version 1.25, 2004/05/13 05:52:53 |
version 1.35, 2004/09/14 03:12:17 |
|
|
% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.24 2004/05/13 05:33:10 takayama Exp $ |
% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.34 2004/09/13 11:24:10 takayama Exp $ |
%[(parse) (hol.sm1) pushfile] extension |
(hol_loaded) boundp { } |
|
{ [(parse) (hol.sm1) pushfile] extension } ifelse |
%[(parse) (appell.sm1) pushfile] extension |
%[(parse) (appell.sm1) pushfile] extension |
|
|
(ecart.sm1 : ecart division for D, 2003/07/25 ) message-quiet |
(ecart.sm1 : ecart division for D, 2003/07/25, 2004/09/14 ) message-quiet |
/ecart.begin { beginEcart } def |
/ecart.begin { beginEcart } def |
/ecart.end { endEcart } def |
/ecart.end { endEcart } def |
/ecart.autoHomogenize 1 def |
/ecart.autoHomogenize 1 def |
/ecart.needSyz 0 def |
/ecart.needSyz 0 def |
/ecartd.gb.oxRingStructure [ ] def |
/ecartd.gb.oxRingStructure [[ ] [ ] ] def |
|
/ecart.partialEcartGlobalVarX [ ] def |
|
|
/ecartd.begin { |
/ecartd.begin { |
ecart.begin |
ecart.begin |
|
|
/ecart.messagen { |
/ecart.messagen { |
ecart.message.quiet { pop } { messagen } ifelse |
ecart.message.quiet { pop } { messagen } ifelse |
} def |
} def |
|
/ecart.setOpt.init { |
|
% Initialize |
|
/ecart.partialEcartGlobalVarX [ ] def |
|
} def |
/ecart.setOpt { |
/ecart.setOpt { |
/arg1 set |
/arg1 set |
[/in-ecart.setOpt /opt /i /n /ans] pushVariables |
[/in-ecart.setOpt /opt /i /n /ans] pushVariables |
|
|
/opt arg1 def |
/opt arg1 def |
/ans [ ] def |
/ans [ ] def |
/n opt length def |
/n opt length def |
|
|
|
ecart.setOpt.init |
|
|
0 2 n 1 sub { |
0 2 n 1 sub { |
/i set |
/i set |
opt i get tag StringP eq not { |
opt i get tag StringP eq not { |
|
|
exit |
exit |
} { } ifelse |
} { } ifelse |
|
|
ans [opt i get opt i 1 add get ] append /ans set |
% Global: ecart.partialEcartGlobalVarX |
|
opt i get (partialEcartGlobalVarX) eq { |
|
/ecart.partialEcartGlobalVarX opt , i 1 add , get def |
|
% do not exit. |
|
} { } ifelse |
|
|
|
ans [opt i get opt i 1 add get ] join /ans set |
exit |
exit |
} loop |
} loop |
} for |
} for |
|
|
ll (0). eq { |
ll (0). eq { |
} { |
} { |
ll getRing /rr set |
ll getRing /rr set |
ll [ [ @@@.Hsymbol rr ,, (1) rr ,, ] |
ll [ [ @@@.Hsymbol rr __ (1) rr __ ] |
[ (h) rr ,, (1) rr ,, ]] replace |
[ (h) rr __ (1) rr __ ]] replace |
/ll set |
/ll set |
} ifelse |
} ifelse |
} ifelse |
} ifelse |
|
|
ll (0). eq { |
ll (0). eq { |
} { |
} { |
ll getRing /rr set |
ll getRing /rr set |
ll [ [ @@@.Hsymbol rr ,, (1) rr ,, ] ] replace |
ll [ [ @@@.Hsymbol rr __ (1) rr __ ] ] replace |
/ll set |
/ll set |
} ifelse |
} ifelse |
} ifelse |
} ifelse |
|
|
$ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] $ |
$ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] $ |
$ [(degreeShift) [[0 1] [-3 1]]] ] ecart.gb pmat ; $ |
$ [(degreeShift) [[0 1] [-3 1]]] ] ecart.gb pmat ; $ |
( ) |
( ) |
|
$Example 6: [ [(1-z) (-x+1-y-z)] (x,y,z) $ |
|
$ [[(y) -1 (z) -1 (Dy) 1 (Dz) 1] [(x) 1 (Dx) 1]] $ |
|
$ [(partialEcartGlobalVarX) [(x)]] ] /std set $ |
|
$ std ecart.gb pmat ; $ |
|
$ std ecart.gb getRing :: $ |
|
( ) |
(cf. gb, groebner, ecarth.gb, ecartd.gb, ecart.syz, ecart.begin, ecart.end, ecart.homogenize01, ) |
(cf. gb, groebner, ecarth.gb, ecartd.gb, ecart.syz, ecart.begin, ecart.end, ecart.homogenize01, ) |
( ecart.dehomogenize, ecart.dehomogenizeH) |
( ecart.dehomogenize, ecart.dehomogenizeH) |
( [(weightedHomogenization) 1 (degreeShift) [[1 2 1]]] : options for ) |
( [(weightedHomogenization) 1 (degreeShift) [[1 2 1]]] : options for ) |
|
|
/hdShift 0 def |
/hdShift 0 def |
/opt [(weightedHomogenization) 1] def |
/opt [(weightedHomogenization) 1] def |
/ecart.useSugar 0 def |
/ecart.useSugar 0 def |
|
ecart.setOpt.init |
aa { tag } map /typev set |
aa { tag } map /typev set |
typev [ ArrayP ] eq |
typev [ ArrayP ] eq |
{ /f aa 0 get def |
{ /f aa 0 get def |
|
|
} { } ifelse |
} { } ifelse |
|
|
%%BUG: case of v is integer |
%%BUG: case of v is integer |
v ecart.checkOrder |
[v ecart.partialEcartGlobalVarX] ecart.checkOrder |
|
|
ecart.begin |
ecart.begin |
|
|
|
|
/wv 0 def |
/wv 0 def |
/degreeShift 0 def |
/degreeShift 0 def |
/opt [(weightedHomogenization) 1] def |
/opt [(weightedHomogenization) 1] def |
|
ecart.setOpt.init |
aa { tag } map /typev set |
aa { tag } map /typev set |
typev [ ArrayP ] eq |
typev [ ArrayP ] eq |
{ /f aa 0 get def |
{ /f aa 0 get def |
|
|
} { } ifelse |
} { } ifelse |
|
|
%%BUG: case of v is integer |
%%BUG: case of v is integer |
v ecart.checkOrder |
[v ecart.partialEcartGlobalVarX] ecart.checkOrder |
|
|
ecartn.begin |
ecartn.begin |
|
|
|
|
/hdShift 0 def |
/hdShift 0 def |
/ecart.useSugar 0 def |
/ecart.useSugar 0 def |
/opt [(weightedHomogenization) 1] def |
/opt [(weightedHomogenization) 1] def |
|
ecart.setOpt.init |
aa { tag } map /typev set |
aa { tag } map /typev set |
typev [ ArrayP ] eq |
typev [ ArrayP ] eq |
{ /f aa 0 get def |
{ /f aa 0 get def |
|
|
} { } ifelse |
} { } ifelse |
|
|
%%BUG: case of v is integer |
%%BUG: case of v is integer |
v ecart.checkOrder |
[v ecart.partialEcartGlobalVarX] ecart.checkOrder |
|
|
|
|
ecartd.begin |
ecartd.begin |
|
|
ecart.gb.verbose { (gb.options = ) ecart.messagen gb.options ecart.message } { } ifelse |
ecart.gb.verbose { (gb.options = ) ecart.messagen gb.options ecart.message } { } ifelse |
|
|
|
|
/ecart.checkOrder { |
/ecart.checkOrder { |
/arg1 set |
/arg1 set |
[/in-ecart.checkOrder /vv /tt /dd /n /i] pushVariables |
[/vv] pushVariables |
[ |
[ |
/vv arg1 def |
/vv arg1 def |
|
vv length 1 eq { |
|
vv 0 get ecart.checkOrder.noGlobal /arg1 set |
|
}{ |
|
vv ecart.checkOrder.global /arg1 set |
|
} ifelse |
|
] pop |
|
popVariables |
|
/arg1 |
|
} def |
|
/ecart.checkOrder.noglobal { |
|
/arg1 set |
|
[/vv /tt /dd /n /i] pushVariables |
|
[ |
|
/vv arg1 def |
vv isArray |
vv isArray |
{ } { [vv to_records pop] /vv set } ifelse |
{ } { [vv to_records pop] /vv set } ifelse |
vv {toString} map /vv set |
vv {toString} map /vv set |
|
|
popVariables |
popVariables |
arg1 |
arg1 |
} def |
} def |
|
|
|
/ecart.checkOrder.global { |
|
/arg1 set |
|
[/vv /vvGlobal /tt /dd /n /i] pushVariables |
|
[ |
|
/vv arg1 def |
|
/vvGlobal vv 1 get def |
|
vv 0 get /vv set |
|
vv isArray |
|
{ } { [vv to_records pop] /vv set } ifelse |
|
vv {toString} map /vv set |
|
vvGlobal isArray |
|
{ } { [vvGlobal to_records pop] /vvGlobal set } ifelse |
|
vvGlobal {toString} map /vv set |
|
|
|
vv vvGlobal setMinus /vv set |
|
vv { /tt set [@@@.Dsymbol tt] cat } map /dd set |
|
% Starting the checks. Check for local variables. |
|
0 1 vv length 1 sub { |
|
/i set |
|
vv i get . dd i get . mul /tt set |
|
tt @@@.hsymbol . add init tt eq { } |
|
{ [@@@.hsymbol ( is larger than ) vv i get ( ) dd i get] cat error} ifelse |
|
} for |
|
|
|
0 1 vv length 1 sub { |
|
/i set |
|
vv i get . /tt set |
|
tt (1). add init (1). eq { } |
|
{ [vv i get ( is larger than 1 ) ] cat error} ifelse |
|
} for |
|
|
|
% check for global variables. |
|
0 1 vvGlobal length 1 sub { |
|
/i set |
|
vvGlobal i get . /tt set |
|
tt (1). add init (1). eq { [vvGlobal i get ( is smaller than 1 ) ] cat error } |
|
{ } ifelse |
|
} for |
|
|
|
|
|
/arg1 1 def |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
[(ecart.checkOrder) |
[(ecart.checkOrder) |
[(v ecart.checkOrder bool checks if the given order is relevant) |
[([v vGlobal] ecart.checkOrder bool checks if the given order is relevant) |
(for the ecart division.) |
(for the ecart division.) |
(cf. ecartd.gb, ecart.gb, ecartn.gb) |
(cf. ecartd.gb, ecart.gb, ecartn.gb) |
] |
] |
|
|
/univ vars 0 get reverse |
/univ vars 0 get reverse |
vars 1 get reverse join |
vars 1 get reverse join |
def |
def |
|
w-vectors to_int32 /w-vectors set |
[ |
[ |
0 1 << w-vectors length 1 sub >> |
0 1 << w-vectors length 1 sub >> |
{ |
{ |
|
|
/gbasis2 gbasis 0 get def |
/gbasis2 gbasis 0 get def |
} { |
} { |
[ [(1)] ] gbasis rest join ecartd.gb 0 get getRing ring_def |
[ [(1)] ] gbasis rest join ecartd.gb 0 get getRing ring_def |
/gbasis2 gbasis 0 get ,,, def |
/gbasis2 gbasis 0 get ___ def |
} ifelse |
} ifelse |
ecartd.begin |
ecartd.begin |
|
|
flist ,,, /flist set |
flist ___ /flist set |
flist tag 6 eq { |
flist tag 6 eq { |
flist { gbasis2 reduction } map /ans set |
flist { gbasis2 reduction } map /ans set |
}{ |
}{ |
|
|
(x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set |
(x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set |
(Dx) ggg ecartd.reduction /gg4 set |
(Dx) ggg ecartd.reduction /gg4 set |
gg4 message |
gg4 message |
[gg2 gg3 gg4] |
|
|
(----------- reduction by h=1 ---------------) message |
|
[[( 2*(1-x-y) Dx + 1 ) ( 2*(1-x-y) Dy + 1 )] |
|
(x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set |
|
[(Homogenize) 0] system_variable |
|
(Dx) ggg ecartd.reduction /gg5 set |
|
[(Homogenize) 1] system_variable |
|
gg5 message |
|
|
|
[gg2 gg3 gg4 gg5] |
} def |
} def |
|
|
/ecarth.reduction { |
/ecarth.reduction { |
|
|
/gbasis2 gbasis 0 get def |
/gbasis2 gbasis 0 get def |
} { |
} { |
[ [(1)] ] gbasis rest join ecarth.gb 0 get getRing ring_def |
[ [(1)] ] gbasis rest join ecarth.gb 0 get getRing ring_def |
/gbasis2 gbasis 0 get ,,, def |
/gbasis2 gbasis 0 get ___ def |
} ifelse |
} ifelse |
ecarth.begin |
ecarth.begin |
|
|
flist ,,, /flist set |
flist ___ /flist set |
flist tag 6 eq { |
flist tag 6 eq { |
flist { gbasis2 reduction } map /ans set |
flist { gbasis2 reduction } map /ans set |
}{ |
}{ |
|
|
$ (Dx+Dy) ggg ecartd.reduction :: $ |
$ (Dx+Dy) ggg ecartd.reduction :: $ |
]] putUsages |
]] putUsages |
|
|
|
/ecartd.reduction_noh { |
|
/arg2 set |
|
/arg1 set |
|
[/in-ecarth.reduction_noh /gbasis /flist] pushVariables |
|
[(Homogenize)] pushEnv |
|
[ |
|
/gbasis arg2 def |
|
/flist arg1 def |
|
[(Homogenize) 0] system_variable |
|
flist gbasis ecartd.reduction /arg1 set |
|
] pop |
|
popEnv |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
[(ecartd.reduction_noh) |
|
[ (f basis ecartd.reduction_noh r) |
|
(f is reduced by basis by the tangent cone algorithm.) |
|
(The first element of basis <g_1,...,g_m> must be a standard basis.) |
|
(r is the return value format of reduction.) |
|
(r=[h,c0,syz,input], h = c0 f + \sum syz_i g_i) |
|
(basis is given in the argument format of ecartd.gb and) |
|
(it should not contain the variable h. cf. dehomogenize) |
|
$h[0,1](D)-homogenization is NOT used.$ |
|
(cf. reduction, ecartd.gb, ecartd.reduction ) |
|
$Example:$ |
|
$ [[( 2*(1-x-y) Dx + 1 ) ( 2*(1-x-y) Dy + 1 )] $ |
|
$ (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set $ |
|
$ (Dx+Dy) ggg ecartd.reduction_noh :: $ |
|
]] putUsages |
|
|
/ecart.stdOrder { |
/ecart.stdOrder { |
/arg1 set |
/arg1 set |
[/in-ecart.stdOrder /vv /tt /dvv /wv1 /wv2 |
[/in-ecart.stdOrder /vv /tt /dvv /wv1 /wv2 |
|
|
} def |
} def |
/ecart.homogenize01Ideal { |
/ecart.homogenize01Ideal { |
/arg1 set |
/arg1 set |
[/in.ecart.homogenize01Ideal /ll /vv /wv] pushVariables |
[/in.ecart.homogenize01Ideal /ll /vv /wv /ans] pushVariables |
[ |
[ |
/ll arg1 0 get def |
/ll arg1 0 get def |
/vv arg1 1 get def |
/vv arg1 1 get def |
vv isArray { vv from_records /vv set } { } ifelse |
vv isArray { vv from_records /vv set } { } ifelse |
vv ecart.01Order /wv set |
vv ecart.01Order /wv set |
[vv ring_of_differential_operators 0] define_ring |
[vv ring_of_differential_operators 0] define_ring |
ll ,,, /ll set ll dehomogenize /ll set |
ll ___ /ll set ll dehomogenize /ll set |
[ll vv wv] gb 0 get /ll set |
[ll vv wv] gb 0 get /ll set |
|
|
ecart.begin |
ecart.begin |
[vv ring_of_differential_operators |
[vv ring_of_differential_operators |
vv ecart.stdOrder weight_vector 0 |
vv ecart.stdOrder weight_vector 0 |
[(weightedHomogenization) 1]] define_ring |
[(weightedHomogenization) 1]] define_ring |
ll ,,, {ecart.homogenize01 ecart.dehomogenizeH} map /arg1 set |
ll ___ {ecart.homogenize01 ecart.dehomogenizeH} map /ans set |
|
ecart.end |
|
/arg1 ans def |
] pop |
] pop |
popVariables |
popVariables |
arg1 |
arg1 |
|
|
|
|
( ) message-quiet |
( ) message-quiet |
|
|
|
/ecart_loaded 1 def |
|
|