一些初等函数：

lilianjie

:=IntegerRing() ;Z;
n := -1666666666234567890;
* A2 `0 z* J' v; i& [( L- o; q/ ^> n;
6 K0 u3 U, I, R; @7 s; t
> n:Hex;                           转16
) q2 z' G& I8 [! q4 zIntegerToString(n, 2);        转2
# y5 e/ \, X  O# KIntegerToString(n, 10);       转10
IntegerToString(n, 16);        转16
# ^3 G+ l+ M# \4 \7 XIntegerToString(n, 36);         转36IntegerToString(n) ;
IntegerToString(-0x17213080A7E55CD2);转串Zero(Z);
8 S4 j) p5 p1 I5 nIdentity(Z);                  
Representative(Z);         环代表元
Eltseq(n);                        取整
Eltseq(-0x17213080A7E55CD2) ;Denominator(n);Denominator(12/13);Denominator(222222/111);

m := elt< Z |  -0x17213080A7E55CD2>;m;         在虚实2次域中进制砖换不变
  J/ ?" z% n) o1 `! Ik := Z ! elt< QuadraticField(3) | -1666666666234567890, 0>;
8 G0 Q+ b5 m; X> k;
n eq k;
0 n' W$ j3 ~) v0 q* l; d2 Z0 }  o7 zkk := Z ! elt< QuadraticField(3) | -0x17213080A7E55CD2, 0>;
> kk;
  a  X+ I. B+ @! f8 U" }kk eq k;
6 Q7 z8 [# F1 ~; k5 |/ q3 O  `0 g, a& Q
k := Z ! elt< QuadraticField(13) | -1666666666234567890, 0>;
> k;
n eq k;
  r$ C" E: x- E& s) lkk := Z ! elt< QuadraticField(13) | -0x17213080A7E55CD2, 0>;
> kk;
kk eq k;
' }( f) o) t$ f
Eltseq(kk) ;Eltseq(-1/14);
4 Y( e8 @& ]: B; z+ n% G# n/ {
9 H0 y; y( ?# j% x6 B! l- r


! V, H. U( U$ u9 \, B+ m7 y: v0 Lk := Z ! elt< QuadraticField(-3) | -1666666666234567890, 0>;
> k;
" b, `( Z/ @( H( l2 S% F+ m: {n eq k;
kk := Z ! elt< QuadraticField(-3) | -0x17213080A7E55CD2, 0>;
> kk;
( F% o4 ]" Y% p) l. kkk eq k;
$ [8 @: x7 k7 p" L, A  k/ h
k := Z ! elt< QuadraticField(-13) | -1666666666234567890, 0>;
7 ?; N* T1 D9 r( g$ v" h) M' e> k;
n eq k;
! Q' W9 {. G" n; Z( q2 j& Rkk := Z ! elt< QuadraticField(-13) | -0x17213080A7E55CD2, 0>;
# \8 ~8 s' x* W$ `> kk;
kk eq k;

Eltseq(kk) ;Eltseq(-1/14);
+ x! ^! @% b) h# ^+ x- ]  `) G8 j

' a6 ?1 {% M" m$ @




; Q* C9 z0 f& E( |# t  n

$ F% A' B7 j6 w* G7 Y6 s
$ i1 h9 G2 Y7 q) V0 @=============
8 W9 o, m9 H! A( M3 W


+ `, x8 A( ^1 x" G" w# s
$ m2 K& w% `* {+ YInteger Ring
-1666666666234567890
-0x17213080A7E55CD2
-1011100100001001100001000000010100111111001010101110011010010
-1666666666234567890
- A9 m4 e: S- f  V$ O-17213080A7E55CD2
5 R& a+ ?. J: p# m2 O2 [; i5 q-CNUO0WGPY9CI
" S+ l- T$ w( g5 J! m-1666666666234567890
-1666666666234567890
0
1
, r$ ?/ T/ o* `8 ?* O# d0
! n% g; A- [8 M- i! r7 y" u3 D& Z2 D[ -1666666666234567890 ]
[ -1666666666234567890 ]
1
. V5 K3 m7 r2 \3 k* d13
1
! P& J+ z- }9 z) p  K8 D
-1666666666234567890
true
# r( p4 D5 O3 J-1666666666234567890
: @% q& X: }' Otrue
-1666666666234567890
true
! D6 Z: {4 _. c0 o& y( ]7 D1 l-1666666666234567890
true
[ -1666666666234567890 ]
' B( D: a( Q4 x; W6 n4 o5 `[ -1/14 ]

* F; l/ H9 V3 \4 R5 {


; Y7 Z1 k- [) w! ]- U* d5 \
: Y. O: ]/ w5 H  W
8 E' Q5 u$ m  n6 }, G
$ n) Q  J6 Z% t2 o1 B. H; r/ O-1666666666234567890
8 u7 _" Y, J- X  _, R-1666666666234567890
( x4 d( O8 c$ ]5 a% Etrue
% T6 Q% Y9 ~$ K8 ^9 A: O2 i-1666666666234567890
1 ], m- ]4 W, J0 H* F0 P% x$ J% a* mtrue
4 X4 e* ?: v" V1 O-1666666666234567890
/ |: l3 K& Z5 S$ E6 |1 {true
-1666666666234567890
true
[ -1666666666234567890 ]
1 c! \/ Q1 e6 W9 D: Y7 m[ -1/14 ]

孤寂冷逍遥

lilianjie

ss:=12345678111;ss;
s:=0x12345678111;ss;
- {0 g4 n! y  V6 {' O
8 L; z/ Y3 w6 j5 msss:=Factorization(ss);sss;
. z2 \& {4 G. c. F* msss1:=Factorisation(s);sss1;
FactorizationToInteger(sss);
5 w9 K4 G! }. q7 R8 ^. v) w7 {FactorisationToInteger(sss1) ;
Facint(sss1);因子分解和还原ssss:=Intseq(ss, 2);ssss;
SequenceToInteger(ssss, 2);
ssss:=Intseq(ss, 17);ssss;
4 m: w* t! \& ]& rSequenceToInteger(ssss, 17);
ssss1:=Intseq(s, 17);ssss1;
  P. e, ]- T3 t8 _! YSequenceToInteger(ssss1, 17);转成2和17进制

12345678111
) X+ f1 R2 X* _: W! b12345678111
& y1 C2 H, Y+ u! f4 s6 X[ <3, 1>, <13, 1>, <31, 1>, <1447, 1>, <7057, 1> ]
2 `: Y3 o* V+ e- @[ <3, 1>, <83, 1>, <34129, 1>, <147209, 1> ]
( L4 L/ ^1 N- G: K$ c12345678111
% [) p6 U. Y  M4 `1250999894289
2 t2 f" B! T% T5 ?% n3 e9 k" W/ C$ x1250999894289
[ 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 ]
5 y3 j: P& t/ b. ^$ @12345678111
7 V1 w, ~; O9 O[ 8, 6, 6, 4, 0, 8, 1, 13, 1 ]
12345678111
[ 14, 6, 7, 11, 9, 15, 11, 5, 9, 10 ]
1250999894289

lilianjie

& ~$ e2 V: E  Q  S: E
Z:=IntegerRing(5) ;Z;           模5等价类环n := 1666666666234567890;
> n;
$ @; m! X6 g& g5 `* b$ y3 h: An1:=Z!1111111111111111111111;n1;
n2:=Z!11333331111111111111111;n2;
0 u* W; u; W3 o; ]3 |$ e/ S+ J. X

9 h' m$ _1 I: C4 t4 r8 w2 ]1 iK:=Z!n1+Z!n2;K;

9 K& h( w. F# H& K4 w) WIsField(Z);      是域吗Characteristic(Z);环特征
7 J" C1 J2 M, @* ]2 ^& KIsFinite(Z);有限环吗
) i/ l. j; w$ C1 @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。。。。
) o7 l$ Y+ O8 _0 L! q2 G7 E) nIsPID(Z) ;主理想整环吗

4 V/ p( H. E. b3 j- m) fIsUFD(Z) ;唯一分解吗
IsDivisionRing(Z) ;除环吗
IsEuclideanRing(Z) ;欧环吗
3 a  Z0 t2 K0 Q. y! fIsPrincipalIdealRing(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
Category(Z) ;范畴Parent(Z) ;父环
! P& N& g: I% O$ t) [' C* [% yPrimeRing(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

( R# x) |/ |$ D/ w2 ^) z6 iZZ:=IntegerRing() ;ZZ;
ClassGroup(ZZ) ;
6 r0 X0 K2 i2 w5 s' d
! ^# r5 @* f/ z1 A===========

Residue class ring of integers modulo 5
0 A, K0 L9 {/ a  m2 q4 H  N1666666666234567890
1
; b* G7 f( ~/ k1
- @/ a( `! O) p: Z2
true
/ n* {" K9 \; o5 S5
true 5
true
false
. V3 X: l9 a7 @/ H# itrue
3 k6 W* R, u1 ~  e2 _! K7 N+ F7 Ltrue
true
true
true
true
: M, a' Q" r6 |0 B( w' {true
Residue class ring of integers modulo 5
4 b% t! m; a+ R! Y+ @0 p0 x# O% NAbelian Group isomorphic to Z/4
Defined on 1 generator
: Z& F& p3 @& x$ ]6 C! k' _$ y7 @Relations:
    4*$.1 = 0
Abelian Group isomorphic to Z/4
Defined on 1 generator
Relations:
    4*$.1 = 0
% X; [# S5 W+ T& SRngIntRes
# I& X5 z. j. p# SPower Structure of RngIntRes
0 i: W# [. V5 J, y3 t" \( [6 dResidue class ring of integers modulo 5
* o& ^( _) a- Z( s, |. R) U0 |Residue class ring of integers modulo 5
* c; `) W: ]: KAbelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
    5*$.1 = 0
8 i2 P$ t* ]7 d% Y/ `: L
>> ClassGroup(Z) ;
4 P/ K3 |" e4 Z" \             ^
" D8 H% Z9 E" z' cRuntime error in 'ClassGroup': Bad argument types
% Z" F* ~+ u  sArgument types given: RngIntRes
' g$ E5 B2 i" j
6 [% M7 `9 F7 cInteger Ring
! M8 b( s" B3 \; k2 @+ ^9 K' tAbelian Group of order 1

lilianjie

Z:=IntegerRing(12) ;Z;   
1 Z1 Y2 N  B/ m4 f; p) o UnitGroup(Z);
' l) U9 P4 D# CMultiplicativeGroup(Z);
3 c! A8 i! S4 GCategory(Z) ;
PrimeRing(Z);
% \& v0 C* d5 D  }% EAdditiveGroup(Z) ;

( G: E% _' d! K' X9 FZ:=IntegerRing(13) ;Z;   
UnitGroup(Z);
2 u" a5 q0 [% G1 D& w- P- x2 k8 IMultiplicativeGroup(Z);
Category(Z) ;
PrimeRing(Z);
AdditiveGroup(Z) ;


" U) V9 ]6 W9 \$ p# r
Residue class ring of integers modulo 12
. j) z' R. m: P, R) V: \5 aAbelian Group isomorphic to Z/2 + Z/2
0 P8 D0 H8 h  \( C  }& j) EDefined on 2 generators
* i& w( t: o: h' h9 S6 PRelations:
    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
$ ]% a6 c; M' V    2*$.2 = 0
3 J/ y% Y" g5 q- vRngIntRes
! w; W3 Z$ @4 sResidue class ring of integers modulo 12
Abelian Group isomorphic to Z/12
Defined on 1 generator
. U0 H& V) }0 x1 ^8 |Relations:
2 w7 h0 w7 Z1 @7 [    12*$.1 = 0
Residue class ring of integers modulo 13
9 {) n) S' `3 T/ `( _Abelian Group isomorphic to Z/12
& i) e. d- L! \# r0 }% \Defined on 1 generator
3 W6 T8 p4 Y! H2 c8 {3 ^- KRelations:
    12*$.1 = 0
7 f# l& Y# O# _6 O1 ?Abelian Group isomorphic to Z/12     素数环的乘群同构Z13-1=Z12Defined on 1 generator
Relations:
, P# {8 I& P; F0 R5 \2 g    12*$.1 = 0
RngIntRes
Residue class ring of integers modulo 13
5 o  L) c. i! h1 l. C1 U& ?! sAbelian Group isomorphic to Z/13
Defined on 1 generator
Relations:
    13*$.1 = 0

lilianjie

Z:=IntegerRing() ;Z;   
5 c/ [& C! \1 y! ?7 F$ d
& S, K% z. D; g, `R:=IntegerRing(12) ;R;   
" B' E! P* h. sS:=IntegerRing(13) ;S;   
( t5 o0 m! v8 e
, ^' F: O, `; u* I
' c1 ?# p2 f, `+ j1 O9 ~PrimeRing(R) ;
0 L# Q# v+ R! N9 O7 |( cCentre(R) ;

Characteristic(R) ;
# 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) ;
9 E, _* _4 R3 \* R# Y# zHas**(R) ;

IsPID(S) ;
IsDomain(S) ;
& {) f6 U6 T0 n0 RHas**(S) ;
R eq S ;
* P* \9 V, l4 k- z5 M  m0 [R ne S ;

Parent(R!123) arent(S!123) ;
Category(R!234) ;Category(S!234) ;

a:=Random(R) ;a;b:=Random(S) ;b;
& {$ X+ g, C% oRepresentative(R) ;
Representative(S) ;

  G$ g% H5 O5 s# H% s9 \! U0 }% ^(R!a) in R ;
) G% B0 z7 W2 {3 d8 i(S!b) notin S ;
IsUnit(a) ;                是单位吗
IsIdempotent(a) ;是幂等元吗
- b  l2 `9 ^$ T0 a$ fIsNilpotent(b) ;是幂零元吗
IsZeroDivisor(a) ;可除零吗
- N! u/ |: q  l9 NIsIrreducible(Z!b) ; 可约吗IsPrime(Z!a) ;

Z!a gt Z!b ;
Z!a ge Z!b ;
3 h1 t3 I5 }' v! u. gZ!a lt Z!b ;
% h' w: X% G6 d( k' o) wZ!a le Z!b ;只有同类环才可比较元素大小，Maximum(Z!a, Z!b) ;
2 Q2 f# J- C8 m4 b5 \Minimum(Z) ;
# U; h' y8 J, |7 N
; C6 X* |( g2 x2 g( z) E) KMaximum(S) ;
Minimum(Z!a, Z!b) ;
Minimum(R) ;
% t) o" Q) G. `$ n8 W. z


3 X8 [( A& u- N5 ZInteger Ring
Residue class ring of integers modulo 12
Residue class ring of integers modulo 13
4 m6 F4 G' }: Q8 @; n6 lResidue class ring of integers modulo 12
Residue class ring of integers modulo 12
12
12
! ?( T, T" D# _* Cfalse
2 v. B6 G2 i, A2 U, [false
, {& Z& G  n7 e5 k6 b# r) [4 O$ jtrue
true
true
true
false
, V- V4 k% G3 M% M% u8 [' g  ytrue
Residue class ring of integers modulo 12
Residue class ring of integers modulo 13
RngIntResElt
) l$ b3 a- P# h0 G  WRngIntResElt
+ i- s6 L" G+ W5 @# @7 E9
6 b. Q( `0 z- I12
6 j' z, x6 {* s0
: n1 }6 P8 S2 Q9 ^' r0
. |3 e% T: w  s: m2 L  ~9 y6 }7 xtrue
- ?* n$ G8 l" Ofalse
false
# c' i  f' w  [" ]) Wtrue
false
true
false
false
! B& f' c- E  k" [# f8 kfalse
false
true
" I5 ^( m1 G  Y+ d4 i3 utrue
12
5 I' g, [5 O- U4 _' o5 z$ ~1
2 H5 n" o, L  X
>> Maximum(S) ;
# y% q" M( R  t          ^
' f% _) N* S9 TRuntime error in 'Maximum': Bad argument types
Argument types given: RngIntRes

6 I1 V0 t  _/ k4 P9
8 E4 M: B2 V6 v" M
8 o7 E2 e- z$ a, r: q>> Minimum(R) ;
) F( v3 ~* r7 z          ^
7 W0 D/ L; I, a, G/ yRuntime error in 'Minimum': Bad argument types
Argument types given: RngIntRes

lilianjie1

Z:=IntegerRing() ;Z;   
4 @/ ]  R- |' b5 ?  p) l) tI12:=ideal< Z | 12 >;
I12;
+ b( l6 n5 S% q# l3 z3 SZZ:=IntegerRing(15) ;ZZ;   
+ C: x* t# l9 ]: y* I7 |IZZ15:=ideal< Z | 15 >;
IZZ15;
7 w) ^- E4 J. Q0 H0 @$ K; PI12 eq IZZ15;
) k1 i$ y1 |; ^. _, \7 CQ1:=quo< Z | 12 >;Q1;
ZZZ:=IntegerRing(5) ;ZZ;   
IZZZ5:=ideal< Z | 5 >;
IZZZ5;

I12 *  IZZ15;            理想和/积/并/交，
理想和是理想对应两（可多个）元素加，
/ r* c4 T9 B) `  ~- K理想积是两理想（可多个）对应元素积，
5 |$ t7 L! p1 I, {理想并就两（可多个）理想元素并，就不一定还是理想，
4 W4 E" t- L0 E2 _- L# x6 K" i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
5 M, s3 m% i% F' u* l. r理想商就理想间同态：是必须能整除
I12 +  IZZ15;
I12 meet  IZZ15;

I12 * IZZZ5;
& D5 D+ Z. J9 Y! S/ {: i. p# y  x( zI12 + IZZZ5;
I12 meet IZZZ5;
I12 / IZZZ5;
! O7 b4 t3 P- F6 |+ g% a% z& HIZZZ5/ I12 ;
, k" G  \3 v' l* z1 ^Z * IZZZ5;
, w: _8 M0 T6 PI12 + IZZZ5;
6 _( ]9 v  o+ e2 o) O  j6 KIZZ15 meet IZZZ5;
1 I4 l/ O7 R  Q+ k+ Z, W6 U+ ~IZZ15 / IZZZ5;Z meet IZZZ5;
I12 meet IZZZ5;
- s) Q2 u) p9 ?  X5 a# N) iIZZ15 meet IZZZ5;
IZZ15 / IZZZ5;
( @7 i" [6 }  v" y0 n# V( [
1 f7 z5 y$ O* B2 _# LI12  subset  IZZZ5;运算后的各种理想互相是否包含IZZ15  subset   IZZZ5;
. T- i" g. B! _# `4 U) U4 SIZZ15 subset IZZZ5;
IZZZ5 subset IZZ15;
/ e' ]4 q0 g5 jInteger Ring
2 S) E: Q: p: ]0 _+ e' X7 XIdeal of Integer Ring generated by 12
Residue class ring of integers modulo 15
& S1 E- v3 {) }) LIdeal of Integer Ring generated by 15
false
Residue class ring of integers modulo 12
Residue class ring of integers modulo 15
Ideal of Integer Ring generated by 5
3 e" H% f! I; q/ _3 r; vIdeal of Integer Ring generated by 180
1 N' k: U$ W7 u6 b2 T5 s' Y; U1 jIdeal of Integer Ring generated by 3
; ~! f# J: ^8 M0 p+ ?. n* e+ ]Ideal of Integer Ring generated by 60
3 ]1 [- x2 s* E% a3 W+ t8 L/ t( i7 N) kIdeal of Integer Ring generated by 60
Integer Ring
. P: D  }2 s" `% R5 G' _5 C: h6 aIdeal of Integer Ring generated by 60
' `! f- ?. P, O4 j8 |' `+ n* t; [" J
>> I12 / IZZZ5;
       ^
* i8 K6 m9 B% K7 d' O& V5 ?, n' jRuntime error in '/': Argument 2 must divide argument 1.


>> IZZZ5/ I12 ;
        ^
Runtime error in '/': Argument 2 must divide argument 1.
, m& K. Q( i& `! C; A6 h- O* o
Ideal of Integer Ring generated by 5
Integer Ring
Ideal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
) y! w$ O$ r# o% i! LMapping from: Ideal of Integer Ring generated by 3 to RngInt: Z
& ]/ E% J6 I2 a* e+ u0 }Ideal of Integer Ring generated by 5
Ideal of Integer Ring generated by 60
Ideal of Integer Ring generated by 15
" O% M" g5 e# Z: j; ~Ideal of Integer Ring generated by 3
! X3 a  u# ~+ m/ p2 ?Mapping from: Ideal of Integer Ring generated by 3 to RngInt: Z

% n5 ~' [( y. H) U) wfalse
$ @) V0 e) V5 @3 Ptrue
! J$ }  C1 T5 c; ]/ h  otrue
false

lilianjie1

Z:=IntegerRing() ;Z;   
0 j  D( w" I: ?9 PI12:=ideal< Z | 13 >;
I12;
" U( X* f: k9 u( ?1 G: F* K) P7 B) ~ZZ:=IntegerRing(60) ;ZZ;   
1 ~& P; d/ d- E- }0 AIZZ15:=ideal< ZZ | 31 >;
( c  e* E6 r; g( CIZZ15;
% R& |8 n" s4 \0 hResidueClassField(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
ext< ZZ | > ;
1 m) W  q; |  i' T6 n% p& Z- e
! z4 I* v# i. q0 _3 t8 ]( next< Z, 2 | > ;超越扩张到多元多项式

ext< Z, 3 | > Completion(Z, I12) ;
" v! V  f# u9 P
8 z5 `: j( Q3 C2 `9 Y0 K- q) W
. l& w& U3 d; t5 ?5 mcomp<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  >;

# Y+ ~: k8 e; n6 ?8 |  x# Y$ ?1 kInteger Ring
Ideal of Integer Ring generated by 13
5 g9 ~! p( \4 N7 u3 l% gResidue class ring of integers modulo 60
! o  I+ A- ^5 ^& hResidue class ring of integers modulo 60
1 F" a0 o& z4 y4 T; N3 U9 xFinite field of size 13
Mapping from: RngInt: Z to GF(13)
  o, P! f  E3 a  y( \modulo 13

3 s5 w% L! `. M# O$ g: C7 X0 L>> ResidueClassField(IZZ15);
                    ^
Runtime error in 'ResidueClassField': Bad argument types
Argument types given: RngIntRes
/ a- }* ]0 p. f6 V4 R8 L0 Z1 p
Valuation ring of Rational Field with generator 19
5 N* D; P2 `3 R' _7 s5 {Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 19
Valuation 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
Mapping from: RngInt: Z to Valuation ring of Rational Field with generator 131
- W& F0 I' s  x+ f0 @/ JUnivariate Polynomial Ring over Integer Ring
Univariate Polynomial Ring over IntegerRing(60)
! l1 d; b6 |. g9 p3 g: G+ c
: V- m9 J5 o# x5 k; k>> ext< Z, 2 | > ;
8 I" i5 W9 Q- V; \3 R4 d7 U      ^
Runtime error: This constructer is no longer supported

1 U5 g; d1 x% v" ~; T* E4 C
>> ext< Z, 3 | >
) |" e% B# B+ [$ s# u; Z      ^
Runtime error: This constructer is no longer supported
9 K( q9 M& I1 w/ ^
13-adic ring
Mapping from: RngInt: Z to pAdicRing(13)
) Y; ^- ]2 _  ?7 }) z
# J5 X' g; D/ k5 t3 P# ?Completion(
    Z: Integer Ring,
    P: Ideal of Integer Ring generated by 0
0 B. T% G0 q' P! v4 p! D