version 1.7, 2004/09/30 07:45:04 |
version 1.18, 2009/12/11 02:09:09 |
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% $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.6 2004/09/30 07:39:42 takayama Exp $ |
% $OpenXM: OpenXM/src/kan96xx/Doc/gfan.sm1,v 1.17 2009/09/04 11:13:11 takayama Exp $ |
% cp cone.sm1 $OpenXM_HOME/src/kan96xx/Doc/gfan.sm1 |
% cp cone.sm1 $OpenXM_HOME/src/kan96xx/Doc/gfan.sm1 |
% $Id$ |
% $Id$ |
% iso-2022-jp |
% iso-2022-jp |
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%%Ref: @s/2004/08/21-note.pdf |
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%% gfan.sm1 works only for polymake 2.0 Use webservice of 2.0. |
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[(gfan) |
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[ |
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(gfan.sm1 is a package to compute global and local Grobner fans.) |
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(See R.Bahloul and N.Takayama, arxiv, math.AG/0412044 and references as to algorithms.) |
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(At the beginning of the source code gfan.sm1, there are sample inputs cone.sample and cone.sample2.) |
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( ) |
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(gfan.sm1 works only with polymake 2.0. We provide a web service of computing ) |
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(with polymake 2.0. /@@@polymake.web 1 def is set by default in gfan.sm1.) |
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(See changelog-ja.tex as to details on the difference between 2.0 and later versions.) |
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( ) |
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( cone.Wt cone.Lpt {vertices in the output} are weights on the rays of the Grobner cone.) |
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( cone.L gives a basis of the linearity space.) |
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] |
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] putUsages |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%% Two examples are given below to get a global Grobner fan and |
%% Two examples are given below to get a global Grobner fan and |
%% a local Grobner fan ; cone.sample and cone.sample2 |
%% a local Grobner fan ; cone.sample and cone.sample2 |
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%% How to input data? An example. (cf. test13.sm1) |
%% How to input data? An example. (cf. test13.sm1) |
%% Modify the following or copy the /cone.sample { ... } def |
%% Modify the following or copy the /cone.sample { ... } def |
%% to your own file, |
%% to your own file, |
%% edit it, and execute if by " cone.sample ; " |
%% edit it, and execute it by " cone.sample ; " |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
/cone.sample { |
/cone.sample { |
cone.load.cohom |
cone.load.cohom |
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/cone.ckmFlip 1 def |
% write a comment about the problem. "nl" means new line. |
% write a comment about the problem. "nl" means new line. |
/cone.comment [ |
/cone.comment [ |
(Toric ideal for 1-simplex x 2-simplex, in k[x]) nl |
(Toric ideal for 1-simplex x 2-simplex, in k[x]) nl |
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] |
] |
def |
def |
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/cone.DhH 0 def |
% Set a function to compute Grobner basis. |
% Set a function to compute Grobner basis. |
% cone.gb_Dh : For computing in Homogenized Weyl algebra h[1,1](D). |
% cone.gb_Dh : For computing in Homogenized Weyl algebra h[1,1](D). |
% cone.gb_DhH : For computing in doubly homogenized Weyl algebra. |
% cone.gb_DhH : For computing in doubly homogenized Weyl algebra. |
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printGrobnerFan |
printGrobnerFan |
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%%%% If you want to save the data to the file sm1out.txt, then uncomment. |
%%%% If you want to save the data to the file sm1out.txt, then uncomment. |
% /cone.wightGblist 1 def saveGrobnerFan /ff set ff output |
% /cone.withGblist 1 def saveGrobnerFan /ff set ff output |
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%%%% Step 2. Dehomogenize the Grobner Cones |
%%%% Step 2. Dehomogenize the Grobner Cones |
%%%% by the equivalence relation in a local ring (uncomment). |
%%%% by the equivalence relation in a local ring (uncomment). |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
/cone.sample2 { |
/cone.sample2 { |
cone.load.cohom |
cone.load.cohom |
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/cone.ckmFlip 1 def |
% write a comment about the problem. "nl" means new line. |
% write a comment about the problem. "nl" means new line. |
/cone.comment [ |
/cone.comment [ |
(BS for y and y-(x-1)^2, t1, t2 space, in doubly homogenized Weyl algebra.) nl |
(BS for y and y-(x-1)^2, t1, t2 space, in doubly homogenized Weyl algebra.) nl |
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cone.input { . homogenize toString } map /cone.input set |
cone.input { . homogenize toString } map /cone.input set |
dh.end |
dh.end |
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/cone.DhH 1 def |
% Set a function to compute Grobner basis. |
% Set a function to compute Grobner basis. |
% cone.gb_Dh : For computing in Homogenized Weyl algebra h[1,1](D). |
% cone.gb_Dh : For computing in Homogenized Weyl algebra h[1,1](D). |
% cone.gb_DhH : For computing in doubly homogenized Weyl algebra. |
% cone.gb_DhH : For computing in doubly homogenized Weyl algebra. |
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printGrobnerFan |
printGrobnerFan |
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%%%% If you want to save the data to the file sm1out.txt, then uncomment. |
%%%% If you want to save the data to the file sm1out.txt, then uncomment. |
% /cone.wightGblist 1 def saveGrobnerFan /ff set ff output |
% /cone.withGblist 1 def saveGrobnerFan /ff set ff output |
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%%%% Step 2. Dehomogenize the Grobner Cones |
%%%% Step 2. Dehomogenize the Grobner Cones |
%%%% by the equivalence relation in a local ring (uncomment). |
%%%% by the equivalence relation in a local ring (uncomment). |
Line 243 dhcone.printGrobnerFan |
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Line 264 dhcone.printGrobnerFan |
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% If you use local polymake, then comment out. |
% If you use local polymake, then comment out. |
% If you use the cgi/polymake on the net, then uncomment out. |
% If you use the cgi/polymake on the net, then uncomment out. |
%/doPolymake {doPolymake.OoHG} def |
%/doPolymake {doPolymake.OoHG} def (Using doPolymake.OoHG ) message |
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%/polymake.start {polymake.start.OoHG} def (Using polymake.start.OoHG ) message |
% My setting. |
/@@@polymake.web 1 def |
[(getenv) (HOST)] extension /cone.hostname set |
%% Choose it automatically. |
cone.hostname tag 0 eq { /cone.hostname (?) def } { } ifelse |
[(which) (polymake)] oxshell tag 0 eq |
cone.hostname (orange2.math.sci.kobe-u.ac.jp) eq |
@@@polymake.web 1 eq |
cone.hostname (orange2-clone.math.sci.kobe-u.ac.jp) eq |
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or |
or |
{ |
{ |
(Using doPolymake.OoHG ) message |
(Polymake is not installed in this system or @@@polymake.web is set.) message |
/doPolymake {doPolymake.OoHG} def |
/doPolymake {doPolymake.OoHG} def |
} { } ifelse |
(Using doPolymake.OoHG ) message |
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/polymake.start {polymake.start.OoHG} def |
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(Using polymake.start.OoHG ) message |
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} { (Local polymake will be used.) message } ifelse |
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/cone.debug 1 def |
/cone.debug 1 def |
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/cone.loaded boundp { } |
/cone.loaded boundp { } |
{ |
{ |
[(parse) (cohom.sm1) pushfile] extension |
[(parse) (cohom.sm1) pushfile] extension |
% [(parse) (cone.sm1) pushfile] extension |
% [(parse) (cone.sm1) pushfile] extension % BUG? cone.sm1 overrides a global |
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% in cohom.sm1? |
[(parse) (dhecart.sm1) pushfile] extension |
[(parse) (dhecart.sm1) pushfile] extension |
/cone.loaded 1 def |
/cone.loaded 1 def |
oxNoX polymake.start ( ) message |
oxNoX |
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polymake.start ( ) message |
} ifelse |
} ifelse |
} def |
} def |
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/dh.autoHomogenize 0 def |
/dh.autoHomogenize 0 def |
[(AutoReduce) 1] system_variable |
[(AutoReduce) 1] system_variable |
[ff { toString } map cone.vv |
[ff { toString } map cone.vv |
[ww cone.vv generateD1_1]] dh.gb 0 get /arg1 set |
[ww cone.vv generateD1_1]] ff getAttributeList setAttributeList |
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dh.gb 0 get /arg1 set |
] pop |
] pop |
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popVariables |
arg1 |
arg1 |
} def |
} def |
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Line 395 cone.comment message |
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Line 422 cone.comment message |
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% cone.d (pointed cones lies in this space. cf. cone.Lp) |
% cone.d (pointed cones lies in this space. cf. cone.Lp) |
% These are set during getting the cone.startingCone |
% These are set during getting the cone.startingCone |
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%< |
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% global |
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%cone.ckmFlip. Collar-Kalkbrener-Mall $B$N(B flip $B%"%k%4%j%:%`$r;H$o$J$$(B 0. $B;H$&(B 1. |
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% Default $B$O(B 0. |
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%> |
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/cone.ckmFlip 0 def |
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%< |
%< |
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% global |
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% cone.DhH dx x = x dx + h H $B$J$i(B 1. dx x = x dx + h^2 $B$J$i(B 0. Default 0. |
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%> |
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/cone.DhH 0 def |
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%< |
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% Global |
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% gbCheck $B$r$9$k$+(B? $B$7$J$$$H7k2L$O$"$d$U$d(B. $B$7$+$7%a%b%j(B exhaust $B$OKI$2$k(B. |
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% $B;H$&$H$-$O(B /cone.epsilon, /cone.epsilon.limit $B$r==J,>.$5$/$7$F$*$/(B. |
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%> |
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/cone.do_gbCheck 1 def |
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% Default $B$N(B cone.gb $B$NDj5A(B. $B3F%W%m%0%i%`$G:FEYDj5A$7$F$b$h$$(B. |
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/cone.gb { |
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cone.DhH { |
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cone.gb_DhH |
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} { |
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cone.gb_Dh |
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} ifelse |
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} def |
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%< |
% Usage: wv g coneEq1 |
% Usage: wv g coneEq1 |
% in(f) $B$,(B monomial $B@lMQ(B. in_w(f) = LT(f) $B$H$J$k(B weight w $B$NK~$?$9(B |
% in(f) $B$,(B monomial $B@lMQ(B. in_w(f) = LT(f) $B$H$J$k(B weight w $B$NK~$?$9(B |
% $BITEy<0@)Ls$r5a$a$k(B. |
% $BITEy<0@)Ls$r5a$a$k(B. |
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%> |
%> |
/getConeInfo { |
/getConeInfo { |
/arg1 set |
/arg1 set |
[/ww /g /ceq /ceq2 /cdim /mmc /mmL /rr /ineq /ppt] pushVariables |
[/ww /g /ceq /ceq2 /cdim /mmc /mmL /rr /ineq /ppt /rr0 /mm0 /mm1] pushVariables |
[ |
[ |
/ceq arg1 def |
/ceq arg1 def |
ceq pruneZeroVector /ceq set |
ceq pruneZeroVector /ceq set |
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ceq length 0 eq { |
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(Monomial ideal is not accepted as an input.) cone_ir_input |
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} { } ifelse |
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/mm1 |
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( Use [(keep_tmp_files) 1] oxshell to check the input to polymake2tfb. See /tmp or $TMP ) |
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def |
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ceq genPo2 /ceq2 set |
ceq genPo2 /ceq2 set |
% ceq2 $B$O(B polymake.data(polymake.INEQUALITIES(...)) $B7A<0(B |
% ceq2 $B$O(B polymake.data(polymake.INEQUALITIES(...)) $B7A<0(B |
% polymake $B$G(B ceq2 $B$N<!85$N7W;;(B. |
% polymake $B$G(B ceq2 $B$N<!85$N7W;;(B. |
/getConeInfo.ceq ceq def /getConeInfo.ceq2 ceq2 def |
/getConeInfo.ceq ceq def /getConeInfo.ceq2 ceq2 def |
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cone.debug { (Calling polymake DIM.) message } { } ifelse |
cone.debug { (Calling polymake DIM.) message } { } ifelse |
[(DIM) ceq2] doPolymake 1 get /rr set |
[(DIM) ceq2] doPolymake /rr0 set |
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% rr0 2 get message |
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rr0 2 get 1 get 0 get /mm0 set |
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mm0 length 0 eq { } |
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{ [mm0 mm1] cat error } ifelse |
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rr0 1 get /rr set |
cone.debug {(Done.) message } { } ifelse |
cone.debug {(Done.) message } { } ifelse |
% test5 $B$K$O<!$N%3%a%s%H$H$j$5$k(B. $B>e$N9T$r%3%a%s%H%"%&%H(B. |
% test5 $B$K$O<!$N%3%a%s%H$H$j$5$k(B. $B>e$N9T$r%3%a%s%H%"%&%H(B. |
% test5.data tfbToTree /rr set |
% test5.data tfbToTree /rr set |
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% FACETS $B$r;}$C$F$$$J$$$J$i:FEY7W;;$9$k(B. |
% FACETS $B$r;}$C$F$$$J$$$J$i:FEY7W;;$9$k(B. |
% POINTED, NOT__POINTED $B$bF@$i$l$k(B |
% POINTED, NOT__POINTED $B$bF@$i$l$k(B |
cone.debug { (Calling polymake FACETS.) message } { } ifelse |
cone.debug { (Calling polymake FACETS.) message } { } ifelse |
[(FACETS) ceq2] doPolymake 1 get /rr set |
[(FACETS) ceq2] doPolymake /rr0 set |
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% rr0 2 get message |
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rr0 2 get 1 get 0 get /mm0 set |
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mm0 length 0 eq { } |
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{ [mm0 mm1] cat error } ifelse |
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rr0 1 get /rr set |
cone.debug { (Done.) message } { } ifelse |
cone.debug { (Done.) message } { } ifelse |
} { } ifelse |
} { } ifelse |
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rr (VERTICES) getNode tag 0 eq { |
rr (VERTICES) getNode tag 0 eq { |
(internal error: VERTICES is not found.) error |
(internal error: VERTICES is not found.) error |
} { } ifelse |
} { |
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rr (VERTICES) getNode |
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(UNDEF) getNode tag 0 eq { } |
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{ (internal error: VERTICES is UNDEF. See rr. Set /@@@polymake.web 1 def) error } ifelse |
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} ifelse |
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/cone.getConeInfo.rr1 rr def |
/cone.getConeInfo.rr1 rr def |
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/vlist arg1 def |
/vlist arg1 def |
/wlist arg2 def |
/wlist arg2 def |
wlist length vlist length eq { |
wlist length vlist length eq { |
} { (cone_wtowv: length of the argument must be the same.) error} ifelse |
} { (cone_wtowv: length of the argument must be the same. Please check the values of cone.vlist cone.vv cone.type parametrizeWeightSpace) error} ifelse |
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wlist to_int32 /wlist set |
wlist to_int32 /wlist set |
[ |
[ |
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% note: 2004.9.2 |
% note: 2004.9.2 |
cone (facetsv) getNode 2 get facet_i get /v set |
cone (facetsv) getNode 2 get facet_i get /v set |
cone (facets) getNode 2 get facet_i get /f set |
cone (facets) getNode 2 get facet_i get /f set |
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v length 0 eq { |
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(The codimension of the linarity space of the Grobner cone seems to be 1 or 0.) cone_ir_input |
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} { } ifelse |
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/vp v 0 get def |
/vp v 0 get def |
1 1 v length 1 sub { |
1 1 v length 1 sub { |
/ii set |
/ii set |
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%> |
%> |
/cone.gb_Dh { |
/cone.gb_Dh { |
/arg2 set /arg1 set |
/arg2 set /arg1 set |
[/ff /ww /gg] pushVariables |
[/ff /ww /gg /gbopt] pushVariables |
[ |
[ |
/ff arg1 def |
/ff arg1 def |
/ww arg2 def |
/ww arg2 def |
[(AutoReduce) 1] system_variable |
[(AutoReduce) 1] system_variable |
[cone.vv ring_of_differential_operators |
[cone.vv ring_of_differential_operators |
[ww] weight_vector 0] define_ring |
[ww] weight_vector 0] define_ring |
[ff {toString .} map] groebner 0 get /gg set |
%(---) messagen ff getAttributeList message |
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ff getAttributeList tag 0 eq {/gbopt [ ] def } |
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{ |
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/gbopt ff getAttributeList def |
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} ifelse |
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[ff {toString .} map gbopt] |
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groebner 0 get /gg set %% groenber $B$O(B attribute $B$r<u$1IU$1$J$$(B. |
/cone.gb_Dh.g gg def |
/cone.gb_Dh.g gg def |
/arg1 gg def |
/arg1 gg def |
] pop |
] pop |
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} def |
} def |
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%< |
%< |
% usages: getNextFlip [cone, k] |
% usages: getNextFlip [cone, k, cid] |
% cone.fan $B$r8!:w$7$F(B $B$^$@(B flip $B$7$F$J$$(B cone $B$H(B facet $B$NAH$rLa$9(B. |
% cone.fan $B$r8!:w$7$F(B $B$^$@(B flip $B$7$F$J$$(B cone $B$H(B facet $B$NAH$rLa$9(B. |
% $B$b$&$J$$$H$-$K$O(B null $B$rLa$9(B. |
% $B$b$&$J$$$H$-$K$O(B null $B$rLa$9(B. |
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% cid $B$O(B cone $B$,(B cone.fan $B$N(B $B2?HVL\$G$"$k$+$N(B index. cone.gblist $B$N8!:wEy$K(B |
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% $BMQ$$$k(B. |
%> |
%> |
/getNextFlip { |
/getNextFlip { |
[/tcone /ans /ii ] pushVariables |
[/tcone /ans /ii /cid] pushVariables |
[ |
[ |
/ans null def |
/ans null def /cid -1 def |
0 1 cone.fan length 1 sub { |
0 1 cone.fan length 1 sub { |
/ii set |
/ii set |
cone.fan ii get /tcone set |
cone.fan ii get /tcone set |
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/cid ii def |
tcone getNextFacet /ans set |
tcone getNextFacet /ans set |
ans tag 0 eq { } { exit } ifelse |
ans tag 0 eq { } { exit } ifelse |
} for |
} for |
ans tag 0 eq { /arg1 null def } |
ans tag 0 eq { /arg1 null def } |
{ /arg1 [tcone ans] def } ifelse |
{ /arg1 [tcone ans cid] def } ifelse |
] pop |
] pop |
popVariables |
popVariables |
arg1 |
arg1 |
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% flip $B$N;~$N(B epsilon |
% flip $B$N;~$N(B epsilon |
/cone.epsilon (1).. (10).. div def |
/cone.epsilon (1).. (10).. div def |
/cone.epsilon.limit (1).. (100).. div def |
/cone.epsilon.limit (1).. (100).. div def |
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% cone.epsilon.limit $B$rIi$K$9$l$PDd;_$7$J$$(B. |
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%< |
%< |
% Usages: result_getNextFlip getNextCone ncone |
% Usages: result_getNextFlip getNextCone ncone |
% flip $B$7$F?7$7$$(B ncone $B$rF@$k(B. |
% flip $B$7$F?7$7$$(B ncone $B$rF@$k(B. |
%> |
%> |
/getNextCone { |
/getNextCone.orig { |
/arg1 set |
/arg1 set |
[/ncone /ccone /kk /w /next_weight_w_wv] pushVariables |
[/ncone /ccone /kk /w /next_weight_w_wv] pushVariables |
[ |
[ |
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% |
% |
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% Todo: save functions. |
% Todo: save functions. |
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%< |
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% Collart, Kalkbrener, Mall $B$N%"%k%4%j%:%`$K$h$k(B gb $B$N(B flip. |
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% See also Sturmfels' book, p.22, 23. |
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% Usages: [reducedGb, vlist, oldWeight, facetWeight, newWeight] ckmFlip rGb |
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% If it fails, then it returns null, else it returns the reducedGb for the |
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% newWeight. |
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% gb $B$N(B check $B$r$d$k$N$G(B, $B$=$l$K<:GT$7$?$i(B null $B$rLa$9(B. |
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% weight $B$O$9$Y$F(B vw $B7A<0$G(B. vw $B7A<0(B = variable weight $B$N7+$jJV$7$N7A<0(B |
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% reducedGb $B$OJ8;zNs$N%j%9%H$G$O$J$/B?9`<0$N7A<0$N$3$H(B. |
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% $BM}M3$O(B reducedGb $B$h$j(B ring $B$N9=B$$rFI$`$?$a(B. |
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%> |
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/ckmFlip { |
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/arg1 set |
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[/arg_ckmFlip /gOld /vlist /oldWeight /facetWeight /newWeight |
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/gNew |
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/ww /ww1 /ww2 % $BK\$NCf$N(B w1, w, w2 ($B8E$$(B, facet, $B?7$7$$(B) |
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/ch1 /ch2 % $BK\$NCf$N(B {\cal H}_1, {\cal H}_2 |
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/grData /rTable |
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/rTable2 % rTable $B$NH?BP$NJQ49(B. |
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/facetWeight_gr /vlist_gr % graded ring $BMQ(B. |
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/oldWeight_gr |
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/ccf % reduction $B$7$?78?t(B. |
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/rwork /ccf2 /gNew |
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] pushVariables |
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[ |
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arg1 /arg_ckmFlip set |
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arg_ckmFlip 0 get /gOld set |
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arg_ckmFlip 1 get /vlist set |
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arg_ckmFlip 2 get /oldWeight set |
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arg_ckmFlip 3 get /facetWeight set |
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arg_ckmFlip 4 get /newWeight set |
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% facet weight vector ww $B$K$D$$$F$N(B initial $B$r<h$j=P$9(B. ch1 $B$X$$$l$k(B. |
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gOld getRing ring_def |
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facetWeight weightv /ww set |
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gOld { ww init } map /ch1 set % facetWeight $B$K$h$k(B initial $B$N<h$j=P$7(B. |
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% $BNc(B: [(x,y) [(x) -1 (Dx) 1 (y) -1 (Dy) 2]] getGrRing |
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% [$x,y,y',$ , [ $x$ , $y$ ] , [ [ $Dy$ , $y'$ ] ] ] |
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% $BJQ?t%j%9%H(B $BCV49I=(B |
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% ch1 $B$r(B gr_ww $B$N85$KJQ49(B. |
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[vlist facetWeight] getGrRing /grData set |
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[grData 0 get ring_of_differential_operators 0] define_ring /rwork set |
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grData 2 get { { . } map } map /rTable set |
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rTable { reverse } map /rTable2 set |
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grData 0 get /vlist_gr set |
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ch1 { toString . rTable replace toString } map /ch1 set |
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oldWeight { dup isString { . rTable replace toString } |
|
{ } ifelse } map /oldWeight_gr set |
|
|
|
% facetWeight $B$b(B $B?7$7$$4D(B gr_ww $B$N(B weight $B$KJQ49(B. |
|
% $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2] |
|
facetWeight { dup isString { . rTable replace toString } |
|
{ } ifelse } map /facetWeight_gr set |
|
|
|
% newWeight $B$b(B $B?7$7$$4D(B gr_ww $B$N(B weight $B$KJQ49(B. |
|
% $BNc(B. [(x) -1 (Dx) 1 (y) -1 (Dy) 2] ==> [(x) -1 (Dx) 1 (y) -1 (y') 2] |
|
newWeight { dup isString { . rTable replace toString } |
|
{ } ifelse } map /newWeight_gr set |
|
|
|
% Dx x = x Dx + h H or Dx x = x Dx + h^2 $B$G7W;;(B. |
|
% $B$I$A$i$r$H$k$+$O(B cone.gb_gr $B$G6hJL$9$k$7$+$J$7(B |
|
%% [ch1 vlist_gr oldWeight_gr] /ttt set |
|
%% ttt cone.gb_gr /ch1 set %$B:FEY$N7W;;$OITMW(B. |
|
[[(1)] vlist_gr oldWeight_gr] cone.gb_gr getRing ring_def % Set Ring. |
|
ch1 {toString .} map /ch1 set |
|
%% $B$3$3$^$G$G$H$j$"$($:%F%9%H$r$7$h$&(B. |
|
%% ch1 /arg1 set |
|
[ch1 { toString } map vlist_gr newWeight_gr] cone.gb_gr /ch2 set |
|
|
|
% Dx x = x Dx + h H or Dx x = x Dx + h^2 $B$G7W;;(B. |
|
% $B$I$A$i$r$H$k$+$O(B cone.reduction_gr $B$G6hJL$9$k$7$+$J$7(B |
|
ch1 getRing ring_def ; |
|
ch2 {toString .} map {ch1 cone.reduction} map /ccf set |
|
%ccf pmat |
|
% $B$H$j$"$($:%F%9%H(B. |
|
% [ch1 ch2] /arg1 set |
|
%% ccf[i][0] $B$O(B 0 $B$G$J$$$HL7=b(B. check $B$^$@$7$F$J$$(B. |
|
|
|
%% ccf[i][2] (syzygy) $B$r(B gr $B$+$i(B $B$b$H$N(B ring $B$XLa$7(B, |
|
%% $B?7$7$$(B reduced gbasis $B$r(B ccf[i][2] * gOld $B$G:n$k(B. |
|
rwork ring_def |
|
ccf { 2 get {toString . rTable2 replace toString} map } map /ccf2 set |
|
%% ccf2 $B$O(B gr $B$G$J$$(B ring $B$N85(B. |
|
gOld getRing ring_def |
|
cone.DhH { cone.begin_DhH } { } ifelse % Hh $B$+(B h^2 $B$+(B. |
|
ccf2 { {.} map gOld mul } map /gNew set |
|
gNew { toString } map /gNew set |
|
cone.DhH { cone.end_DhH } { } ifelse % Hh $B$+(B h^2 $B$+(B. |
|
% gNew /arg1 set |
|
%gNew $B$,(B newWeight $B$G$N(B GB $B$+(B check. Yes $B$J$i(B reduced basis $B$X(B. |
|
%No $B$J$i(B null $B$rLa$9(B. |
|
%%Ref: note @s/2005/06/30-note-gfan.pdf |
|
cone.do_gbCheck not { |
|
(Warning! gbCheck is skipped.) message |
|
} { |
|
(Doing gbCheck.) message |
|
} ifelse |
|
cone.do_gbCheck { |
|
gNew [(gbCheck) 1] setAttributeList newWeight |
|
cone.gb (gb) getAttribute |
|
} { 1 } ifelse |
|
1 eq { |
|
gNew [(reduceOnly) 1] setAttributeList newWeight cone.gb /arg1 set |
|
}{ /arg1 null def } ifelse |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
%< |
|
% Usages: f gbasis cone.reduction_DhH |
|
% dx x = x dx + h H $B$G$N(B reduction. |
|
%> |
|
/cone.reduction_DhH { |
|
/arg2 set /arg1 set |
|
[/ff /ggbasis /eenv /ans] pushVariables |
|
[ |
|
/ff arg1 def /ggbasis arg2 def |
|
cone.begin_DhH |
|
ff ggbasis reduction /ans set |
|
cone.end_DhH |
|
/arg1 ans def |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
%< |
|
% Usages: f gbasis cone.reduction_Dh |
|
% dx x = x dx + h^2 $B$G$N(B reduction. |
|
%> |
|
/cone.reduction_Dh { |
|
/arg2 set /arg1 set |
|
[/ff /ggbasis /eenv /ans] pushVariables |
|
[ |
|
/ff arg1 def /ggbasis arg2 def |
|
ff ggbasis reduction /ans set |
|
/arg1 ans def |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
%< |
|
% Usages: cone.begin_DhH dx x = x dx + h H $B$r3+;O(B. |
|
%> |
|
/cone.begin_DhH { |
|
[(Homogenize) (AutoReduce) (KanGBmessage)] pushEnv /cone.eenv set |
|
[(Homogenize) 3] system_variable |
|
} def |
|
|
|
%< |
|
% Usages: cone.begin_DhH dx x = x dx + h H $B$r=*N;(B. |
|
%> |
|
/cone.end_DhH { |
|
cone.eenv popEnv |
|
} def |
|
|
|
%< |
|
% Usages: ff vv ww cone.gb_gr_DhH dx x = x dx + h H $B$G7W;;(B. |
|
% dh.gb $B$O(B dhecart.sm1 $B$GDj5A$5$l$F$*$j(B, dx x = x dx + h H $B$G$N7W;;(B. |
|
% gr $B$r$H$C$F$b(B, -w,w $B$N>l9g$O(B $BHyJ,:nMQAG4D$N$^$^$G$"$j(B, $B$3$l$,I,MW(B. |
|
% bug? cone.gb $B$G==J,(B? |
|
%> |
|
/cone.gb_gr_DhH { |
|
/arg1 set |
|
[/ff /ww /vv] pushVariables |
|
[ |
|
/ff arg1 0 get def |
|
/vv arg1 1 get def |
|
/ww arg1 2 get def |
|
/dh.gb.verbose 1 def |
|
/dh.autoHomogenize 0 def |
|
[(AutoReduce) 1] system_variable |
|
[ff { toString } map vv |
|
[ww vv generateD1_1]] dh.gb 0 get /arg1 set |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
%< |
|
% Usages: ff vv ww cone.gb_gr_Dh dx x = x dx + h^2 $B$G7W;;(B. |
|
% gb $B$O(B dhecart.sm1 $B$GDj5A$5$l$F$*$j(B, dx x = x dx + h^2 $B$G$N7W;;(B. |
|
% gr $B$r$H$C$F$b(B, -w,w $B$N>l9g$O(B $BHyJ,:nMQAG4D$N$^$^$G$"$j(B, $B$3$l$,I,MW(B. |
|
% bug? cone.gb $B$G==J,(B? |
|
%> |
|
/cone.gb_gr_Dh { |
|
/arg1 set |
|
[/ff /ww /vv /gg /envtmp] pushVariables |
|
[ |
|
/ff arg1 0 get def |
|
/vv arg1 1 get def |
|
/ww arg1 2 get def |
|
|
|
[(AutoReduce) (KanGBmessage)] pushEnv /envtmp set |
|
[(AutoReduce) 1] system_variable |
|
[(KanGBmessage) 1] system_variable |
|
[vv ring_of_differential_operators |
|
[ww] weight_vector 0] define_ring |
|
[ff {toString .} map] ff getAttributeList setAttributeList |
|
groebner 0 get /gg set |
|
envtmp popEnv |
|
|
|
/arg1 gg def |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
|
|
% $B$3$l$i$O(B cone.ckmFlip 1 $B$N;~$7$+;H$o$:(B. |
|
/cone.reduction { |
|
cone.DhH { |
|
cone.reduction_DhH |
|
}{ |
|
cone.reduction_Dh |
|
} ifelse |
|
} def |
|
/cone.gb_gr { |
|
cone.DhH { |
|
cone.gb_gr_DhH |
|
}{ |
|
cone.gb_gr_Dh |
|
} ifelse |
|
} def |
|
|
|
|
|
/test1.ckmFlip { |
|
% cf. cone.sample2 |
|
cone.load.cohom |
|
/cone.comment [ |
|
(BS for y and y-(x-1)^2, t1, t2 space, in doubly homogenized Weyl algebra.) nl |
|
(The Grobner cones are dehomogenized to get local Grobner fan.) nl |
|
] cat def |
|
/cone.vlist [(t1) (t2) (x) (y) (Dt1) (Dt2) (Dx) (Dy) (h) (H)] def |
|
/cone.vv (t1,t2,x,y) def |
|
/cone.type 1 def |
|
/cone.parametrizeWeightSpace { |
|
4 2 parametrizeSmallFan |
|
} def |
|
|
|
/cone.DhH 1 def |
|
/cone.ckmFlip 1 def |
|
|
|
/cone.local 1 def |
|
/cone.w_start null def |
|
/cone.h0 1 def |
|
/cone.input |
|
[ |
|
(t1-y) (t2 - (y-(x-1)^2)) |
|
((-2 x + 2)*Dt2+Dx) |
|
(Dt1+Dt2+Dy) |
|
] |
|
def |
|
% homogenize |
|
[cone.vv ring_of_differential_operators |
|
[[(t1) -1 (t2) -1 (Dt1) 1 (Dt2) 1]] ecart.weight_vector |
|
0] define_ring |
|
dh.begin |
|
cone.input { . homogenize toString } map /cone.input set |
|
dh.end |
|
|
|
|
|
% $B%F%9%H$r3+;O$9$k(B. |
|
% getStartingCone /cone.ncone set |
|
% cone.ncone updateFan |
|
% cone.gblist 0 get message |
|
% cone.ncone /cone.ccone set |
|
% getNextFlip /cone.nextflip set |
|
% cone.nextflip message |
|
|
|
/wOld [(t1) , -29 , (t2) , -38 , (Dt1) , 29 , (Dt2) , 38 ] def |
|
/wFacet [(t1) , -1 , (t2) , -1 , (Dt1) , 1 , (Dt2) , 1 ] def |
|
/wNew [(t1) , -39 , (t2) , -38 , (Dt1) , 39 , (Dt2) , 38 ] def |
|
cone.input wOld cone.gb /ff set |
|
[ff (t1,t2,x,y) wOld wFacet wNew] ckmFlip /ff2 set |
|
(See ff and ff2) message |
|
|
|
} def |
|
|
|
%< |
|
% Usages: cone i getaVectorOnFacet |
|
% cone $B$N(B i $BHVL\$N(B facet $B$N>e$N(B vector $B$r5a$a$k(B. |
|
% cf. liftWeight |
|
%> |
|
/getaVectorOnFacet { |
|
/arg2 set /arg1 set |
|
[/cone /facet_i /ep /vp /v /v /ii] pushVariables |
|
[ |
|
/cone arg1 def /facet_i arg2 def |
|
facet_i to_int32 /facet_i set |
|
|
|
cone (facetsv) getNode 2 get facet_i get /v set |
|
/vp v 0 get def |
|
1 1 v length 1 sub { |
|
/ii set |
|
vp v ii get add /vp set |
|
} for |
|
vp nnormalize_vec /vp set |
|
/arg1 vp def |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
/getNextCone { |
|
getNextCone_ckm |
|
} def |
|
|
|
%< |
|
% Usages: result_getNextFlip getNextCone_ckm ncone |
|
% flip $B$7$F?7$7$$(B ncone $B$rF@$k(B. Collar-Kalkbrener-Moll $B$N%"%k%4%j%:%`$r;H$&(B |
|
% if (cone.ckmFlip == 0) $BIaDL$N7W;;(B else CKM. |
|
%> |
|
/getNextCone_ckm { |
|
/arg1 set |
|
[/ncone /ccone /kk /w /next_weight_w_wv /cid /ttt] pushVariables |
|
[ |
|
/ccone arg1 def |
|
/ncone null def |
|
/kk ccone 1 get def % kk $B$O(B cid $BHVL\$N(B cone $B$N(B kk $BHVL\$N(B facet $B$rI=$9(B. |
|
/cid ccone 2 get def % cid $B$O(B cone $B$N(B $BHV9f(B. |
|
ccone 0 get /ccone set |
|
{ |
|
ccone tag 0 eq { exit } { } ifelse |
|
|
|
% ccone $B$N(B kk $BHVL\$N(B facet $B$K$D$$$F(B flip $B$9$k(B. |
|
ccone kk cone.epsilon flipWeight /w set |
|
(Trying new weight is ) messagen w message |
|
w liftWeight /next_weight_w_wv set |
|
(Trying new weight [w,wv] is ) messagen next_weight_w_wv message |
|
|
|
cone.ckmFlip { |
|
[ |
|
cone.gblist cid get (grobnerBasis) getNode 2 get % reduce gb |
|
cone.vv |
|
cone.gblist cid get (weight) getNode [2 0 2] get % weight |
|
ccone kk getaVectorOnFacet liftWeight 1 get % weight on facet |
|
next_weight_w_wv 1 get % new weight |
|
] /ttt set |
|
ttt message |
|
ttt ckmFlip /cone.cgb set |
|
}{ |
|
cone.input next_weight_w_wv 1 get cone.gb /cone.cgb set |
|
} ifelse |
|
|
|
cone.cgb tag 0 eq not { |
|
[w] next_weight_w_wv join /cone.cgb_weight set |
|
next_weight_w_wv 1 get cone.cgb coneEq /cone.g_ineq set |
|
cone.g_ineq cone.w_ineq join cone.Wt mul cone.Lpt mul |
|
pruneZeroVector /cone.gw_ineq_projectedWtLpt set |
|
|
|
(cone.gw_ineq_projectedWtLpt is obtained.) message |
|
|
|
cone.gw_ineq_projectedWtLpt getConeInfo /cone.nextConeInfo set |
|
% $B<!85$rD4$Y$k(B. $B$@$a$J$i(B retry |
|
cone.nextConeInfo 0 get 0 get to_int32 cone.d eq { |
|
cone.nextConeInfo 1 get newCone /ncone set |
|
ccone ncone getCommonFacet 0 get { |
|
(Flip succeeded.) message |
|
exit |
|
} { } ifelse |
|
} { } ifelse |
|
% common face $B$,$J$1$l$P(B $B$d$O$j(B epsilon $B$r>.$5$/(B. |
|
cone.nextConeInfo 0 get 0 get to_int32 cone.d eq { |
|
(ccone and ncone do not have a common facet.) message |
|
} { |
|
(ncone is not maximal dimensional. ) message |
|
} ifelse |
|
}{ } ifelse |
|
|
|
(Decreasing epsilon to ) messagen |
|
cone.epsilon (1).. (2).. div mul /cone.epsilon set |
|
cone.epsilon cone.epsilon.limit sub numerator (0).. lt { |
|
(Too small cone.epsilon ) error |
|
} { } ifelse |
|
cone.epsilon message |
|
} loop |
|
/arg1 ncone def |
|
] pop |
|
popVariables |
|
arg1 |
|
} def |
|
|
|
%%change |
|
/cone_ir_input { |
|
/arg1 set |
|
[/msg ] pushVariables |
|
[ |
|
/msg arg1 def |
|
(---------------) message |
|
msg message |
|
( ) message |
|
(Please also refer to the value of the variables cone.getConeInfo.rr0) message |
|
( cone.getConeInfo.rr1 cone.Lp cone.cinit) message |
|
$ cone.cinit (FACETS) getNode :: $ message |
|
(We are sorry that we cannot accept this input.) error |
|
] pop |
|
popVariables |
|
} def |