res cherif arithm
DESCRIPTION
bacTRANSCRIPT
-
Z fr.ift.arabmaths://http
: . :
I- Z : rq ba +=/ ( ) ( ) INZrq,! Zb,a * 2
b r 0. ) )rq,
. b a a b q r
. II- - Z :
.Z b a kab = /Zk) a b (b/a.
/aa : Z a ( ) b/ab / a :INn Z b,a n* 2 ba = ab ( ) ba: Z b,a 2 5 ( ) Z c,b,a 3 ( ) ba d:Z, + 2 bd a/d
III- : [ ] ( ) banZk knban ba =
[ ] [ ]n bcacn ba [ ]n cbca ++[ ]n ba
[ ][ ] [ ]n bdacn dcn ba
5 [ ][ ] [ ]n dbcan dcn ba
++
IV- : . Z d b a d a b :ad bd. b a
: b a ba ) )b,a pgdc ( )b ; a
bd adbad =
ba 'd b 'd
a 'd
5 a b 1 = ba
6 ( )
===
=2
d.b'b d.a'a1 b' a' /Zb',a'
bad
7 vbuad +=/ ( ) 2= Zvu,bad 8 1=+ vbua 1= ba) bezout(
9 c abba
c b c a
1=
( ) b/dad
ab/d:Zc,b,a
1= 3 )Gauss(
( ) 1=
1=1=
bcacaba
Zc;b;a
( ) 1=1= 2 nn* baba:INm,n [ ] rbbabr/rbqa =0+=
V- : . Z m b a m a b m/a m/b
b a : b a
ba ) )b;appcm m/b m/ a bam =
( ) ( ) c ba c b
c a : Zc,b,a
3
5 ( ) ( ) ( ) b.a ba ba:Zc,b,a = 2 VI- :
a d .Z d a a , -a , 1, -1: a d
a . -1 1
: . 1 , -1, 0: - . -
. p apap n
bp ap abp
5 { } iin ap :n,....,a.......aap 1 21 6 a p pap =
7 1 a p a p = VII- : b a: IN b a .
: b a 00 += rbqa br 0 0
0r=0 : *bba : ab : =.
br 0: * 0 .0r b
110 += rqrb b r r 0 01. 1r=0 : *
-
Z fr.ift.arabmaths://http
: . :
00: br0: == rrbba. 1r0 : *
.1r 0r 2210 += rqrr12 0 rr.
* .
VIII - :
-1 1 n :
( ) rrp........pp n 21 =1= 21 rp..... 2p 1p :
. , 12 ...... r
.
1=
=n
ii
ipa 1=
=n
ii
ipb
)ip . ;IN ii nj;i : 1
( )1=
=n
i
;infi
iipba ( )1=
=n
i
;supi
iipba
IX - Nz/Z: ( ) [ ] k.nb-a nba : Zb ; a = 2
. "" ) x )Zx:
[ ]{ }n xy/Zyx ={ }Zk /n.kxx +=
"" ) : nZ/Z ){ }1-n;...; 1 ; nZ/Z 0=
( )
yx y x ; yx y x
: nZ/ZnZ/Zy ; x
=+=+
( )+ ; nZ/Z . ( )+ ; ; nZ/Z
. n a nZ/Z 1= na
==1: ( xaax / nZ/Zx (
X : :x 2 x
: b 01
11 ++++= ax.a....x.ax.ab
nn
nn
] na0 ]1-n ; a i 0 : [ ]n ; i 0 :
( )nnn aa....aab 011=
( )n
nn aa....aa b 011 .x
:
( )bnn aa.....aax ) =011 )bmm cc.....ccy 011= n m: . xy :
:
( )bnn aa.....aax ) =011 )bnn cc.....ccy 011=
nn ac = , 11 = nn ac , 1+1+ = ii ac ii ac ic ia y x
Baltasar Graci 1601-56 Spanish