ÿþ ( A - G )
n m
i j
g ( t ) = g ( t 1 , . . . , t m ) = c i ( t j ) ±
i = 1 j = 1
t = ( t 1 , . . . , t m ) t j > 0 j = 1 , . . . , m
c i > 0 ±i j " R j = 1 , . . . , m i = 1 , . . . , n
R o z ( A - G )
x 1 . . . x n > 0 ´1 , . . . , ´n
» = ´1 + . . . + ´n
n n
»
i i
x i e" »» ( x ) ´ , R o z ( A - G )
´i
i = 1 i = 1
i
0 0 = 1 ( x ) 0 = 1
0
R o z ( A - G ) ´1 = . . . =
´n = 0 » = 0
n
´i
x i = x i , i = 1 , . . . , n , » > 0 .
»
i = 1
t = ( t 1 , . . . , t m ) g 0 , g 1 , . . . , g k
ñø
ôø
ôøg 0 ( t ) ’! m i n
ôø
òø
( C G P )
ôøg 1 ( t ) d" 1 , . . . , g k ( t ) d" 1 ,
ôø
ôø
óø
t 1 , . . . , t m > 0 ,
( C G P ) k + 1
n m
i j
g ( t ) = g ( t 1 , . . . , t m ) = c i ( t j ) ± .
i = 1 j = 1
l 1
l m
u l ( t ) = c l t ± . . . t ± .
1 m
( C G P )
ñø
ôø
0
ôøg 0 ( t ) = u 1 ( t ) + . . . + u n ( t ) ’! m i n
ôø
ôø
ôø
ôø
ôø
ôø
òøg ( t ) = u n ( t ) + . . . + u n ( t ) d" 1 ,
1 + 1
0 1
( C G P )
ôø. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,
ôø
ôø
ôø
ôøg k ( t ) = u n + 1 ( t ) + . . . + u n ( t ) d" 1 ,
ôø
ôø k - 1 k
ôø
óø
t 1 , . . . , t m > 0 , n k = p .
p u l
( A - G )
R o z ( A - G ) ( C G P )
ñø
p k
ôø
c j
ôøv ( ´) = v ( ´1 , . . . , ´p ) = ´j »i ( ´) » ( ´)
i
ôø
’! m a x
ôø
´j
ôø
ôø
ôø
j = 1 i = 1
ôø
ôø
ôø
ôø
ôø
ôø
ôø
ôø´1 + . . . + ´n = 1 ,
ôø
ôø 0
ôø
òø
±1 1 ´1 + . . . + ±p 1 ´p = 0 ,
( D C G P )
ôø. . . . . . . . . . . . . . . . . . . . . ,
ôø
ôø
ôø
ôø± ´1 + . . . + ±p m ´p = 0 ,
ôø
ôø
1 m
ôø
ôø
ôø ´i > 0 , i = 1 , . . . , n 0 ,
ôø
ôø
ôø
ôø
ôø( ´l > 0 n i - 1 + 1 d" l d" n i ´l = 0 n i - 1 + 1 d" l d" n i ) ,
ôø
ôø
ôø
óø
»i ( ´) = ´n + 1 + . . . + ´n , i = 1 , . . . , k .
i - 1 i
( C G P ) v ( ´)
( D C G P )
( D C G P ) ( ´1 , . . . , ´p ) "
R p ( D C G P )
( D C G P )
( D C G P ) ( D C G P )
( D C G P ) v
( D C G P )
( C G P ) t ’! t ± ± "
( 0 , 1 )
n m
i j
g ( t 1 , . . . , t m ) = c i ( t j ) ±
i = 1 j = 1
h ( x 1 , . . . , x m ) R m
j
t j = e x , t j > 0 j = 1 , . . . , m .
n
m
±i j
x j
j = 1
h ( x 1 , . . . , x m ) = c i e .
i = 1
ñø
ôø
ôøg 0 ( t ) ’! m i n
ôø
òø
( C G P )
ôøg 1 ( t ) d" 1 , . . . , g k ( t ) d" 1 ,
ôø
ôø
óø
t 1 , . . . , t m > 0 ,
ñø
ôø
ôøh 0 ( x ) ’! m i n
ôø
òø
( C G P )
ôøh 1 ( x ) - 1 d" 0 , . . . , h k ( x ) - 1 d" 0 ,
ôø
ôø
óø
x " R m .
x ’! e x R ( C G P ) ( C G P )
t = ( t 1 , . . . , t m ) ( C G P )
i
x = ( x 1 , . . . , x m ) ( C G P ) t i = e x i = 1 , . . . , m
t ( C G P ) ´
( D C G P )
g 0 ( t ) e" v ( ´) .
( C G P )
t ( C G P ) ( C G P )
( D C G P ) ´
g 0 ( t ) = v ( ´ ) ,
u i ( t )
, i = 1 , . . . , n 0 ,
g 0 ( t )
´i =
»j ( ´ ) u i ( t ) , i = n j - 1 + 1 , . . . , n j , j = 1 , . . . , k , n k = p .
t ( C G P ) ´
( D C G P ) l = 1 , . . . , k »l > 0 0 < g l ( t ) d" 1
l
( g l ( t ) ) » d" 1
k k
l l
g 0 ( t ) e" g 0 ( t ) ( g l ( t ) ) » = [ u 1 ( t ) + . . . + u n ( t ) ] ( g l ( t ) ) » =
0
l = 1 l = 1
k n 0 k
i
l i l
= ´1 u 1 ( t ) + . . . + ´n u n 0 ( t ) ( g l ( t ) ) » e"( A - G ) ( u ( t ) ) ´ ( g l ( t ) ) » =
0
´1 ´n 0 ´i
l = 1 i = 1 l = 1
( A - G ) ( ´1 , . . . , ´p )
n 0
´1 , . . . , ´n > 0 ´i = 1
0
i = 1
n 0 m k
n 0
±i j
´i
i i l
i = 1
g 0 ( t ) e" ( c ) ´ ( t j ) ( u n + 1 ( t ) + . . . + u n ( t ) ) » e"R o z ( A - G )
l - 1 l
´i
i = 1 j = 1 l = 1
n 0 m k
´n l - 1 + 1 ´n l
n 0
u n l - 1 + 1 ( t )
u n l ( t )
c i i ±i j l
´i
i = 1
e" ( ´ ) ´ ( t j ) ( »l ) » · . . . · =
´n l - 1 + 1 ´n l
i
i = 1 j = 1 l = 1
k R o z ( A - G ) g i i = 1 , . . . , k
( ´1 , . . . , ´p ) ´n + 1 , . . . , ´n
i - 1 i
i = 1 , . . . , k
n 0 m k n l
n l
´n s m k
n 0
±l s ´l
c n s
´i
c i i ±i j l
l = 1 s = n l - 1 + 1
i = 1
g 0 ( t ) e" ( ´ ) ´ ( t j ) ( »l ) » · ( t j ) =
´n s
i
i = 1 j = 1 l = 1 s = n l - 1 + 1 j = 1
p k m
p
c i i ±i j
´i
l
i = 1
= ( ´ ) ´ · ( »l ) » · ( t j ) .
i
i = 1 l = 1 j = 1
( ´1 , . . . , ´p )
p
±i j ´i = 0 , j = 1 , . . . , m
i = 1
( t 1 , . . . , t m )
g 0
g 0 ( t ) e" v ( ´) .
t = ( t 1 , . . . , t m ) ( C G P )
( C G P ) x = ( x 1 , . . . , x m )
x i = l n t i , i = 1 , . . . , m .
» = ( » 1 , . . . , » k )
» i e" 0 i = 1 , . . . , k
» i ( h i ( x ) - 1 ) = 0 i = 1 , . . . , k
k
( h 0 ) x ( x ) + » i ( h i ) x ( x ) = 0 j = 1 , . . . , m
i = 1
j j
j
t j = e x j = 1 , . . . , m
"h i "h i "t i "g i j
= = e x , i = 0 , 1 , . . . , k , j = 1 , . . . , m
"x j "t j "x j "t j
j
e x > 0 j = 1 , . . . , m
k
( g 0 ) t ( t ) + » i ( g i ) t ( t ) = 0 j = 1 , . . . , m
i = 1
j j
t j > 0 j = 1 , . . . , m
k
t j ( g 0 ) t ( t ) + » i t j ( g i ) t ( t ) = 0 j = 1 , . . . , m
i = 1
j j
l j
u l ( t ) = c l m ( t j ) ±
j = 1
n 0
t j ( g 0 ) t ( t ) = ±l j u l ( t ) , j = 1 , . . . , m ,
j
l = 1
n i
t j ( g i ) t ( t ) = ±l j u l ( t ) , j = 1 , . . . , m , i = 1 , . . . , k .
j
l = n i - 1 + 1
n 0 k n r
±l j u l ( t ) + » r ±r j u r ( t ) = 0 , j = 1 , . . . , m .
l = 1 r = 1 l = n r - 1 + 1
n 0
g 0 ( t ) = u l ( t ) > 0
l = 1
n 0 k n r
u l ( t )
±l j g 0 ( t ) + » r ±r j u r ( t ) = 0 , j = 1 , . . . , m .
) g 0 ( t
l = 1 r = 1 l = n r - 1 + 1
´
u l ( t )
, l = 1 , . . . , n 0 ,
g 0 ( t )
´l =
» r u l ( t )
, l = n r - 1 + 1 , . . . , n r , r = 1 , . . . , k .
g 0 ( t )
´l > 0 l = 1 , . . . , n 0 r = 1 , . . . , k
´i > 0 » r > 0 ´i > 0 » r > 0 n r - 1 + 1 d" i d" n r
» r e" 0
n 0 n 0
u l ( t )
´l = = 1 .
g 0 ( t )
l = 1 l = 1
» r »r ( ´ ) ( D C G P )
n r n r
)
»r ( ´ ) = ´q = » r u q ( t ) = » r g r ( t ) , r = 1 , . . . , k .
g 0 ( t g 0 ( t )
q = n r - 1 + 1 q = n r - 1 + 1
» r g r ( t ) = » r , r = 1 , . . . , k .
u l ( t
´l = » r g 0 ( t ) = » r g r ( t ) u l ( t ) = »r ( ´ ) u l ( t ) , l = n r - 1 + 1 , . . . , n r , r = 1 , . . . , k .
) g 0 ( t )
´ ( D C G P ) ´l i = 1 , . . . , p
( A - G ) k
R o z ( A - G ) ( »r ( ´ ) = 0 (" g r ( t ) = 1 )
r
r = 1 , . . . , k ( g r ( t ) ) » ( ´ ) = 1 r = 1 , . . . , k
g ( t ) = v ( ´ ) .
´
( D C G P )
( C G P ) ( C G P ) ( D C G P )
( C G P )
( C G P )
´ ( D C G P )
( A - G ) k R o z ( A - G ) ( D C G P )
´ ( D C G P )
( C G P )
( C G P ) ( D C G P )
( C G P ) ( D C G P )
ñø
"
ôø
ôøg 0 ( x , y , z ) = x + y - 2 z - 1 ’! m i n
ôø
òø
( C G P ) 1
ôøg 1 ( x , y , z ) = x - 1 y 2 + x - 1 z 2 d" 1 ,
ôø
ôø
óø
x , y , z > 0 .
p = 4
1
1
u 1 ( x , y , z ) = x 2 c 1 = 1 ±1 1 = ±1 2 = 0 ±1 3 = 0
2
u 2 ( x , y , z ) = y - 2 z - 1 c 2 = 1 ±2 1 = 0 ±2 2 = - 2 ±2 3 = - 1
u 3 ( x , y , z ) = x - 1 y 2 c 3 = 1 ±3 1 = - 1 ±3 2 = 2 ±3 3 = 0
u 4 ( x , y , z ) = x - 1 z 2 c 4 = 1 ±4 1 = - 1 ±4 2 = 0 ±4 3 = 2 .
( C G P ) 1
ñø
- ´1 - ´2 - ´3 - ´4
3
ôøv ( ´) = ´1 ´2 ´3 ´4 ( ´3 + ´4 ) ´ + ´4 ’! m a x
ôø
ôø
ôø
ôø
ôø
ôø
ôø
ôø´ + ´2 = 1 ,
ôø
ôø
ôø
ôø1 1
òø
´1 - ´3 - ´4 = 0 ,
2
( D C G P ) 1
ôø- 2 ´2 + 2 ´3 = 0 ,
ôø
ôø
ôø
ôø- ´2 + 2 ´4 = 0 ,
ôø
ôø
ôø
ôø
ôø´1 , ´2 > 0 ,
ôø
ôø
ôø
óø( ´ , ´4 > 0 ) ( ´3 = ´4 = 0 ) .
3
( D C G P ) 1
( D C G P )
1 1 1
( ´1 , ´2 , ´3 , ´4 ) = ( 3 , , , ) .
4 4 4 8
7 3
1 1 1
v ( ´1 , ´2 , ´3 , ´4 ) = v ( 3 , , , ) = 2 4 3 - 8 .
4 4 4 8
( C G P ) 1
"
u 1 ( x , y , z ) u 1 ( x , y , z )
3 x
= ´1 = = = ,
7 3
4 g 0 ( x , y , z ) v ( ´1 , ´2 , ´3 , ´4 )
-
4 8
2 3
u 2 ( x , y , z ) u 2 ( x , y , z ) ( y ) - 2 ( z ) - 1
1
= ´2 = = = = ,
7 3
4 g 0 ( x , y , z ) v ( ´1 , ´2 , ´3 , ´4 )
-
4 8
2 3
1 3
= ´3 = ( ´3 + ´4 ) u 3 ( x , y , z ) = ( x ) - 1 ( y ) 2 ,
4 8
1 3
= ´4 = ( ´3 + ´4 ) u 4 ( x , y , z ) = ( x ) - 1 ( z ) 2 .
8 8
( C G P ) 1
1 5 1 1 1 1 7 3
( x , y , z ) = ( 2 - 2 3 4 , 2 4 3 8 , 2 - 4 3 8 ) , g 0 ( x , y , z ) = 2 4 3 - 8 .