数学建模社区-数学中国

标题: 一些初等函数： [打印本页]

---

作者: lilianjie    时间: 2012-1-11 12:30
标题: 一些初等函数：
:=IntegerRing() ;Z;
6 `1 P- m* }, Z6 m3 Vn := -1666666666234567890;
) m6 D( |0 i0 b8 x2 O5 S2 c> n;
: ~2 a% E; C4 }( y5 b  H
  N  J( t0 Q5 }  h> n:Hex;                           转16
; S, E8 T$ J' L- UIntegerToString(n, 2);        转2
IntegerToString(n, 10);       转10
: I# M& L7 _, N: F; W3 hIntegerToString(n, 16);        转16
7 I8 R+ V" M3 @) g& d% nIntegerToString(n, 36);         转36IntegerToString(n) ;
$ q9 E; z- H# o/ r4 A2 |% oIntegerToString(-0x17213080A7E55CD2);转串Zero(Z);
/ J' y; X$ Y* w1 Z. m* zIdentity(Z);                  
5 a3 P; @( P! N4 WRepresentative(Z);         环代表元
0 s# l/ v9 ?( n* r, F( Z7 P6 XEltseq(n);                        取整
/ i; b% J, e& Y3 m3 \Eltseq(-0x17213080A7E55CD2) ;Denominator(n);Denominator(12/13);Denominator(222222/111);
3 A; {+ O! d# ?* I
m := elt< Z |  -0x17213080A7E55CD2>;m;         在虚实2次域中进制砖换不变
k := Z ! elt< QuadraticField(3) | -1666666666234567890, 0>;
> k;
n eq k;
kk := Z ! elt< QuadraticField(3) | -0x17213080A7E55CD2, 0>;
! u* Y* p+ P2 M2 a) E> kk;
kk eq k;

k := Z ! elt< QuadraticField(13) | -1666666666234567890, 0>;
- I; D* K8 S: f3 Y> k;
5 h7 j% a8 f4 i" y# O8 i7 xn eq k;
kk := Z ! elt< QuadraticField(13) | -0x17213080A7E55CD2, 0>;
> kk;
* [! G+ P2 \* e9 |kk eq k;
( W2 W+ R8 O6 b8 c
; t* D  R) p0 P& U- \Eltseq(kk) ;Eltseq(-1/14);
, r% g/ p( K3 [" l! |2 c3 f
- j5 x: b; l) H" l4 z! s9 X1 E
6 f/ P4 }3 h6 @) A! l; a

k := Z ! elt< QuadraticField(-3) | -1666666666234567890, 0>;
> k;
n eq k;
kk := Z ! elt< QuadraticField(-3) | -0x17213080A7E55CD2, 0>;
% ]3 C, A) z& E4 Y) o8 x> kk;
# O$ O0 X8 _" ~/ H6 V2 @kk eq k;

: t. L# d0 X! L% p! Q8 k8 i# Dk := Z ! elt< QuadraticField(-13) | -1666666666234567890, 0>;
> k;
3 x, j1 C' C. i% E5 h$ bn eq k;
. ^1 Q- @1 s. D1 P; B* Kkk := Z ! elt< QuadraticField(-13) | -0x17213080A7E55CD2, 0>;
3 V3 X- r. u9 M/ e& j$ |> kk;
" I/ }& B$ |2 E# Lkk eq k;

9 V' X5 o0 O8 c6 |8 W. ]# A1 }' O% KEltseq(kk) ;Eltseq(-1/14);
/ C  F  n4 ~1 ^

1 Q9 U& m' k$ X& ^

; T5 d* o+ n2 c4 l, v$ Z
  T8 N0 b7 D; K6 Z7 m$ Y
6 j4 s6 F3 r: D3 _2 e* Q


  x) e, Y( w& E5 f# ~/ ]8 U2 t$ {1 V
% U# a6 b$ _2 y. _5 ~=============


) d5 k0 |" M+ D. E0 J# R& `

6 ]$ r4 v6 ~" U2 @/ r1 eInteger Ring
6 z) q. R7 J1 ~$ Z0 u# @6 k/ R-1666666666234567890
3 F: ~; ]* H, h- x% b& z, R-0x17213080A7E55CD2
-1011100100001001100001000000010100111111001010101110011010010
-1666666666234567890
-17213080A7E55CD2
-CNUO0WGPY9CI
-1666666666234567890
$ |; u* Q/ J3 |7 V# J! O4 s! c-1666666666234567890
0
+ w+ w9 y# U% \% b1 \& `1 a8 X1
  w# ?) `' K  o( e' @2 D0
' }( B  {4 _& {. S2 a6 Z[ -1666666666234567890 ]
[ -1666666666234567890 ]
. V: D8 r9 K9 q  Y( w$ W1
13
/ e; Z' b5 H$ [! f1

, `& N. l: U2 j1 d. A/ P, s-1666666666234567890
true
* N% G5 u: \+ ?5 F  B-1666666666234567890
true
- r4 {3 z5 ~& ?  G, X-1666666666234567890
6 n. j7 n5 y2 \2 ]" ?! w# dtrue
8 K# k2 q( ^! S3 \8 l-1666666666234567890
true
0 j8 C& o: W: {/ o$ h1 ][ -1666666666234567890 ]
8 g# _5 E! s$ ^* Y[ -1/14 ]

* U" R7 E; l) G2 ?) {6 W/ J' V

4 V" E& s" |2 _/ @/ `
- [3 u% Y2 H3 i, p9 }$ k
( h4 r7 [- ^% |" Z' V
  I; v- A/ q$ A+ T& U  a% W
-1666666666234567890
-1666666666234567890
true
-1666666666234567890
, C9 R# Z& V$ K( o6 i. Btrue
-1666666666234567890
; Y) l4 B5 `8 ~' \true
-1666666666234567890
true
[ -1666666666234567890 ]
+ n7 \( S  o) K8 D4 P[ -1/14 ]
) i" ~& F2 H" z5 }$ a. b2 v8 Z

---

作者: 孤寂冷逍遥    时间: 2012-1-11 12:42

---

作者: lilianjie    时间: 2012-1-11 12:49
ss:=12345678111;ss;
s:=0x12345678111;ss;
, q/ e/ ^: {( Z! v) d1 Y5 f
& }1 P( f4 H" B/ z4 V" dsss:=Factorization(ss);sss;
6 ]" D+ {  J! Q8 t) u" fsss1:=Factorisation(s);sss1;
FactorizationToInteger(sss);
! t2 h! Y" s. X) V8 [5 D9 Q+ |; L' aFactorisationToInteger(sss1) ;
. `, U1 |0 @/ u% }' ^7 IFacint(sss1);因子分解和还原ssss:=Intseq(ss, 2);ssss;
4 `2 H) _$ X+ R* w; T: BSequenceToInteger(ssss, 2);
& C3 M, m8 i: t7 R2 ?* Rssss:=Intseq(ss, 17);ssss;
4 k" t3 A0 B9 C" lSequenceToInteger(ssss, 17);
1 ]- J/ r6 f/ V, ?7 V0 i% y7 H* Vssss1:=Intseq(s, 17);ssss1;
# L4 ]1 }3 N7 ^) cSequenceToInteger(ssss1, 17);转成2和17进制
+ S0 S8 P. F  y( P8 t+ m4 T
/ v( a8 Q  t5 d1 q  G2 J. u  O12345678111
12345678111
& I1 H8 p6 L" O& L7 p[ <3, 1>, <13, 1>, <31, 1>, <1447, 1>, <7057, 1> ]
/ y1 n& A! L5 m1 n6 A. w[ <3, 1>, <83, 1>, <34129, 1>, <147209, 1> ]
12345678111
1250999894289
8 d4 W4 [' e/ [7 O/ }. `* ^+ l, r1250999894289
[ 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,
, {7 B# Z( A5 v2 t- }# U8 v3 A1, 1, 1, 0, 1, 1, 0, 1 ]
12345678111
) u, |' Y* b; _* n9 r$ o% b5 z[ 8, 6, 6, 4, 0, 8, 1, 13, 1 ]
12345678111
5 \7 U. i) }7 O9 \( ~% g; v[ 14, 6, 7, 11, 9, 15, 11, 5, 9, 10 ]
1250999894289

---

作者: lilianjie    时间: 2012-1-11 13:12


7 C# k( S& J) C: b. jZ:=IntegerRing(5) ;Z;           模5等价类环n := 1666666666234567890;
1 u3 F: E: O4 \5 [5 f& X/ K& [> n;
- ?/ L) X7 z( G; C) M4 bn1:=Z!1111111111111111111111;n1;
& R$ M2 o4 V  Y( Vn2:=Z!11333331111111111111111;n2;


- U2 k% Q) w% ]+ C0 `) tK:=Z!n1+Z!n2;K;
$ ]  v& z6 ~/ H' A) x1 m
IsField(Z);      是域吗Characteristic(Z);环特征
IsFinite(Z);有限环吗
* J2 \5 E5 ~/ R7 ^& {IsCommutative(Z);可换吗
* [( W. U( k7 X5 _. {( {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。。。。
. p, u4 S  U1 Q5 Q, qIsPID(Z) ;主理想整环吗

% f4 X' v" W. X9 S; L" QIsUFD(Z) ;唯一分解吗
IsDivisionRing(Z) ;除环吗
IsEuclideanRing(Z) ;欧环吗
IsPrincipalIdealRing(Z) ;主理想整环吗
IsDomain(Z) ;整环吗FieldOfFractions(Z);分式域
UnitGroup(Z);单位群
7 k7 o1 W2 p5 y  c( k/ MMultiplicativeGroup(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;
5 a& D4 v2 Q; B& z8 [ClassGroup(ZZ) ;
+ C$ B8 ^# d3 ]  B% H6 S: Z
===========

% v0 E6 _+ p: v2 \" `- }Residue class ring of integers modulo 5
' b- s! W, g8 m5 I; J1666666666234567890
1
1
( l0 B6 ^  j, @2
7 x2 S! P4 B' o' F- D" i' j/ B9 l8 vtrue
5
0 u( a# w+ Z$ ~1 j4 A& _true 5
2 O2 _/ a7 v! n5 Rtrue
false
true
) \( |, y5 t3 ]true
true
true
4 C: }# ]; y1 L/ e9 vtrue
- _- f# T. ~1 |. B2 [# ytrue
true
! a: J( Z. V# d; ?  V  f+ bResidue class ring of integers modulo 5
* a. a1 h- [; ]' i. ]! n" eAbelian Group isomorphic to Z/4
& W  Z$ w" U- v. [Defined on 1 generator
4 L, [5 ^' d6 ^' v4 _9 XRelations:
* M2 k7 f& F/ O, F7 p    4*$.1 = 0
2 |) y, t% F- N$ X2 xAbelian Group isomorphic to Z/4
3 d2 t/ P6 b0 T+ S- P' {8 lDefined on 1 generator
  C" w, I3 ~4 }5 X4 c& aRelations:
. ]. b- Y. _3 ]0 P+ Q5 X; y    4*$.1 = 0
& ~& ?# @% `  HRngIntRes
1 o8 F! [. e( G3 F" MPower Structure of RngIntRes
Residue class ring of integers modulo 5
1 @; M( b( s6 ]; I0 ]2 \& r0 uResidue class ring of integers modulo 5
Abelian Group isomorphic to Z/5
Defined on 1 generator
Relations:
    5*$.1 = 0

>> ClassGroup(Z) ;
/ m! q, P7 d" h& y6 V9 Z             ^
* X+ g1 F5 X; S. V; c* F# w5 r, @. ZRuntime error in 'ClassGroup': Bad argument types
. Y2 Z2 ~6 p% E9 J( V8 t# ?Argument types given: RngIntRes
2 o/ h7 L; C! V/ o
$ Q2 u: J  U: P8 J, @. \& XInteger Ring
/ I) o: j6 L6 @9 `- K: R# ^9 mAbelian Group of order 1

---

作者: lilianjie    时间: 2012-1-11 13:52
Z:=IntegerRing(12) ;Z;   
UnitGroup(Z);
% O. E. f7 d2 S# A& D' ]# kMultiplicativeGroup(Z);
Category(Z) ;
( _: g3 ]% k* ~- Y! `PrimeRing(Z);
AdditiveGroup(Z) ;

Z:=IntegerRing(13) ;Z;   
UnitGroup(Z);
MultiplicativeGroup(Z);
% w  k3 A3 y+ a' U$ zCategory(Z) ;
0 [% @2 j) Z9 Z: QPrimeRing(Z);
AdditiveGroup(Z) ;

; \! I* b" r  D8 X

" V7 A; ]' x# Q1 f( _' o2 b) `$ OResidue class ring of integers modulo 12
# P4 X/ ~/ }" H3 \1 x- v* e# NAbelian Group isomorphic to Z/2 + Z/2
Defined on 2 generators
/ h1 D2 q& y2 q) lRelations:
    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*$.1 = 0
4 G2 e6 Y& L; o% y3 A    2*$.2 = 0
+ R. Y& X" R8 y. g  yRngIntRes
Residue class ring of integers modulo 12
* r$ I/ }* L4 F' ^) J8 @+ z; B8 IAbelian Group isomorphic to Z/12
2 P' ^/ s; c# DDefined on 1 generator
Relations:
    12*$.1 = 0
Residue class ring of integers modulo 13
9 _5 E$ Z  L) m' XAbelian Group isomorphic to Z/12
' |" w! a7 y% L; C) k5 W' z* W+ l- YDefined on 1 generator
7 y7 i/ o- \2 W9 A$ eRelations:
- Z6 I" _' S5 O7 x9 r! ^    12*$.1 = 0
Abelian Group isomorphic to Z/12     素数环的乘群同构Z13-1=Z12Defined on 1 generator
/ f$ M' B+ p9 |! M$ u# v" gRelations:
    12*$.1 = 0
RngIntRes
. H$ u8 V' R1 N& D! w( RResidue class ring of integers modulo 13
Abelian Group isomorphic to Z/13
4 T5 Z. i. ?! j0 t/ r! ADefined on 1 generator
9 Z7 o+ ]' ]5 D; l4 T8 Y: ~Relations:
    13*$.1 = 0

---

作者: lilianjie    时间: 2012-1-11 14:24

% n  [: A& r6 B- s- C% _6 G& o
Z:=IntegerRing() ;Z;   

R:=IntegerRing(12) ;R;   
* m1 ]) V7 m7 H6 e& k. t1 h6 FS:=IntegerRing(13) ;S;   


PrimeRing(R) ;
3 j5 m4 X  R9 J# f6 fCentre(R) ;
0 A* {9 ~$ e1 D( ]6 d9 W
) H8 @1 v( G5 eCharacteristic(R) ;
# R ;阶----元素数
, v3 K0 a% V% r5 `3 dIsPID(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) ;

: V5 I; J, s6 D) fIsPID(S) ;
3 Z: D9 Z" M- Z# \% p# p" AIsDomain(S) ;
Has**(S) ;
R eq S ;
R ne S ;
$ f$ `. F+ w; q, f% O4 s
Parent(R!123) arent(S!123) ;
. k  q0 J/ _- ^# d" N; SCategory(R!234) ;Category(S!234) ;

+ E) C( V3 p, }4 h+ ja:=Random(R) ;a;b:=Random(S) ;b;
( `* N) c; K7 i& zRepresentative(R) ;
Representative(S) ;
. ~5 I6 B: I$ u6 J% H
(R!a) in R ;
(S!b) notin S ;
: C  a5 n5 U# l. l. K( NIsUnit(a) ;                是单位吗
- C6 v$ Y+ N: i0 kIsIdempotent(a) ;是幂等元吗
IsNilpotent(b) ;是幂零元吗
' Y; ?+ ]) ?+ Z% u+ ZIsZeroDivisor(a) ;可除零吗
. q) B' [( W  ]: r( tIsIrreducible(Z!b) ; 可约吗IsPrime(Z!a) ;
% v: y* @, X0 g% `% ?/ j4 I  v
0 i6 q  n5 v6 TZ!a gt Z!b ;
Z!a ge Z!b ;
; X  o5 {$ U# I; o( GZ!a lt Z!b ;
6 \1 D$ ~% ?$ L3 W; vZ!a le Z!b ;只有同类环才可比较元素大小，Maximum(Z!a, Z!b) ;
! _* E' M5 N: Q+ |8 VMinimum(Z) ;

Maximum(S) ;
Minimum(Z!a, Z!b) ;
) D0 u% p& C) O5 N# [, sMinimum(R) ;


% H. `% ^% W' x" F% T
Integer Ring
0 T* O' U# l' I9 w$ KResidue class ring of integers modulo 12
4 X- j! d+ d% ^, i- VResidue class ring of integers modulo 13
! }9 n1 e4 V  w2 \# xResidue class ring of integers modulo 12
Residue class ring of integers modulo 12
( j1 g0 {; n) _) c  I5 I' K12
12
false
false
+ l# l& n4 d- l6 X! k( z: ?4 rtrue
true
true
true
false
, i" f! K8 t1 n2 strue
Residue class ring of integers modulo 12
: V0 R, z5 O! ]; qResidue class ring of integers modulo 13
RngIntResElt
% w- n/ y8 K/ }. MRngIntResElt
4 C) `9 w% @" l4 i" B9
# d4 {  Y) J) a" U4 b1 W12
* X( \1 h7 k3 o% k. c- A) G! R5 l0
0
true
0 z# B, K! H( F& R$ Q: \/ A0 D  z/ Nfalse
false
true
false
& o5 E1 K# f$ B8 X. [1 g& V/ Atrue
false
9 W. v; L- r/ B( E& s, c" Efalse
false
false
true
true
. D3 @1 P( q* N6 h12
1

>> Maximum(S) ;
          ^
# I  O5 N, ^9 |# lRuntime error in 'Maximum': Bad argument types
) k9 b7 w- V. ]' cArgument types given: RngIntRes
/ t; h, J, O( |8 c( N
% l) T' x- R& W+ I# H9
0 A% O. A8 w: u# B6 J
>> Minimum(R) ;
          ^
0 b  n  k: _! HRuntime error in 'Minimum': Bad argument types
Argument types given: RngIntRes

---

作者: lilianjie1    时间: 2012-1-11 15:48

& P3 ^/ _( k* M( t; O, e
Z:=IntegerRing() ;Z;   
# D' j% L2 U' E, x+ ~1 B5 i/ ]I12:=ideal< Z | 12 >;
I12;
ZZ:=IntegerRing(15) ;ZZ;   
  ?; S# s1 y4 ]- T4 JIZZ15:=ideal< Z | 15 >;
% ?) L: ~3 Q3 ]+ _  |9 D9 WIZZ15;
- h2 O! w# K; u' Z+ @I12 eq IZZ15;
Q1:=quo< Z | 12 >;Q1;
ZZZ:=IntegerRing(5) ;ZZ;   
7 m7 ^9 {' e/ n6 u6 ^+ u( L/ kIZZZ5:=ideal< Z | 5 >;
IZZZ5;
9 N4 z" Z& y8 ]( D, f& s
I12 *  IZZ15;            理想和/积/并/交，
, W* A" x' j# q# V  ]5 @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，
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，
' `& R: y9 x* o( l" }
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
8 d+ Q2 o4 V! y0 mI12 +  IZZ15;
I12 meet  IZZ15;
( v7 F) v/ m, G1 |3 J
I12 * IZZZ5;
I12 + IZZZ5;
- `) C; ~& [' m2 J6 V/ j) gI12 meet IZZZ5;
I12 / IZZZ5;
! K$ F  H4 p' G  W0 o/ E$ C3 G5 NIZZZ5/ I12 ;
0 ^9 F$ [# J; mZ * IZZZ5;
I12 + IZZZ5;
IZZ15 meet IZZZ5;
* y  a; _+ O9 ?  v& `IZZ15 / IZZZ5;Z meet IZZZ5;
I12 meet IZZZ5;
0 j% k% |' @$ D2 B  @$ f& B* cIZZ15 meet IZZZ5;
8 H( H! D. b. S+ a' HIZZ15 / IZZZ5;

! i" V/ O, X; j. b5 ?  P/ gI12  subset  IZZZ5;运算后的各种理想互相是否包含IZZ15  subset   IZZZ5;
IZZ15 subset IZZZ5;
0 L3 w+ `! i* W: x* MIZZZ5 subset IZZ15;
Integer Ring
Ideal of Integer Ring generated by 12
" o! }/ u4 o" `* A$ n9 ^; C! hResidue class ring of integers modulo 15
Ideal of Integer Ring generated by 15
# T) D7 W8 w0 c% p/ Q% ~9 ]false
, X1 L; a! r: X, H, ~Residue class ring of integers modulo 12
* x9 v2 w4 S3 y3 xResidue class ring of integers modulo 15
, W+ I0 F" ?6 X( fIdeal of Integer Ring generated by 5
; P( P% ~! C6 [8 z0 _5 }3 Y$ `Ideal of Integer Ring generated by 180
Ideal of Integer Ring generated by 3
5 `7 M1 _9 t: K- x: LIdeal of Integer Ring generated by 60
$ `; @) f9 _$ U. y6 ~  Y& {6 nIdeal of Integer Ring generated by 60
8 s# U, N3 C8 z" E2 q& _Integer Ring
Ideal of Integer Ring generated by 60

8 u8 H7 g  V1 I( k5 Y. V& \>> I12 / IZZZ5;
  R1 p: G& o4 v4 ^       ^
Runtime error in '/': Argument 2 must divide argument 1.
0 f' ]5 [! `% S; u: _! G! S
- U' M2 B, K6 Q' I& G8 ~  }2 Y
>> IZZZ5/ I12 ;
; ~$ v+ y  F) t; ~. r- h8 Y" b+ w        ^
Runtime error in '/': Argument 2 must divide argument 1.
, f- E5 C- J! D7 A6 T
( n$ w0 A2 J4 w1 C, {1 lIdeal of Integer Ring generated by 5
Integer Ring
7 j$ A6 W. L/ p* O9 j" \Ideal of Integer Ring generated by 15
2 N) X5 z8 }, Q/ f- d7 XIdeal of Integer Ring generated by 3
Mapping from: Ideal of Integer Ring generated by 3 to RngInt: Z
% Q4 o4 c& c9 _Ideal of Integer Ring generated by 5
Ideal of Integer Ring generated by 60
2 T1 t3 V# w7 S/ H; c7 g6 G$ }6 DIdeal of Integer Ring generated by 15
Ideal of Integer Ring generated by 3
# o) U" q5 |1 N9 @( A* l- }Mapping from: Ideal of Integer Ring generated by 3 to RngInt: Z

false
true
1 R$ u  P9 R8 G, qtrue
; D- B  V0 g. kfalse

---

作者: lilianjie1    时间: 2012-1-11 16:39
Z:=IntegerRing() ;Z;   
! }" ]; j, v* LI12:=ideal< Z | 13 >;
! Z6 h: J. i1 X) \# t6 ~0 CI12;
* `, G$ A* w/ `# J% ]2 O  BZZ:=IntegerRing(60) ;ZZ;   
IZZ15:=ideal< ZZ | 31 >;
IZZ15;
ResidueClassField(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> ;
% E' b" j) s: _- ]; g" zloc< Z | 17> ;
; p4 T! I: E7 b$ cloc< 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 Z9 U* x( l0 O# G. H  aext< ZZ | > ;
1 X% _* V3 l/ S8 H& [6 Q. s
4 z- z$ Z% x" H+ \2 p3 vext< Z, 2 | > ;超越扩张到多元多项式

ext< Z, 3 | > Completion(Z, I12) ;
/ m1 O( X9 m% G% A9 w8 X
" k6 [) i  n* P! Y. U/ n
8 Z2 q- s2 S( _. Vcomp<Z |I12  >;
4 ~0 N3 @  ~9 j. M8 t4 `( n  a    素理想零理想完备化，和P进环联系起来
  y" D* U; a9 i! y- u! p2 |Completion(Z, 0) ;
3 g" ~0 f" j/ U. e2 T' s5 z- f( g. Ccomp<Z |0  >;

Integer Ring
+ l4 }, p; a) \% I2 h- T) WIdeal of Integer Ring generated by 13
Residue class ring of integers modulo 60
3 i! n! ]2 H' I# Q* dResidue class ring of integers modulo 60
' n. g# L" {7 bFinite field of size 13
Mapping from: RngInt: Z to GF(13)
/ K1 y/ N8 N, w2 m$ x7 Omodulo 13

>> ResidueClassField(IZZ15);
* }, V8 F) b1 e) @                    ^
Runtime error in 'ResidueClassField': Bad argument types
Argument types given: RngIntRes

Valuation ring of Rational Field with generator 19
; \, G6 p' a) K6 K: wMapping 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
" n$ L* V8 o0 vMapping from: RngInt: Z to Valuation ring of Rational Field with generator 131
Univariate Polynomial Ring over Integer Ring
; M9 C. V+ h3 @  }3 ]- iUnivariate Polynomial Ring over IntegerRing(60)

( N5 O. M& g# I7 ?0 h/ d: A; Z3 v>> ext< Z, 2 | > ;
) c) b* A; n1 }2 v% u; u/ U( R, e      ^
Runtime error: This constructer is no longer supported
) ^) J- s# _/ u! a# h6 L
9 i, d3 Q* s- i/ @0 u; [; U( S$ J. H
4 z, A- C/ G0 }& N6 m2 x>> ext< Z, 3 | >
3 u. [4 \  u/ }      ^
7 S; H8 a6 z, h8 F; p  z8 G" D" h# |Runtime error: This constructer is no longer supported

% a7 w: _2 ?- J  u  G# k5 Y13-adic ring
Mapping from: RngInt: Z to pAdicRing(13)
) o% }8 W; g% T1 z' k
Completion(
% a# c# c2 M3 x" o: _9 l    Z: Integer Ring,
    P: Ideal of Integer Ring generated by 0
# I5 _( C7 d& G% s

---

欢迎光临 数学建模社区-数学中国 (http://www.madio.net/)

Powered by Discuz! X2.5