 'Maximum': Bad argument types
Argument types given: RngIntRes
) Z1 I3 b) Q7 p9 c2 d
, `  o/ d4 @7 p  ]! p9

) ^/ L- A7 o- Q) b6 i/ N>> Minimum(R) ;
          ^
Runtime error in 'Minimum': Bad argument types
Argument types given: RngIntRes

lilianjie1

Z:=IntegerRing() ;Z;   
I12:=ideal< Z | 12 >;
I12;
* f5 _$ b; M; R* J# vZZ:=IntegerRing(15) ;ZZ;   
IZZ15:=ideal< Z | 15 >;
" g" j: Z6 c; `( K: @IZZ15;
I12 eq IZZ15;
' X. K+ A# t5 F% s3 s' z0 }Q1:=quo< Z | 12 >;Q1;
ZZZ:=IntegerRing(5) ;ZZ;   
IZZZ5:=ideal< Z | 5 >;
IZZZ5;
# `- D( H: `3 ?0 k* T
I12 *  IZZ15;            理想和/积/并/交，
4 k* [& T: ^. Q% I+ O0 Y) w理想和是理想对应两（可多个）元素加，
4 I  O) |' L$ i7 V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，
. F  F: a% B/ E3 c理想交是理想（可多个）元素交，理想交一定还是理想，
1 e0 t  z" y. G5 y$ ]2 u! m. m; n: H
6 j# E9 y0 b' N# D( A$ ?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
  P; P9 P0 J* U& |& S3 OI12 +  IZZ15;
* V# h- \/ x+ Q& J/ \I12 meet  IZZ15;

I12 * IZZZ5;
I12 + IZZZ5;
I12 meet IZZZ5;
I12 / IZZZ5;
IZZZ5/ I12 ;
. r1 P' N) H. M! k7 w# D+ [3 s0 M* B6 V, dZ * IZZZ5;
" B4 R" x5 R5 ^" H1 KI12 + IZZZ5;
7 q( V- P0 F6 g! S( ^+ FIZZ15 meet IZZZ5;
7 J- z4 _. V/ B/ x, r3 T! gIZZ15 / IZZZ5;Z meet IZZZ5;
3 B, K( K4 d; e$ |+ X# d( LI12 meet IZZZ5;
8 _6 S8 G0 |9 N9 q! GIZZ15 meet IZZZ5;
+ X/ z! A/ f. d- C# v8 G0 bIZZ15 / IZZZ5;
, i5 M8 t- F2 @0 M" {
I12  subset  IZZZ5;运算后的各种理想互相是否包含IZZ15  subset   IZZZ5;
4 N0 }$ t& v* [) _) YIZZ15 subset IZZZ5;
+ [3 l0 ~/ }) x( |+ F- Q, N; c' e7 iIZZZ5 subset IZZ15;
Integer Ring
Ideal of Integer Ring generated by 12
Residue class ring of integers modulo 15
5 O# O+ C  Q  M1 ^1 i% zIdeal of Integer Ring generated by 15
8 H! ]  o/ ^8 h: v1 n3 R6 Zfalse
Residue class ring of integers modulo 12
Residue class ring of integers modulo 15
Ideal of Integer Ring generated by 5
, R3 t" r. `3 F$ Q8 MIdeal of Integer Ring generated by 180
Ideal of Integer Ring generated by 3
Ideal of Integer Ring generated by 60
; `! O* ]! L% J' ?9 t9 K0 |Ideal of Integer Ring generated by 60
Integer Ring
Ideal of Integer Ring generated by 60

>> I12 / IZZZ5;
. M* ~' o5 @/ ]) M3 Y4 u* D       ^
Runtime error in '/': Argument 2 must divide argument 1.

) ^$ u& U2 F1 t, V( {
' H$ O; V# O+ o>> IZZZ5/ I12 ;
        ^
  V+ i# s0 r. Q: v6 V( y2 C' n: z/ LRuntime error in '/': Argument 2 must divide argument 1.

Ideal of Integer Ring generated by 5
  \9 @! s6 {( G5 s8 rInteger Ring
Ideal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
; F: l/ y+ i$ T1 d$ u0 O3 r* DMapping from: Ideal of Integer Ring generated by 3 to RngInt: Z
8 W) L5 q; p+ x* h( G+ c  C, y) l) JIdeal of Integer Ring generated by 5
2 [2 ^( l% |" A% P, @; A" h1 ?Ideal of Integer Ring generated by 60
Ideal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
! E: |1 i9 ~3 \Mapping from: Ideal of Integer Ring generated by 3 to RngInt: Z

false
& _4 U- ~# x4 j& b! m8 J6 z8 Otrue
2 @  o8 p5 J7 U; |& Wtrue
1 N9 @1 \2 @4 ~5 h7 |* Yfalse

lilianjie1

Z:=IntegerRing() ;Z;   
+ G! O, X/ ?1 [/ EI12:=ideal< Z | 13 >;
& D: }! C# f+ T. q" QI12;
ZZ:=IntegerRing(60) ;ZZ;   
IZZ15:=ideal< ZZ | 31 >;
IZZ15;
* P7 R& @7 B/ }9 }* B. IResidueClassField(I12);
- e3 A- _/ \& \2 ^: n  IResidueClassField(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> ;
" X0 F* E, `" c5 }% o1 k; e9 vloc< 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
ext< ZZ | > ;
4 T( T& l6 y1 Z5 J0 |- s
ext< Z, 2 | > ;超越扩张到多元多项式
. _2 ~$ [3 F; p& W! ^2 ]$ R
8 Q# \" Y- o" `' x6 d8 sext< Z, 3 | > Completion(Z, I12) ;

5 v, }* l% a5 n! v9 g! g
# C" }' w, u3 b& J5 Acomp<Z |I12  >;
& ?* Q* F* l- r* g% F# t    素理想零理想完备化，和P进环联系起来
Completion(Z, 0) ;
comp<Z |0  >;
8 M% b: `3 w. V2 F( e& d! w
Integer Ring
Ideal of Integer Ring generated by 13
9 L  T5 {8 x+ R( `, zResidue class ring of integers modulo 60
Residue class ring of integers modulo 60
  A" d  R9 F- H( t. ~4 _4 t7 l1 b* ~Finite field of size 13
/ u. o- g' w. s; vMapping from: RngInt: Z to GF(13)
0 T. p# ]+ n7 l3 |& L, bmodulo 13

0 X& _* u% F+ v' F1 ?* u8 u>> ResidueClassField(IZZ15);
                    ^
  U9 N* p6 ?; L: P  aRuntime error in 'ResidueClassField': Bad argument types
Argument types given: RngIntRes

Valuation ring of Rational Field with generator 19
Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 19
Valuation ring of Rational Field with generator 17
/ A. I( o5 K7 z" \Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 17
Valuation ring of Rational Field with generator 131
Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 131
5 S# t+ Y2 \" A0 lUnivariate Polynomial Ring over Integer Ring
Univariate Polynomial Ring over IntegerRing(60)
8 k# G1 l+ {2 D
>> ext< Z, 2 | > ;
, T5 _1 o7 Q4 t( u1 `" N8 m      ^
' U2 h0 H$ `: l% k( d; x# _Runtime error: This constructer is no longer supported


>> ext< Z, 3 | >
9 N0 f) L  [; \. M7 f      ^
Runtime error: This constructer is no longer supported

) i* H/ |! f0 \7 g7 K/ `! @13-adic ring
8 s* ^5 O0 ]1 m% W7 _8 ?: \* Y2 tMapping from: RngInt: Z to pAdicRing(13)
  J- k( e) L: H  L) t( `1 O; N; g
Completion(
9 T9 ?- ?& e" R' Y    Z: Integer Ring,
: D6 Y' O: {8 G# i5 n9 _! F1 Y    P: Ideal of Integer Ring generated by 0
0 n- s- [  J& X