| version 1.2, 2000/05/24 15:24:54 |
version 1.4, 2000/06/09 08:04:54 |
|
|
| $OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.1 2000/05/19 11:16:51 takayama Exp $ |
$OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.3 2000/06/08 08:37:53 takayama Exp $ |
| |
|
| SpairAndReduction() : |
SpairAndReduction() : |
| $BM?$($i$l$?(B pair $B$r(B reduction $B$9$k(B. |
$BM?$($i$l$?(B pair $B$r(B reduction $B$9$k(B. |
| Line 77 test8() $B$G(B sm1 $B$G=q$$$?J}$N(B Schreyer $B$r |
|
| Line 77 test8() $B$G(B sm1 $B$G=q$$$?J}$N(B Schreyer $B$r |
|
| kernel = image |
kernel = image |
| $B$H$J$C$F$$$k$N$G0J8e$3$N(B option $B$O(B 1 $B$N$^$^;H$&$3$H$H$9$k(B. |
$B$H$J$C$F$$$k$N$G0J8e$3$N(B option $B$O(B 1 $B$N$^$^;H$&$3$H$H$9$k(B. |
| $BMW$9$k$K(B k0 $B$N%3!<%I$,$I$&$d$i$*$+$7$$$i$7$$(B. |
$BMW$9$k$K(B k0 $B$N%3!<%I$,$I$&$d$i$*$+$7$$$i$7$$(B. |
| |
==> |
| |
6/8 $B$N%N!<%H$h$j(B. |
| |
syzygy $B$r(B homogenization $B$r2p$7$F7W;;$9$k$N$OLdBj$"$j(B. |
| |
--> usage of isExact |
| |
$BMW$9$k$K(B kernel = image $B$N%3!<%I$bJQ(B. Homogenized $B$N$^$^$d$kI,MW$"$j(B. |
| |
|
| |
----------------------------------- |
| |
June 8, 2000 (Thu), 9:10 (Spain local time) |
| |
hol.sm1 : gb_h, syz_h, isSameIdeal, isSameIdeal_h |
| |
complex.sm1 : isExact, isExact_h |
| |
|
| |
syzygy $B$r(B homogenization $B$r2p$7$F7W;;$9$k$N$OLdBj$"$j(B. |
| |
--> usage of isExact |
| |
|
| |
[(Homogenize_vec) 0] system_variable : vector $B$N(B homogenize $B$r$7$J$$(B. |
| |
(grade) (module1v) switch_function : vector $BJQ?t$O(B, total |
| |
degree $B$K?t$($J$$(B. |
| |
==> $BL58B%k!<%W$KCm0U(B ---> gb_h, syz_h $B$N(B usage. |
| |
|
| |
minimal-test.k $B$N(B ann(x^3-y^2*z^2) $B$N(B laplace $BJQ49$N(B |
| |
betti $B?t$,JQ(B, exact $B$G$J$$(B, $B$r(B isExact_h $B$G(B check |
| |
$B$7$h$&(B. |
| |
|
| |
minimal-test.k |
| |
test10(); |
| |
LaScala-Stillman $B$NJ}K!$G$D$/$C$?(B, schreyer resol $B$,(B exact $B$+(B |
| |
$BD4$Y$k(B. |
| |
$BNcBj$O(B, ann(1/(x^3-y^2 z^2)) $B$N(B Laplace $BJQ49(B. |
| |
==> OK. IsExact_h $B$G$7$i$Y$k(B. (IsExact $B$O$@$a$h(B) |
| |
|
| |
June 8, 2000 (Thu), 19:35 |
| |
load["minimal-test.k"];; |
| |
test11(); |
| |
LaScala-Stillman $B$NJ}K!$G$D$/$C$?(B, minimal resol $B$,(B exact $B$+(B |
| |
$BD4$Y$k(B. |
| |
$BNcBj$O(B, ann(1/(x^3-y^2 z^2)) $B$N(B Laplace $BJQ49(B. |
| |
|
| |
SwhereInTower $B$r;H$&$H$-$O(B, |
| |
SsetTower() $B$G(B gbList $B$rJQ99$7$J$$$H$$$1$J$$(B. |
| |
$B$b$A$m$s;HMQ$7$?$i(B, $B$=$l$rLa$9$3$H(B. |
| |
SpairAndReduction, SpairAndReduction2 $B$G(B, |
| |
SsetTower(StowerOf(tower,level)); |
| |
pos = SwhereInTower(syzHead,tower[level]); |
| |
|
| |
SsetTower(StowerOf(tower,level-1)); |
| |
pos2 = SwhereInTower(tmp[0],tower[level-1]); |
| |
$B$H(B, SwhereInTower $B$NA0$K(B setTower $B$r$/$o$($?(B. |
| |
( $B0c$&%l%Y%k$G$NHf3S$N$?$a(B.) |
| |
|
| |
IsExact_h $B$O(B, 0 $B%Y%/%H%k$r4^$`>l9g(B, $B$?$@$7$/F0:n$7$J$$$h$&$@(B. |
| |
test11(). |
| |
test11a() $B$G(B, 0 $B%Y%/%H%k$r<j$G=|$$$?9TNs$N(B exactness $B$r%A%'%C%/(B. ==> OK. |
| |
|
| |
|
| |
--------------------------------- |
| |
June 9, 6:20 |
| |
SpairAndReduction |
| |
$B$H(B |
| |
SpairAndReduction2 |
| |
$B$N0c$$(B. |
| |
SpairAndReduction : SlaScala (LaScala-Stillman's algorithm $B$G;H$&(B) |
| |
SpairAndReduction2 : Sschreyer (schreyer algorithm $B$G;H$&(B, laScala $B$O$J$7(B.) |
| |
|
| |
0 $B$r<+F0$G=|$/%3!<%I$r=q$3$&(B. |
| |
|
| |
SpruneZeroRow() $B$r(B Sminimal() $B$K2C$($?(B. |
| |
test11() $B$b@5$7$/F0:n$9$k$O$:(B. |
| |
IsExact_h $B$O(B schreyer $B$r(B off $B$7$F(B, ReParse $B$7$F$+$i(B, |
| |
$B8F$S=P$9$3$H(B. |
| |
|
| |
|
| |
#ifdef TOTAL_STRATEGY |
| |
return(StotalDegree(f)+Sdegree(tower[level-2,i],tower,level-1)); |
| |
#endif |
| |
/* Strategy must be compatible with ordering. */ |
| |
/* Weight vector must be non-negative, too. */ |
| |
/* See Sdegree, SgenerateTable, reductionTable. */ |
| |
wd = Sord_w(f,ww); |
| |
return(wd+Sdegree(tower[level-2,i],tower,level-1)); |
| |
TOTAL_STRATEGY $B$rMQ$$$kI,MW$,$"$k$N$G$O(B?? |
| |
Example 1: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); |
| |
v=[[2*x*Dx + 3*y*Dy+6, 0], |
| |
[3*x^2*Dy + 2*y*Dx, 0], |
| |
[0, x^2+y^2], |
| |
[0, x*y]]; |
| |
a=Sminimal(v); |
| |
strategy $B$,$*$+$7$$$H$$$C$F$H$^$k(B. $BM}M3$O(B? |
| |
|
| |
a=test_ann3("x^3+y^3+z^3); $B$O;~4V$,$+$+$j$=$&(B. |
| |
a=test_ann3("x^3+y^3"); OK. |
| |
a=test_ann3("x^2+y^2+z"); OK. |
| |
|
| |
|
| |
$B>e$N(B example 1 $B$N%(%i!<(B $B$N8+J}(B: |
| |
Processing [ 1 , 3 ] Strategy = 2 |
| |
1 $B$N(B 3 $BHVL\$N(B spair $B$N(B reduction $B$r=hM}Cf(B. |
| |
In(7)=reductionTable: |
| |
[[ 1 , 1 , 1 , 2 , 2 , 3 ] , [ 3 , 2 , 1 , 2 , 3 ] , [ 2 ] ] |
| |
-- $B$3$l(B. |
| |
SpairAndReduction: |
| |
[ p and bases , [ [ 0 , 3 ] , [ y*h , -x ] ] , [ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , %[null] ] ] |
| |
0 $B$N(B 0 $BHVL\$H(B 3 $BHVL\(B $B$N(B spair $B$r7W;;$7$F(B, 0 $B%l%Y%k$N(B gb $B$G(B reduction. |
| |
[ 1 , 1 , 1 , 2 , 2 , 3 ] $B$K$"$k$h$&$K(B, strategy 3 $B0J30$O7W;;$:$_(B. |
| |
( $B7W;;$7$F$J$$$b$N$O(B %[null] $B$H$J$C$F$k(B. ) |
| |
[ level= , 1 ] |
| |
[ tower2= , [ [ ] ] ] ( $B0lHV2<$J$N$G(B, tower $B$O$J$7$h(B. ) |
| |
[ y*h , -es^3*x ] |
| |
[gi, gj] = [ 2*x*Dx+3*y*Dy+6*h^2 , 2*y*Dx*h+3*x^2*Dy ] |
| |
1 |
| |
Reduce the element 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy |
| |
by [ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , %[null] ] |
| |
result is [ 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy , 1 , [ 0 , 0 , 0 , 0 , 0 , 0 ] ] |
| |
vdegree of the original = -1 |
| |
vdegree of the remainder = -1 |
| |
[ 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy , [ y*h , 0 , 0 , -x , 0 , 0 ] , 3 , 5 , -1 , -1 ] |
| |
|
| |
In(11)=freeRes: |
| |
[ [ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy ] , [ %[null] , [ 0 , 0 , y^2 , 0 , -x , 0 ] , [ 0 , -y , x , 0 , 1 , 0 ] , [ -y*h , 0 , 0 , x , 0 , 1 ] , %[null] ] , [ %[null] ] ] |
| |
$B$r$_$l$P$o$+$k$h$&$K(B, SlaScala $B$G(B, freeRes $B$K$3$N85$,(B [0,5] $B$K2C$((B |
| |
$B$i$l$?(B. |
| |
|
| |
$B<!$K(B SnextI $B$,(B SlaScala $B$h$j8F$P$l$F$3$N%(%i!<(B. |
| |
i = SnextI(reductionTable_tmp,strategy,redundantTable, |
| |
skel,level,freeRes); |
| |
In(22)=reductionTable: |
| |
[ [ 1 , 1 , 1 , 2 , 2 , 3 ] , [ 3 , 2 , 1 , 2 , 3 ] , [ 2 ] ] |
| |
$B$J$N$G(B, $B:G8e(B $B$N(B 2 $B$,=hM}$5$l$k$O$:$@$,(B, |
| |
In(25)=skel[2]: |
| |
[ [ [ 0 , 2 ] , [ 1 , -y^2 ] ] ] |
| |
$B$N$h$&$K(B, 0 $BHVL\$H(B, 2 $BHVL\$N(B spair. |
| |
$B$7$+$7(B, |
| |
In(26)=bases: |
| |
[ %[null] , [ 0 , 0 , y^2 , 0 , -x , 0 ] , [ 0 , -y , x , 0 , 1 , 0 ] , [ -y*h , 0 , 0 , x , 0 , 1 ] , %[null] ] |
| |
$B$N$h$&$K(B, 0 $BHVL\$O(B strategy 3 $B$J$N$G(B, $B$^$@$b$H$^$C$F$$$J$$(B. |
| |
|
| |
reductionTable_tmp=[ 2 ] |
| |
See also reductionTable, strategy, level,i |
| |
ERROR(sm): error operator : SnextI: bases[i] or bases[j] is null for all combinations. |
| |
--- Engine error or interrupt : In function : Error of class PrimitiveObject |
| |
|
| |
Type in Cleards() to exit the debug mode and Where() to see the stack trace. |
| |
In(7)=reductionTable: |
| |
[ [ 1 , 1 , 1 , 2 , 2 , 3 ] , [ 3 , 2 , 1 , 2 , 3 ] , [ 2 ] ] |
| |
In(8)=strategy: |
| |
2 |
| |
In(9)=level: |
| |
2 |
| |
|
| |
RemoveRedundantInSchreyerSkelton = 0 |
| |
$B$H$7$F$bF1$8%(%i!<(B. |
| |
|
| |
------------------------------------------------- |
| |
test_ann3("x*y+y*z+z*x"); OK. |
| |
|
| |
6/9 (Fri) |
| |
Sminimal $B$N<BAu$KAjJQ$o$i$:6lO+$7$F$^$9(B. |
| |
Sevilla $B$G$$$m$$$m$HD>$7$?7k2L(B, |
| |
Sminimal $B$O$&$^$/$&$4$1$P@5$7$$Ez$($r$@$7$F$k$_$?$$$G$9$,(B |
| |
(D<h> : homogenized Weyl $B$G(B ker = im $B$r(B check $B$7$F$k(B, |
| |
V-adapted (strict) $B$+$I$&$+$N(B check routing $B$O$^$@=q$$$F$J$$(B), |
| |
strategy $B$,$&$^$/$&$4$+$J$/$F$H$^$k>l9g$b$"$j$^$9(B |
| |
( strategy = 2 $B$N(B sp $B$r7W;;$9$k$N$K(B, strategy 3 $B$N(B $B85$rI,MW$H(B |
| |
$B$7$?$j$9$k>l9g$"$j(B). |
| |
|
| |
|
| |
strategy $B$O(B |
| |
def Sdegree(f,tower,level) { |
| |
local i,ww, wd; |
| |
/* extern WeightOfSweyl; */ |
| |
ww = WeightOfSweyl; |
| |
f = Init(f); |
| |
if (level <= 1) return(StotalDegree(f)); |
| |
i = Degree(f,es); |
| |
return(StotalDegree(f)+Sdegree(tower[level-2,i],tower,level-1)); |
| |
} |
| |
$B$rMQ$$$F(B, |
| |
ans_at_each_floor[j] = Sdegree(tower[i,j],tower,i+1)-(i+1) |
| |
$B$G7W;;$7$F$^$9(B. |
| |
|
| |
$B$$$/$D$+=PNO$r$D$1$F$*$-$^$9$N$G(B, $B8!F$(B!!! |
| |
|
| |
$BNc(B 1: |
| |
load["minimal-test.k"];; |
| |
a=test_ann3("x^3-y^2*z^2"); $B0z?t$N(B annihilating ideal $B$N(B laplace $BJQ49$N(B |
| |
homogenization $B$N(B resolution. |
| |
weight vector $B$O(B (-1,-1,-1,1,1,1) |
| |
|
| |
In(4)=sm1_pmat(a[1]); |
| |
[ |
| |
[ 0 $B<!(B |
| |
[ y*Dy-z*Dz ] |
| |
[ -2*x*Dx-3*z*Dz+h^2 ] |
| |
[ 2*x*Dy*Dz^2-3*y*Dx^2*h ] |
| |
[ 2*x*Dy^2*Dz-3*z*Dx^2*h ] |
| |
] |
| |
[ 1 $B<!(B |
| |
[ 3*Dx^2*h , 0 , Dy , -Dz ] |
| |
[ 6*x*Dy*Dz^2-9*y*Dx^2*h , -2*x*Dy*Dz^2+3*y*Dx^2*h , -2*x*Dx-3*y*Dy , 0 ] |
| |
[ 0 , 2*x*Dy^2*Dz-3*z*Dx^2*h , 0 , 2*x*Dx+3*z*Dz ] |
| |
[ 2*x*Dx+3*z*Dz-h^2 , y*Dy-z*Dz , 0 , 0 ] |
| |
[ 2*x*Dy*Dz , 0 , z , -y ] |
| |
] |
| |
[ 2 $B<!(B |
| |
[ -2*x*Dx-3*y*Dy-3*z*Dz-6*h^2 , -Dy , -Dz , 3*Dx^2*h , 3*Dy*Dz ] |
| |
[ 3*y*z , z , y , -2*x*Dy*Dz , 2*x*Dx ] |
| |
] |
| |
] |
| |
In(5)= |
| |
|
| |
$BNc(B 2: |
| |
load["minimal-test.k"];; |
| |
a=test_ann3("x*y+y*z+z*x"); |
| |
In(6)=sm1_pmat(a[1]); |
| |
[ |
| |
[ 0 $B<!(B |
| |
[ 2*x*Dx+x*Dz-y*Dz+z*Dz+h^2 ] |
| |
[ -2*y*Dy+x*Dz-y*Dz-z*Dz-h^2 ] |
| |
[ -2*x*Dy+2*z*Dy+x*Dz-y*Dz+3*z*Dz+h^2 ] |
| |
[ -2*y*Dx+2*z*Dx-x*Dz+y*Dz+3*z*Dz+h^2 ] |
| |
] |
| |
[ 1 $B<!(B |
| |
[ y-z , x-z , -y , x ] |
| |
[ 2*Dy-2*Dz , 2*Dx-2*Dz , 2*Dx+2*Dz , -2*Dy-2*Dz ] |
| |
[ 2*y*Dx-2*z*Dx+x*Dz-y*Dz-3*z*Dz-2*h^2 , 0 , 0 , 2*x*Dx+x*Dz-y*Dz+z*Dz+2*h^2 ] |
| |
[ 2*y*Dy-2*z*Dy+y*Dz-z*Dz+h^2 , 2*x*Dz-y*Dz+2*z*Dz+h^2 , -x*Dz+z*Dz , 2*x*Dy+x*Dz ] |
| |
[ -2*y*Dy+2*z*Dy+y*Dz-z*Dz , y*Dz-4*z*Dz , -2*y*Dx+2*z*Dx-y*Dz+2*z*Dz , -2*z*Dy+y*Dz-3*z*Dz ] |
| |
] |
| |
[ 2 $B<!(B |
| |
[ -2*y*Dx+2*z*Dx-y*Dz+2*z*Dz , x*y-x*z-y*z+z^2 , y-z , y , x+y-z ] |
| |
[ -6*Dx*Dz-2*Dz^2 , x*Dz+y*Dz-5*z*Dz-4*h^2 , -2*Dy+2*Dz , 2*Dx+2*Dz , 4*Dz ] |
| |
] |
| |
] |
| |
In(7)= |
| |
|
| |
$BNc(B 3: $B$&$^$/9T$+$J$$Nc(B: |
| |
|
| |
Example 1: Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); |
| |
v=[[2*x*Dx + 3*y*Dy+6, 0], |
| |
[3*x^2*Dy + 2*y*Dx, 0], |
| |
[0, x^2+y^2], |
| |
[0, x*y]]; |
| |
a=Sminimal(v); |
| |
strategy $B$,$*$+$7$$$H$$$C$F$H$^$k(B. $BM}M3$O(B? |
| |
Negative weight vector $B$r;H$o$J$$$H$-$A$s$HF0$-$^$9(B. |
| |
|
| |
|
| |
DEBUG $B=PNO(B: |
| |
rf= [ |
| |
[ |
| |
[ Schreyer frame. |
| |
[ 0 , y^3 , 0 , 0 , -x^2 , 0 ] |
| |
[ 0 , 0 , y^2 , 0 , -x , 0 ] |
| |
[ 0 , y , -x , 0 , 0 , 0 ] |
| |
[ y*h , 0 , 0 , -x , 0 , 0 ] |
| |
[ 0 , 0 , 0 , 3*y*Dy , 0 , -2*Dx ] |
| |
] |
| |
[ |
| |
[ 1 , 0 , -y^2 , 0 , 0 ] |
| |
] |
| |
[ ] |
| |
] |
| |
[ |
| |
[ 2*x*Dx , e_*x^2 , e_*x*y , 2*y*Dx*h , e_*y^3 , 3*y^2*Dy*h ] |
| |
[ es*y^3 , es^2*y^2 , es*y , y*h , 3*es^3*y*Dy ] |
| |
[ 1 ] |
| |
] |
| |
[ |
| |
[ ] |
| |
[ |
| |
[ |
| |
[ 1 , 4 ] |
| |
[ y^3 , -x^2 ] |
| |
] |
| |
[ |
| |
[ 2 , 4 ] |
| |
[ y^2 , -x ] |
| |
] |
| |
[ |
| |
[ 1 , 2 ] |
| |
[ y , -x ] |
| |
] |
| |
[ |
| |
[ 0 , 3 ] |
| |
[ y*h , -x ] |
| |
] |
| |
[ |
| |
[ 3 , 5 ] |
| |
[ 3*y*Dy , -2*Dx ] |
| |
] |
| |
] |
| |
[ |
| |
[ |
| |
[ 0 , 2 ] |
| |
[ 1 , -y^2 ] |
| |
] |
| |
] |
| |
[ ] |
| |
] |
| |
[ resolution $B$9$Y$-(B $BItJ,2C72(B e_ $B$O(B $B%Y%/%H%k@.J,$N%^!<%/(B. |
| |
[ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy ] |
| |
] |
| |
] |
| |
|
| |
$BN,(B |
| |
Processing [ 1 , 3 ] Strategy = 2 |
| |
1 $B$N(B 3 $BHVL\$N(B spair $B$N(B reduction $B$r=hM}Cf(B. |
| |
In(7)=reductionTable: |
| |
[[ 1 , 1 , 1 , 2 , 2 , 3 ] , [ 3 , 2 , 1 , 2 , 3 ] , [ 2 ] ] |
| |
-- $B$3$l(B. |
| |
SpairAndReduction: |
| |
[ p and bases , [ [ 0 , 3 ] , [ y*h , -x ] ] , [ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , %[null] ] ] |
| |
0 $B$N(B 0 $BHVL\$H(B 3 $BHVL\(B $B$N(B spair $B$r7W;;$7$F(B, 0 $B%l%Y%k$N(B gb $B$G(B reduction. |
| |
[ 1 , 1 , 1 , 2 , 2 , 3 ] $B$K$"$k$h$&$K(B, strategy 3 $B0J30$O7W;;$:$_(B. |
| |
( $B7W;;$7$F$J$$$b$N$O(B %[null] $B$H$J$C$F$k(B. ) |
| |
[ level= , 1 ] |
| |
[ tower2= , [ [ ] ] ] ( $B0lHV2<$J$N$G(B, tower $B$O$J$7$h(B. ) |
| |
[ y*h , -es^3*x ] |
| |
[gi, gj] = [ 2*x*Dx+3*y*Dy+6*h^2 , 2*y*Dx*h+3*x^2*Dy ] |
| |
1 |
| |
Reduce the element 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy |
| |
by [ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , %[null] ] |
| |
result is [ 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy , 1 , [ 0 , 0 , 0 , 0 , 0 , 0 ] ] |
| |
vdegree of the original = -1 |
| |
vdegree of the remainder = -1 |
| |
[ 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy , [ y*h , 0 , 0 , -x , 0 , 0 ] , 3 , 5 , -1 , -1 ] |
| |
|
| |
In(11)=freeRes: |
| |
[ [ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy ] , [ %[null] , [ 0 , 0 , y^2 , 0 , -x , 0 ] , [ 0 , -y , x , 0 , 1 , 0 ] , [ -y*h , 0 , 0 , x , 0 , 1 ] , %[null] ] , [ %[null] ] ] |
| |
$B$r$_$l$P$o$+$k$h$&$K(B, SlaScala $B$G(B, freeRes $B$K$3$N85$,(B [0,5] $B$K2C$((B |
| |
$B$i$l$?(B. |
| |
|
| |
$B<!$K(B SnextI $B$,(B SlaScala $B$h$j8F$P$l$F$3$N%(%i!<(B. |
| |
i = SnextI(reductionTable_tmp,strategy,redundantTable, |
| |
skel,level,freeRes); |
| |
In(22)=reductionTable: |
| |
[ [ 1 , 1 , 1 , 2 , 2 , 3 ] , [ 3 , 2 , 1 , 2 , 3 ] , [ 2 ] ] |
| |
$B$J$N$G(B, $B:G8e(B $B$N(B 2 $B$,=hM}$5$l$k$O$:$@$,(B, |
| |
In(25)=skel[2]: |
| |
[ [ [ 0 , 2 ] , [ 1 , -y^2 ] ] ] |
| |
$B$N$h$&$K(B, 0 $BHVL\$H(B, 2 $BHVL\$N(B spair. |
| |
$B$7$+$7(B, |
| |
In(26)=bases: |
| |
[ %[null] , [ 0 , 0 , y^2 , 0 , -x , 0 ] , [ 0 , -y , x , 0 , 1 , 0 ] , [ -y*h , 0 , 0 , x , 0 , 1 ] , %[null] ] |
| |
$B$N$h$&$K(B, 0 $BHVL\$O(B strategy 3 $B$J$N$G(B, $B$^$@$b$H$^$C$F$$$J$$(B. |
| |
|
| |
reductionTable_tmp=[ 2 ] |
| |
See also reductionTable, strategy, level,i |
| |
ERROR(sm): error operator : SnextI: bases[i] or bases[j] is null for all combinations. |
| |
--- Engine error or interrupt : In function : Error of class PrimitiveObject |
| |
|
| |
Type in Cleards() to exit the debug mode and Where() to see the stack trace. |
| |
In(7)=reductionTable: |
| |
[ [ 1 , 1 , 1 , 2 , 2 , 3 ] , [ 3 , 2 , 1 , 2 , 3 ] , [ 2 ] ] |
| |
In(8)=strategy: |
| |
2 |
| |
In(9)=level: |
| |
2 |
| |
$B$3$N;~E@$^$G$G$b$H$^$C$?(B basis |
| |
[ |
| |
[ 2*x*Dx+3*y*Dy+6*h^2 , e_*x^2+e_*y^2 , e_*x*y , 2*y*Dx*h+3*x^2*Dy , e_*y^3 , 3*y^2*Dy*h+6*y*h^3-3*x^3*Dy ] |
| |
[ %[null] , [ 0 , 0 , y^2 , 0 , -x , 0 ] , [ 0 , -y , x , 0 , 1 , 0 ] , [ -y*h , 0 , 0 , x , 0 , 1 ] , %[null] ] |
| |
[ %[null] ] |
| |
] |
| |
|
| |
------------------------------------- |
| |
|
| |
Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); |
| |
a=Sminimal([x^2+y^2,x*y]); |
| |
$B$3$l$G$b;w$?$h$&$J%(%i!<$r$@$;$k(B. |
| |
$B$3$NJ}$,(B debug $B$7$d$9$$(B: |
| |
Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]); |
| |
a=Sminimal([x*y,x^2+y^2]); |
| |
$B$G$O%(%i!<$,$G$J$$$N$,IT;W5D(B. |
| |
pruneZero $B$,F0$$$F$J$$$N$,JQ(B. |
| |
|
| |
rf= [ |
| |
[ |
| |
[ |
| |
[ y^3 , 0 , -x^2 ] |
| |
[ 0 , y^2 , -x ] |
| |
[ y , -x , 0 ] |
| |
] |
| |
[ |
| |
[ 1 , 0 , -y^2 ] |
| |
] |
| |
[ ] |
| |
] |
| |
[ |
| |
[ x^2 , x*y , y^3 ] |
| |
[ y^3 , es*y^2 , y ] |
| |
[ 1 ] |
| |
] |
| |
[ |
| |
[ ] |
| |
[ |
| |
[ |
| |
[ 0 , 2 ] |
| |
[ y^3 , -x^2 ] |
| |
] |
| |
[ |
| |
[ 1 , 2 ] |
| |
[ y^2 , -x ] |
| |
] |
| |
[ |
| |
[ 0 , 1 ] |
| |
[ y , -x ] |
| |
] |
| |
] |
| |
[ |
| |
[ |
| |
[ 0 , 2 ] |
| |
[ 1 , -y^2 ] |
| |
] |
| |
] |
| |
[ ] |
| |
] |
| |
[ |
| |
[ x^2+y^2 , x*y , y^3 ] |
| |
] |
| |
] |
| |
[ 0 , 0 ] |
| |
Processing [ 0 , 0 ] Strategy = 1 |
| |
[ 0 , 1 ] |
| |
Processing [ 0 , 1 ] Strategy = 1 |
| |
[ 1 , 2 ] |
| |
Processing [ 1 , 2 ] Strategy = 1 |
| |
SpairAndReduction: |
| |
[ p and bases , [ [ 0 , 1 ] , [ y , -x ] ] , [ x^2+y^2 , x*y , %[null] ] ] |
| |
[ level= , 1 ] |
| |
[ tower2= , [ [ ] ] ] |
| |
[ y , -es*x ] |
| |
[gi, gj] = [ x^2+y^2 , x*y ] |
| |
1 |
| |
Reduce the element y^3 |
| |
by [ x^2+y^2 , x*y , %[null] ] |
| |
result is [ y^3 , 1 , [ 0 , 0 , 0 ] ] |
| |
vdegree of the original = -3 |
| |
vdegree of the remainder = -3 |
| |
[ y^3 , [ y , -x , 0 ] , 2 , 2 , -3 , -3 ] |
| |
[ 0 , 2 ] |
| |
Processing [ 0 , 2 ] Strategy = 2 |
| |
[ 1 , 1 ] |
| |
Processing [ 1 , 1 ] Strategy = 2 |
| |
SpairAndReduction: |
| |
[ p and bases , [ [ 1 , 2 ] , [ y^2 , -x ] ] , [ x^2+y^2 , x*y , y^3 ] ] |
| |
[ level= , 1 ] |
| |
[ tower2= , [ [ ] ] ] |
| |
[ es*y^2 , -es^2*x ] |
| |
[gi, gj] = [ x*y , y^3 ] |
| |
1 |
| |
Reduce the element 0 |
| |
by [ x^2+y^2 , x*y , y^3 ] |
| |
result is [ 0 , 1 , [ 0 , 0 , 0 ] ] |
| |
vdegree of the original = -4 |
| |
vdegree of the remainder = %[null] |
| |
[ 0 , [ 0 , y^2 , -x ] , 1 , -1 , -4 , %[null] ] |
| |
reductionTable_tmp=[ 2 ] |
| |
See also reductionTable, strategy, level,i |
| |
ERROR(sm): error operator : SnextI: bases[i] or bases[j] is null for all combinations. |
| |
--- Engine error or interrupt : In function : Error of class PrimitiveObject |
| |
|
| |
Type in Cleards() to exit the debug mode and Where() to see the stack trace. |
| |
In(10)=reductionTable : |
| |
[ [ 1 , 1 , 2 ] , [ 3 , 2 , 1 ] , [ 2 ] ] |
| |
In(11)=bases: |
| |
[ %[null] , [ 0 , y^2 , -x ] , [ -y , x , 1 ] ] |
| |
In(12)= $B$3$l$O(B, [3, 2, 1] $B$N85$N$&$A(B, 2,1 $B$,$b$H$^$C$F$$$k(B. |
| |
[ 2 ] $B$N7W;;$K(B 0 $BHVL\$,I,MW$G$3$l$,$^$@$J$$(B. |
| |
|
| |
|
| |
|
| |
|
![[BACK]](/icons/cvsweb/back.gif){kind=icon}
Return to minimal-note-ja.txt CVS log ![[TXT]](/icons/cvsweb/text.gif){kind=icon}
![[DIR]](/icons/cvsweb/dir.gif){kind=icon}
Up to [local] / OpenXM / src / k097 / lib / minimal