=================================================================== RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/ecart.sm1,v retrieving revision 1.22 retrieving revision 1.29 diff -u -p -r1.22 -r1.29 --- OpenXM/src/kan96xx/Doc/ecart.sm1 2004/05/05 06:57:09 1.22 +++ OpenXM/src/kan96xx/Doc/ecart.sm1 2004/05/28 08:11:31 1.29 @@ -1,4 +1,4 @@ -% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.21 2004/05/04 08:29:35 takayama Exp $ +% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.28 2004/05/27 11:13:49 takayama Exp $ %[(parse) (hol.sm1) pushfile] extension %[(parse) (appell.sm1) pushfile] extension @@ -7,6 +7,8 @@ /ecart.end { endEcart } def /ecart.autoHomogenize 1 def /ecart.needSyz 0 def +/ecartd.gb.oxRingStructure [[ ] [ ] ] def + /ecartd.begin { ecart.begin [(EcartAutomaticHomogenization) 1] system_variable @@ -87,7 +89,7 @@ ll (0). eq { } { ll getRing /rr set - ll [ [ (H) rr ,, (1) rr ,, ] + ll [ [ @@@.Hsymbol rr ,, (1) rr ,, ] [ (h) rr ,, (1) rr ,, ]] replace /ll set } ifelse @@ -113,7 +115,7 @@ ll (0). eq { } { ll getRing /rr set - ll [ [ (H) rr ,, (1) rr ,, ] ] replace + ll [ [ @@@.Hsymbol rr ,, (1) rr ,, ] ] replace /ll set } ifelse } ifelse @@ -195,7 +197,7 @@ [/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 @@ -244,6 +246,7 @@ $ [(degreeShift) ds (noAutoHomogenize) 1 (sugar) 1] -->use the sugar strate $ ( ) $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 ; $ @@ -919,14 +922,14 @@ (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.useSugar { @@ -971,6 +974,7 @@ ecartd.end + ans getRing (oxRingStructure) dc /ecartd.gb.oxRingStructure set %% env1 restoreOptions %% degreeShift changes "grade" @@ -1624,7 +1628,16 @@ (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set (Dx) ggg ecartd.reduction /gg4 set 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 /ecarth.reduction { @@ -1678,6 +1691,38 @@ $ (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 @@ -1692,7 +1737,8 @@ dvv { 1 } map /wv1 set vv { -1 } map dvv { 1 } map join /wv2 set /arg1 [wv1 wv2 ] def - ] popVariables + ] pop + popVariables arg1 } def @@ -1773,6 +1819,53 @@ $The ideals ii and jj will be compared in the ring h[0,1](D).$ $ii and jj are re-parsed.$ $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