=================================================================== RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/ecart.sm1,v retrieving revision 1.14 retrieving revision 1.35 diff -u -p -r1.14 -r1.35 --- OpenXM/src/kan96xx/Doc/ecart.sm1 2003/08/27 03:11:13 1.14 +++ OpenXM/src/kan96xx/Doc/ecart.sm1 2004/09/14 03:12:17 1.35 @@ -1,12 +1,16 @@ -% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.13 2003/08/26 12:46:03 takayama Exp $ -%[(parse) (hol.sm1) pushfile] extension +% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.34 2004/09/13 11:24:10 takayama Exp $ +(hol_loaded) boundp { } +{ [(parse) (hol.sm1) pushfile] extension } ifelse %[(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.end { endEcart } def /ecart.autoHomogenize 1 def /ecart.needSyz 0 def +/ecartd.gb.oxRingStructure [[ ] [ ] ] def +/ecart.partialEcartGlobalVarX [ ] def + /ecartd.begin { ecart.begin [(EcartAutomaticHomogenization) 1] system_variable @@ -16,6 +20,79 @@ [(EcartAutomaticHomogenization) 0] system_variable } def +/ecart.message.quiet 0 def +/ecart.message { + ecart.message.quiet { pop } { message } ifelse +} def +/ecart.messagen { + ecart.message.quiet { pop } { messagen } ifelse +} def +/ecart.setOpt.init { +% Initialize + /ecart.partialEcartGlobalVarX [ ] def +} def +/ecart.setOpt { + /arg1 set + [/in-ecart.setOpt /opt /i /n /ans] pushVariables + [ + /opt arg1 def + /ans [ ] def + /n opt length def + + ecart.setOpt.init + + 0 2 n 1 sub { + /i set + opt i get tag StringP eq not { + (ecart.setOpt : [keyword value keyword value ....] ) error + } { } ifelse + { % start of the loop +% Global: degreeShift + opt i get (degreeShift) eq { + /degreeShift opt i 1 add get def + exit + } { } ifelse +% Global: hdShift + opt i get (startingShift) eq { + /hdShift opt i 1 add get def + exit + } { } ifelse +% Global: hdShift + opt i get (noAutoHomogenize) eq { + /hdShift -1 def + exit + } { } ifelse +% Global: ecart.useSugar + opt i get (sugar) eq { + /ecart.useSugar opt i 1 add get def + exit + } { } ifelse + +% 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 + } loop + } for + + ecart.gb.verbose { + (ecart.setOpt:) message + (degreeShift=) messagen degreeShift message + $hdShift(startingShift)=$ messagen hdShift message + (sugar=) messagen ecart.useSugar message + (Other options=) messagen ans message + } { } ifelse + + /arg1 ans def + ] pop + popVariables + arg1 +} def + /ecart.dehomogenize { /arg1 set [/in.ecart.dehomogenize /ll /rr] pushVariables @@ -27,8 +104,8 @@ ll (0). eq { } { ll getRing /rr set - ll [ [ (H) rr ,, (1) rr ,, ] - [ (h) rr ,, (1) rr ,, ]] replace + ll [ [ @@@.Hsymbol rr __ (1) rr __ ] + [ (h) rr __ (1) rr __ ]] replace /ll set } ifelse } ifelse @@ -53,7 +130,7 @@ ll (0). eq { } { ll getRing /rr set - ll [ [ (H) rr ,, (1) rr ,, ] ] replace + ll [ [ @@@.Hsymbol rr __ (1) rr __ ] ] replace /ll set } ifelse } ifelse @@ -93,7 +170,7 @@ ( [(h) 1 (Dx1) 1 (Dx2) 1] ) ( [(Dx1) 1 (Dx2) 1] ) ( [(x1) -1 (x2) -1]) - ( ] weight_vector ) + ( ] ecart.weight_vector ) ( 0 ) ( [(weightedHomogenization) 1 (degreeShift) [[0 0 0]]]) ( ] define_ring) @@ -135,7 +212,7 @@ [/in.ecart.wv1 /v] pushVariables [ /v arg1 def - [(H) (h) v to_records pop] /v set + [@@@.Hsymbol (h) v to_records pop] /v set v { 1 } map /v set /arg1 v def ] pop @@ -158,6 +235,9 @@ /ecart.gb {ecartd.gb} def +[(ecartd.gb) +[(See ecart.gb)]] putUsages + [(ecart.gb) [(a ecart.gb b) (array a; array b;) @@ -171,15 +251,17 @@ (a : [f ]; array f; f is a set of generators of an ideal in a ring.) (a : [f v]; array f; string v; v is the variables. ) (a : [f v w]; array f; string v; array of array w; w is the weight matirx.) - (a : [f v w ds]; array f; string v; array of array w; w is the weight matirx.) + $a : [f v w [(degreeShift) ds]]; array f; string v; array of array w; w is the weight matirx.$ ( array ds; ds is the degree shift for the ring. ) - (a : [f v w ds hdShift]; array f; string v; array of array w; w is the weight matirx.) + $a : [f v w [(degreeShift) ds (startingShift) hdShift]]; array f; string v; array of array w; w is the weight matirx.$ ( array ds; ds is the degree shift for the ring. ) ( array hsShift is the degree shift for the homogenization. cf.homogenize ) - $a : [f v w ds (no)]; array f; string v; array of array w; w is the weight matirx.$ + $a : [f v w [(degreeShift) ds (noAutoHomogenize) 1]]; array f; string v; array of array w; w is the weight matirx.$ ( No automatic homogenization.) + $ [(degreeShift) ds (noAutoHomogenize) 1 (sugar) 1] -->use the sugar strate $ ( ) - $cf. ecarth.gb (homogenized), ecartd.gb (dehomogenize) $ + $cf. ecarth.gb (homogenized), ecartd.gb (dehomogenize), ecartd.reduction $ + ( ecartd.gb.oxRingStructure ) ( ) $Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) $ $ [ [ (Dx) 1 ] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecart.gb pmat ; $ @@ -198,8 +280,15 @@ ( This example will cause an error on order.) ( ) $Example 5: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $ - $ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] [[0 1] [-3 1] ] ] ecart.gb pmat ; $ + $ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] $ + $ [(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, ) ( ecart.dehomogenize, ecart.dehomogenizeH) ( [(weightedHomogenization) 1 (degreeShift) [[1 2 1]]] : options for ) @@ -216,6 +305,7 @@ /gg /wv /vec /ans /rr /mm /degreeShift /env2 /opt /ans.gb /hdShift + /ecart.useSugar ] pushVariables [(CurrentRingp) (KanGBmessage)] pushEnv [ @@ -226,6 +316,8 @@ /degreeShift 0 def /hdShift 0 def /opt [(weightedHomogenization) 1] def + /ecart.useSugar 0 def + ecart.setOpt.init aa { tag } map /typev set typev [ ArrayP ] eq { /f aa 0 get def @@ -259,61 +351,21 @@ /wv aa 2 get def /setarg 1 def } { } ifelse + typev [ArrayP StringP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get def /wv aa 2 get def - /degreeShift aa 3 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse - - typev [ArrayP StringP ArrayP ArrayP ArrayP] eq - { /f aa 0 get def - /v aa 1 get def - /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def - /setarg 1 def - } { } ifelse typev [ArrayP ArrayP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get from_records def /wv aa 2 get def - /degreeShift aa 3 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse - typev [ArrayP ArrayP ArrayP ArrayP ArrayP] eq - { /f aa 0 get def - /v aa 1 get from_records def - /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def - /setarg 1 def - } { } ifelse - typev [ArrayP ArrayP ArrayP ArrayP StringP] eq - { /f aa 0 get def - /v aa 1 get from_records def - /wv aa 2 get def - /degreeShift aa 3 get def - aa 4 get (no) eq { - /hdShift -1 def - } { - (Unknown keyword for the 5th argument) error - } ifelse - /setarg 1 def - } { } ifelse - typev [ArrayP StringP ArrayP ArrayP StringP] eq - { /f aa 0 get def - /v aa 1 get def - /wv aa 2 get def - /degreeShift aa 3 get def - aa 4 get (no) eq { - /hdShift -1 def - } { - (Unknown keyword for the 5th argument) error - } ifelse - /setarg 1 def - } { } ifelse /env1 getOptions def @@ -339,23 +391,23 @@ } { } ifelse wv isInteger { [v ring_of_differential_operators -% [ v ecart.wv1 v ecart.wv2 ] weight_vector +% [ v ecart.wv1 v ecart.wv2 ] ecart.weight_vector gb.characteristic opt ] define_ring }{ degreeShift isInteger { [v ring_of_differential_operators -% [v ecart.wv1 v ecart.wv2] wv join weight_vector - wv weight_vector +% [v ecart.wv1 v ecart.wv2] wv join ecart.weight_vector + wv ecart.weight_vector gb.characteristic opt ] define_ring }{ [v ring_of_differential_operators -% [v ecart.wv1 v ecart.wv2] wv join weight_vector - wv weight_vector +% [v ecart.wv1 v ecart.wv2] wv join ecart.weight_vector + wv ecart.weight_vector gb.characteristic [(degreeShift) degreeShift] opt join ] define_ring @@ -388,7 +440,7 @@ } { } ifelse %%BUG: case of v is integer - v ecart.checkOrder + [v ecart.partialEcartGlobalVarX] ecart.checkOrder ecart.begin @@ -414,10 +466,18 @@ f {/fi set [(degreeShift) hdShift fi] homogenize} map /f set }ifelse - ecart.needSyz { - [f [(needSyz)] gb.options join ] groebner /gg set - } { - [f gb.options] groebner 0 get /gg set + ecart.useSugar { + ecart.needSyz { + [f [(needSyz)] gb.options join ] groebner_sugar /gg set + } { + [f gb.options] groebner_sugar 0 get /gg set + } ifelse + } { + ecart.needSyz { + [f [(needSyz)] gb.options join ] groebner /gg set + } { + [f gb.options] groebner 0 get /gg set + } ifelse } ifelse ecart.needSyz { @@ -472,7 +532,7 @@ (a : [f ]; array f; f is a set of generators of an ideal in a ring.) (a : [f v]; array f; string v; v is the variables. ) (a : [f v w]; array f; string v; array of array w; w is the weight matirx.) - (a : [f v w ds]; array f; string v; array of array w; w is the weight matirx.) + $a : [f v w [(degreeShift) ds]]; array f; string v; array of array w; w is the weight matirx.$ ( array ds; ds is the degree shift ) ( ) (/ecart.autoHomogenize 0 def ) @@ -492,7 +552,8 @@ $ [ [ (x) -1 (y) -1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecarth.gb pmat ; $ ( ) $Example 5: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $ - $ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] [[0 1] [-3 1] ] ] ecarth.gb pmat ; (buggy infinite loop)$ + $ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] $ + $ [(degreeShift) [[0 1] [-3 1] ]] ] ecarth.gb pmat ; $ ( ) (cf. gb, groebner, ecart.gb, ecartd.gb, ecart.syz, ecart.begin, ecart.end, ecart.homogenize01, ) ( ecart.dehomogenize, ecart.dehomogenizeH) @@ -559,6 +620,7 @@ /wv 0 def /degreeShift 0 def /opt [(weightedHomogenization) 1] def + ecart.setOpt.init aa { tag } map /typev set typev [ ArrayP ] eq { /f aa 0 get def @@ -592,18 +654,19 @@ /wv aa 2 get def /setarg 1 def } { } ifelse + typev [ArrayP StringP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get def /wv aa 2 get def - /degreeShift aa 3 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse typev [ArrayP ArrayP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get from_records def /wv aa 2 get def - /degreeShift aa 3 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse @@ -630,21 +693,21 @@ } { } ifelse wv isInteger { [v ring_of_differential_operators - [ v ecart.wv1 v ecart.wv2 ] weight_vector + [ v ecart.wv1 v ecart.wv2 ] ecart.weight_vector gb.characteristic opt ] define_ring }{ degreeShift isInteger { [v ring_of_differential_operators - [v ecart.wv1 v ecart.wv2] wv join weight_vector + [v ecart.wv1 v ecart.wv2] wv join ecart.weight_vector gb.characteristic opt ] define_ring }{ [v ring_of_differential_operators - [v ecart.wv1 v ecart.wv2] wv join weight_vector + [v ecart.wv1 v ecart.wv2] wv join ecart.weight_vector gb.characteristic [(degreeShift) degreeShift] opt join ] define_ring @@ -677,7 +740,7 @@ } { } ifelse %%BUG: case of v is integer - v ecart.checkOrder + [v ecart.partialEcartGlobalVarX] ecart.checkOrder ecartn.begin @@ -743,6 +806,7 @@ /gg /wv /vec /ans /rr /mm /degreeShift /env2 /opt /ans.gb /hdShift + /ecart.useSugar ] pushVariables [(CurrentRingp) (KanGBmessage)] pushEnv [ @@ -752,7 +816,9 @@ /wv 0 def /degreeShift 0 def /hdShift 0 def + /ecart.useSugar 0 def /opt [(weightedHomogenization) 1] def + ecart.setOpt.init aa { tag } map /typev set typev [ ArrayP ] eq { /f aa 0 get def @@ -786,67 +852,28 @@ /wv aa 2 get def /setarg 1 def } { } ifelse + typev [ArrayP StringP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get def /wv aa 2 get def - /degreeShift aa 3 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse typev [ArrayP ArrayP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get from_records def /wv aa 2 get def - /degreeShift aa 3 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse - typev [ArrayP StringP ArrayP ArrayP ArrayP] eq - { /f aa 0 get def - /v aa 1 get def - /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def - /setarg 1 def - } { } ifelse - typev [ArrayP ArrayP ArrayP ArrayP ArrayP] eq - { /f aa 0 get def - /v aa 1 get from_records def - /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def - /setarg 1 def - } { } ifelse - typev [ArrayP ArrayP ArrayP ArrayP StringP] eq - { /f aa 0 get def - /v aa 1 get from_records def - /wv aa 2 get def - /degreeShift aa 3 get def - aa 4 get (no) eq { - /hdShift -1 def - } { - (Unknown keyword for the 5th argument) error - } ifelse - /setarg 1 def - } { } ifelse - typev [ArrayP StringP ArrayP ArrayP StringP] eq - { /f aa 0 get def - /v aa 1 get def - /wv aa 2 get def - /degreeShift aa 3 get def - aa 4 get (no) eq { - /hdShift -1 def - } { - (Unknown keyword for the 5th argument) error - } ifelse - /setarg 1 def - } { } ifelse /env1 getOptions def setarg { } { (ecart.gb : Argument mismatch) error } ifelse [(KanGBmessage) ecart.gb.verbose ] system_variable - $ecartd.gb dehomogenizes at each reduction step w.r.t. s (H).$ message + $ecartd.gb dehomogenizes at each reduction step w.r.t. s (H).$ ecart.message %%% Start of the preprocess v tag RingP eq { @@ -864,18 +891,18 @@ (Error in gb: Specify variables) error } { } ifelse wv isInteger { - (Give an weight vector such that x < 1) error + (Give a weight vector such that x < 1) error }{ degreeShift isInteger { [v ring_of_differential_operators - wv weight_vector + wv ecart.weight_vector gb.characteristic opt ] define_ring }{ [v ring_of_differential_operators - wv weight_vector + wv ecart.weight_vector gb.characteristic [(degreeShift) degreeShift] opt join ] define_ring @@ -904,11 +931,12 @@ } { } ifelse %%BUG: case of v is integer - v ecart.checkOrder + [v ecart.partialEcartGlobalVarX] ecart.checkOrder + ecartd.begin - ecart.gb.verbose { (gb.options = ) messagen gb.options message } { } ifelse + ecart.gb.verbose { (gb.options = ) ecart.messagen gb.options ecart.message } { } ifelse hdShift tag 1 eq { ecart.autoHomogenize not hdShift -1 eq or { @@ -916,23 +944,31 @@ f { {. } map} map /f set } { % Automatic h-homogenization without degreeShift - (ecartd.gb : Input polynomial or vectors are automatically homogenized without degreeShift) message + (ecartd.gb : Input polynomial or vectors are automatically homogenized without degreeShift) ecart.message f { {. ecart.dehomogenize} map} map /f set f ecart.homogenize01 /f set - f { { [[(H). (1).]] replace } map } map /f set + f { { [[@@@.Hsymbol . (1).]] replace } map } map /f set } ifelse } { % Automatic h-homogenization with degreeShift (ecartd.gb : Input polynomial or vectors are automatically homogenized with degreeShift) message f { {. ecart.dehomogenize} map} map /f set f {/fi set [(degreeShift) hdShift fi] homogenize} map /f set - f { { [[(H). (1).]] replace } map } map /f set + f { { [[@@@.Hsymbol . (1).]] replace } map } map /f set }ifelse - ecart.needSyz { - [f [(needSyz)] gb.options join ] groebner /gg set - } { - [f gb.options] groebner 0 get /gg set + ecart.useSugar { + ecart.needSyz { + [f [(needSyz)] gb.options join ] groebner_sugar /gg set + } { + [f gb.options] groebner_sugar 0 get /gg set + } ifelse + } { + ecart.needSyz { + [f [(needSyz)] gb.options join ] groebner /gg set + } { + [f gb.options] groebner 0 get /gg set + } ifelse } ifelse ecart.needSyz { @@ -963,6 +999,7 @@ ecartd.end + ans getRing (oxRingStructure) dc /ecartd.gb.oxRingStructure set %% env1 restoreOptions %% degreeShift changes "grade" @@ -976,9 +1013,23 @@ /ecart.checkOrder { /arg1 set - [/in-ecart.checkOrder /vv /tt /dd /n /i] pushVariables + [/vv] pushVariables [ /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 to_records pop] /vv set } ifelse vv {toString} map /vv set @@ -1002,8 +1053,54 @@ popVariables arg1 } 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) - [(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.) (cf. ecartd.gb, ecart.gb, ecartn.gb) ] @@ -1049,7 +1146,7 @@ /shift [ [1 0 1 0 0] ] def /weight [ [(t) -1 (Dt) 1] [(t) -1 (x) -1 (y) -1 (Dt) 1 (Dx) 1 (Dy) 1]] def - [ff (t,x,y) weight shift nmshift] ecart.minimalBase + [ff (t,x,y) weight [(degreeShift) shift (startingShift) nmshift]] ecart.minimalBase } def @@ -1145,21 +1242,20 @@ /wv 0 def /degreeShift 0 def /hdShift 0 def + /opt [ ] def aa { tag } map /typev set - typev [ArrayP StringP ArrayP ArrayP ArrayP] eq + typev [ArrayP StringP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get def /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse - typev [ArrayP ArrayP ArrayP ArrayP ArrayP] eq + typev [ArrayP ArrayP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get from_records def /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse setarg { } { (ecart.minimalBase : Argument mismatch) error } ifelse @@ -1169,51 +1265,53 @@ f 0 get tag ArrayP eq { } { f { /tt set [ tt ] } map /f set } ifelse - [f v wv degreeShift [hdShift 0 get degreeShift 0 get]] + [f v wv [(degreeShift) degreeShift (startingShift) [hdShift 0 get degreeShift 0 get]] opt join] ecart.gb /ff set ff getRing ring_def ff 0 get { {toString } map } map /ff set - [ff v wv degreeShift [hdShift 0 get degreeShift 0 get]] /arg1 set + [ff v wv + [(degreeShift) degreeShift (startingShift) [hdShift 0 get degreeShift 0 get]] opt join + ] /arg1 set ] pop popVariables arg1 } def [(ecart.gen_input) -[([ff v weight_vector uv_shift_m [D_shift_n uv_shift_m]] ecart.gen_input ) - ( [gg_h v weight_vector uv_shift_m [D_shift_n uv_shift_m]] ) +[$[ff v ecart.weight_vector [(degreeShift) uv_shift_m (startingShift) [D_shift_n uv_shift_m]] ] ecart.gen_input $ + $ [gg_h v ecart.weight_vector [(degreeShift) uv_shift_m (startingShift) [D_shift_n uv_shift_m]]] $ (It generates the input for the minimal filtered free resolution.) (Current ring is changed to the ring of gg_h.) (cf. ecart.minimalBase) $Example: [ [(t-x^3+y^2) (Dx+ 3 x^2 Dt) (Dy - 2 y Dt)] (t,x,y) $ $ [ [(t) -1 (Dt) 1] [(t) -1 (x) -1 (y) -1 (Dt) 1 (Dx) 1 (Dy) 1]] $ - $ [ [0] ] $ - $ [ [0] [0] ] ] ecart.gen_input /gg set gg pmat $ + $ [(degreeShift) [ [0] ] $ + $ (startingShift) [ [0] [0] ]] ] ecart.gen_input /gg set gg pmat $ ]] putUsages [(ecart.minimalBase) -[([ff v weight_vector uv_shift_m [D_shift_n uv_shift_m]] ecart.minimalBase ) +[$[ff v ecart.weight_vector [(degreeShift) uv_shift_m (startingShift) [D_shift_n uv_shift_m]]] ecart.minimalBase $ ( [mbase gr_of_mbase ) - ( [syz v weight_vector new_uv_shift_m [new_D_shift_n new_uv_shift_m]]) + $ [syz v ecart.weight_vector [(degreeShift) new_uv_shift_m (startingShift) [new_D_shift_n new_uv_shift_m]]]$ ( gr_of_syz ]) (mbase is the minimal generators of ff in D^h in the sense of filtered minimal) (generators.) $Example: [ [(t-x^3+y^2) (Dx+ 3 x^2 Dt) (Dy - 2 y Dt)] (t,x,y) $ $ [ [(t) -1 (Dt) 1] [(t) -1 (x) -1 (y) -1 (Dt) 1 (Dx) 1 (Dy) 1]] $ - $ [ [0] ] $ - $ [ [0] [0] ] ] ecart.gen_input /gg0 set $ + $ [(degreeShift) [ [0] ] $ + $ (startingShift) [ [0] [0] ] ] ] ecart.gen_input /gg0 set $ $ gg0 ecart.minimalBase /ss0 set $ $ ss0 2 get ecart.minimalBase /ss1 set $ $ ss1 2 get ecart.minimalBase /ss2 set $ $ (--------- minimal filtered resolution -------) message $ $ ss0 0 get pmat ss1 0 get pmat ss2 0 get pmat $ $ (--------- degree shift (n,m) n:D-shift m:uv-shift -------) message $ - $ gg0 4 get message $ - $ ss0 2 get 4 get message $ - $ ss1 2 get 4 get message $ - $ ss2 2 get 4 get message ; $ + $ gg0 3 get 3 get message $ + $ ss0 2 get 3 get 3 get message $ + $ ss1 2 get 3 get 3 get message $ + $ ss2 2 get 3 get 3 get message ; $ ]] putUsages /ecart.minimalBase { @@ -1236,21 +1334,20 @@ /wv 0 def /degreeShift 0 def /hdShift 0 def + /opt [ ] def aa { tag } map /typev set - typev [ArrayP StringP ArrayP ArrayP ArrayP] eq + typev [ArrayP StringP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get def /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse - typev [ArrayP ArrayP ArrayP ArrayP ArrayP] eq + typev [ArrayP ArrayP ArrayP ArrayP] eq { /f aa 0 get def /v aa 1 get from_records def /wv aa 2 get def - /degreeShift aa 3 get def - /hdShift aa 4 get def + opt aa 3 get ecart.setOpt join /opt set /setarg 1 def } { } ifelse setarg { } { (ecart.minimalBase : Argument mismatch) error } ifelse @@ -1259,7 +1356,7 @@ f 0 get tag ArrayP eq { } { f { /tt set [ tt ] } map /f set } ifelse - [f v wv degreeShift (no)] ecart.syz /ss0 set + [f v wv [(degreeShift) degreeShift (noAutoHomogenize) 1] opt join] ecart.syz /ss0 set ss0 getRing ring_def /degreeShiftD hdShift 0 get def @@ -1352,7 +1449,7 @@ /arg1 [ ai1 ai1 {[wv 0 get weightv degreeShift 0 get] init} map %Getting gr of A_{i-1} - [ai v wv [degreeShiftUVnew] [degreeShiftDnew degreeShiftUVnew]] + [ai v wv [(degreeShift) [degreeShiftUVnew] (startingShift) [degreeShiftDnew degreeShiftUVnew]]] ai {[wv 0 get weightv degreeShiftUVnew] init} map %Getting gr of A_i ] def @@ -1361,6 +1458,504 @@ arg1 } def +/ecart.minimalResol { + /arg1 set + [/in-ecart.minimalResol /aa /ans /gg0 /ansds /ans_gr /c] pushVariables + [ + /aa arg1 def + /ans [ ] def + /ansds [ ] def + /ans_gr [ ] def + /c 0 def + (---- ecart.gen_input ----) message + aa ecart.gen_input /gg0 set + ansds gg0 3 get 3 get append /ansds set + (---- ecart.minimalBase --- Degree ) messagen c message c 1 add /c set + gg0 ecart.minimalBase /ssi set + ansds ssi 2 get 3 get 3 get append /ansds set + ans ssi 0 get append /ans set + ans_gr ssi 1 get append /ans_gr set + { + ssi 3 get [ ] eq { exit } { } ifelse + (---- ecart.minimalBase --- Degree ) messagen c message c 1 add /c set + ssi 2 get ecart.minimalBase /ssi_new set + ans ssi_new 0 get append /ans set + ansds ssi_new 2 get 3 get 3 get append /ansds set + ans_gr ssi_new 1 get append /ans_gr set + /ssi ssi_new def + } loop + /arg1 [ans ansds ans_gr] def + ] pop + popVariables + arg1 +} def + +(ecart.minimalResol) message + +[(ecart.minimalResol) +[ + + $[ff v ecart.weight_vector [(degreeShift) uv_shift_m (startingShift) [D_shift_n uv_shift_m]]] ecart.minimalResol $ + ( [resol degree_shifts gr_of_resol_by_uv_shift_m] ) + $Example1: [ [(t-x^3+y^2) (Dx+ 3 x^2 Dt) (Dy - 2 y Dt)] (t,x,y) $ + $ [ [(t) -1 (Dt) 1] [(t) -1 (x) -1 (y) -1 (Dt) 1 (Dx) 1 (Dy) 1]] $ + $ [(degreeShift) [ [0] ] $ + $ (startingShift) [ [0] [0] ] ] ] ecart.minimalResol /gg set gg pmat $ +]] putUsages + +%% for ecart.weight_vector +/ecart.eliminationOrderTemplate { %% esize >= 1 +%% if esize == 0, it returns reverse lexicographic order. +%% m esize eliminationOrderTemplate mat + /arg2 set /arg1 set + [/m /esize /m1 /m2 /k /om /omtmp] pushVariables + [ + /m arg1 def /esize arg2 def + /m1 m esize sub 1 sub def + /m2 esize 1 sub def + [esize 0 gt + { + [1 1 esize + { pop 1 } for + esize 1 << m 1 sub >> + { pop 0 } for + ] %% 1st vector + } + { } ifelse + + m esize gt + { + [1 1 esize + { pop 0 } for + esize 1 << m 1 sub >> + { pop 1 } for + ] %% 2nd vector + } + { } ifelse + + m1 0 gt + { + m 1 sub -1 << m m1 sub >> + { + /k set + m k evec_neg + } for + } + { } ifelse + + m2 0 gt + { + << esize 1 sub >> -1 1 + { + /k set + m k evec_neg + } for + } + { } ifelse + + ] /om set + om [ 0 << m 2 idiv >> 1 sub] 0 put + om [ << m 2 idiv >> 1 add << m 2 idiv >> 1 sub] 0 put + /arg1 om def + ] pop + popVariables + arg1 +} def + +%note 2003.09.29 +/ecart.elimination_order { +%% [x-list d-list params] (x,y,z) elimination_order +%% vars evars +%% [x-list d-list params order] + /arg2 set /arg1 set + [/vars /evars /univ /order /perm /univ0 /compl /m /omtmp] pushVariables + /vars arg1 def /evars [arg2 to_records pop] def + [ + /univ vars 0 get reverse + vars 1 get reverse join + def + + << univ length 2 sub >> + << evars length >> + ecart.eliminationOrderTemplate /order set + + [[1]] order oplus [[1]] oplus /order set + + /m order length 2 sub def + /omtmp [1 1 m 2 add { pop 0 } for ] def + omtmp << m 2 idiv >> 1 put + order omtmp append /order set + % order pmat + + /univ0 [univ reverse aload pop pop] reverse def %% [e,x,y,h] --> [x,y,h] + + /compl + [univ 0 get] evars join evars univ0 complement join + def + compl univ + getPerm /perm set + %%perm :: univ :: compl :: + + order perm permuteOrderMatrix /order set + + + vars [order] join /arg1 set + ] pop + popVariables + arg1 +} def + +/ecart.define_ring { + /arg1 set + [/rp /param /foo] pushVariables + [/rp arg1 def + + rp 0 get length 3 eq { + rp 0 [rp 0 get 0 get rp 0 get 1 get rp 0 get 2 get ] + ( ) ecart.elimination_order put + } { } ifelse + + [ + rp 0 get 0 get %% x-list + rp 0 get 1 get %% d-list + rp 0 get 2 get /param set + param 0 << rp 1 get >> put %% << rp 1 get >> is 17 in the example. + param %% parameters. + rp 0 get 3 get %% order matrix. + rp length 2 eq + { [ ] } %% null optional argument. + { rp 2 get } + ifelse + ] /foo set + foo aload pop set_up_ring@ + ] pop + popVariables + [(CurrentRingp)] system_variable +} def +/ecart.weight_vector { + /arg2 set /arg1 set + [/vars /univ /w-vectors /www /k /order1 /order2] pushVariables + /vars arg1 def /w-vectors arg2 def + [ + /univ vars 0 get reverse + vars 1 get reverse join + def + w-vectors to_int32 /w-vectors set + [ + 0 1 << w-vectors length 1 sub >> + { + /k set + univ w-vectors k get w_to_vec + } for + ] /order1 set + %% order1 :: + + vars ( ) ecart.elimination_order 3 get /order2 set + vars [ << order1 order2 join >> ] join /arg1 set + ] pop + popVariables + arg1 +} def + +%% end of for ecart.define_ring + +/ecartd.reduction { + /arg2 set + /arg1 set + [/in-ecartd.reduction /gbasis /flist /ans /gbasis2] pushVariables + [(CurrentRingp) (KanGBmessage)] pushEnv + [ + /gbasis arg2 def + /flist arg1 def + gbasis 0 get tag 6 eq { } + { (ecartd.reduction: the second argument must be a list of lists) error } + ifelse + + gbasis length 1 eq { + gbasis getRing ring_def + /gbasis2 gbasis 0 get def + } { + [ [(1)] ] gbasis rest join ecartd.gb 0 get getRing ring_def + /gbasis2 gbasis 0 get ___ def + } ifelse + ecartd.begin + + flist ___ /flist set + flist tag 6 eq { + flist { gbasis2 reduction } map /ans set + }{ + flist gbasis2 reduction /ans set + } ifelse + /arg1 ans def + + ecartd.end + ] pop + popEnv + popVariables + arg1 +} def + +/ecartd.reduction.test { + [ + [( 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]]] + ecartd.gb /gg set + + (Dx) [gg 0 get] ecartd.reduction /gg2 set + gg2 message + (-----------------------------) message + + [(Dx) (Dy) (Dx+x*Dy)] [gg 0 get] ecartd.reduction /gg3 set + gg3 message + + (-----------------------------) message + [[( 2*(1-x-y) Dx + h ) ( 2*(1-x-y) Dy + h )] + (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set + (Dx) ggg ecartd.reduction /gg4 set + gg4 message + + (----------- 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 + +/ecarth.reduction { + /arg2 set + /arg1 set + [/in-ecarth.reduction /gbasis /flist /ans /gbasis2] pushVariables + [(CurrentRingp) (KanGBmessage)] pushEnv + [ + /gbasis arg2 def + /flist arg1 def + gbasis 0 get tag 6 eq { } + { (ecarth.reduction: the second argument must be a list of lists) error } + ifelse + + gbasis length 1 eq { + gbasis getRing ring_def + /gbasis2 gbasis 0 get def + } { + [ [(1)] ] gbasis rest join ecarth.gb 0 get getRing ring_def + /gbasis2 gbasis 0 get ___ def + } ifelse + ecarth.begin + + flist ___ /flist set + flist tag 6 eq { + flist { gbasis2 reduction } map /ans set + }{ + flist gbasis2 reduction /ans set + } ifelse + /arg1 ans def + + ecarth.end + ] pop + popEnv + popVariables + arg1 +} def + +[(ecartd.reduction) +[ (f basis ecartd.reduction r) + (f is reduced by basis by the tangent cone algorithm.) + (The first element of basis 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.) + $h[0,1](D)-homogenization is used.$ + (cf. reduction, ecartd.gb, ecartd.reduction.test ) + $Example:$ + $ [[( 2*(1-x-y) Dx + h ) ( 2*(1-x-y) Dy + h )] $ + $ (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set $ + $ (Dx+Dy) ggg ecartd.reduction :: $ +]] 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 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 { + /arg1 set + [/in-ecart.stdOrder /vv /tt /dvv /wv1 /wv2 + ] pushVariables + [ + /vv arg1 def + vv isString { [ vv to_records pop] /vv set } + { } ifelse + vv { toString} map /vv set + + vv { /tt set [@@@.Dsymbol tt] cat } map /dvv set + dvv { 1 } map /wv1 set + vv { -1 } map dvv { 1 } map join /wv2 set + /arg1 [wv1 wv2 ] def + ] pop + popVariables + arg1 +} def + +/ecartd.isSameIdeal_h { + /arg1 set + [/in-ecartd.isSameIdeal_h /aa /ii /jj /iigg /jjgg /vv /ans /k /n /f + /ecartd.isSameIdeal_h.opt + /save-ecart.autoHomogenize /wv /save-ecart.message.quiet + ] pushVariables + [(CurrentRingp) (Homogenize_vec)] pushEnv + [ + /aa arg1 def + gb.verbose { (Getting in ecartd.isSameIdeal_h) message } { } ifelse + %% comparison of hilbert series has not yet been implemented. + /save-ecart.message.quiet ecart.message.quiet def + aa length 3 eq { } + { ([ii jj vv] ecartd.isSameIdeal_h) error } ifelse + /ii aa 0 get def + /jj aa 1 get def + /vv aa 2 get def + ii length 0 eq jj length 0 eq and + { /ans 1 def /LLL.ecartd.isSame_h goto } { } ifelse + + vv ecart.stdOrder /wv set + + /save-ecart.autoHomogenize ecart.autoHomogenize def + /ecart.autoHomogenize 0 def + [ii vv wv] ecartd.gb /iigg set + [jj vv wv] ecartd.gb /jjgg set + save-ecart.autoHomogenize /ecart.autoHomogenize set + + iigg getRing ring_def + + getOptions /ecartd.isSameIdeal_h.opt set + + /ans 1 def + iigg 0 get /iigg set + jjgg 0 get /jjgg set + %%Bug: not implemented for the case of module. + + /save-ecart.message.quiet ecart.message.quiet def + /ecart.message.quiet 1 def + gb.verbose { (Comparing) message iigg message (and) message jjgg message } + { } ifelse + gb.verbose { ( ii < jj ?) messagen } { } ifelse + iigg length /n set + 0 1 n 1 sub { + /k set + iigg k get + [jjgg vv wv] ecartd.reduction 0 get + (0). eq not { /ans 0 def /LLL.ecartd.isSame_h goto} { } ifelse + gb.verbose { (o) messagen } { } ifelse + } for + gb.verbose { ( jj < ii ?) messagen } { } ifelse + jjgg length /n set + 0 1 n 1 sub { + /k set + jjgg k get + [iigg vv wv] ecartd.reduction 0 get + (0). eq not { /ans 0 def /LLL.ecartd.isSame_h goto} { } ifelse + gb.verbose { (o) messagen } { } ifelse + } for + /LLL.ecartd.isSame_h + gb.verbose { ( Done) message } { } ifelse + save-ecart.message.quiet /ecart.message.quiet set + ecartd.isSameIdeal_h.opt restoreOptions + /arg1 ans def + ] pop + popEnv + popVariables + arg1 +} def +(ecartd.isSameIdeal_h ) messagen-quiet + +[(ecartd.isSameIdeal_h) +[([ii jj vv] ecartd.isSameIdeal_h bool) + (ii, jj : ideal, vv : variables) + $The ideals ii and jj will be compared in the ring h[0,1](D).$ + $ii and jj are re-parsed.$ + $Example 1: [ [((1-x) Dx + h)] [((1-x)^2 Dx + h (1-x))] (x)] ecartd.isSameIdeal_h $ +]] putUsages + +/ecart.01Order { + /arg1 set + [/in-ecart.01Order /vv /tt /dvv /wv1 /wv2 + ] pushVariables + [ + /vv arg1 def + vv isString { [ vv to_records pop] /vv set } + { } ifelse + vv { toString} map /vv set + + vv { /tt set [@@@.Dsymbol tt] cat } map /dvv set + dvv { 1 } map /wv1 set + /arg1 [wv1] def + ] pop + popVariables + arg1 +} def +/ecart.homogenize01Ideal { + /arg1 set + [/in.ecart.homogenize01Ideal /ll /vv /wv /ans] pushVariables + [ + /ll arg1 0 get def + /vv arg1 1 get def + vv isArray { vv from_records /vv set } { } ifelse + vv ecart.01Order /wv set + [vv ring_of_differential_operators 0] define_ring + ll ___ /ll set ll dehomogenize /ll set + [ll vv wv] gb 0 get /ll set + + ecart.begin + [vv ring_of_differential_operators + vv ecart.stdOrder weight_vector 0 + [(weightedHomogenization) 1]] define_ring + ll ___ {ecart.homogenize01 ecart.dehomogenizeH} map /ans set + ecart.end + /arg1 ans def + ] pop + popVariables + arg1 +} def +[(ecart.homogenize01Ideal) +[([ii vv] ecartd.homogenize01Ideal) + (ii : ideal, vv : variables) + $The ideal ii is homogenized in h[0,1](D).$ + $Example 1: [ [((1-x) Dx + 1)] (x)] ecart.homogenize01Ideal $ +]] putUsages + + + ( ) message-quiet +/ecart_loaded 1 def \ No newline at end of file