===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Doc/ecart.sm1,v
retrieving revision 1.8
retrieving revision 1.12
diff -u -p -r1.8 -r1.12
--- OpenXM/src/kan96xx/Doc/ecart.sm1	2003/08/21 12:28:58	1.8
+++ OpenXM/src/kan96xx/Doc/ecart.sm1	2003/08/26 05:06:00	1.12
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.7 2003/08/18 06:36:50 takayama Exp $ 
+% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.11 2003/08/24 05:19:44 takayama Exp $ 
 %[(parse) (hol.sm1) pushfile] extension
 %[(parse) (appell.sm1) pushfile] extension
 
@@ -69,11 +69,18 @@
 
 /ecart.homogenize01 {
  /arg1 set
- [/in.ecart.homogenize01 /ll ] pushVariables
+ [/in.ecart.homogenize01 /ll /ll0] pushVariables
  [
    /ll arg1 def
-   [(degreeShift) [ ] ll ] homogenize
-   /arg1 set
+   ll tag ArrayP eq {
+     ll 0 get tag ArrayP eq not {
+       [(degreeShift) [ ] ll ] homogenize   /arg1 set
+     } {
+       ll { ecart.homogenize01 } map /arg1 set
+     } ifelse
+   } {
+       [(degreeShift) [ ] ll ] homogenize   /arg1 set
+   } ifelse
  ] pop
  popVariables
  arg1
@@ -88,30 +95,38 @@
   (    [(x1) -1 (x2) -1])
   (   ] weight_vector )
   (   0  )
-  (   [(degreeShift) [[0 0 0]]])
+  (   [(weightedHomogenization) 1 (degreeShift) [[0 0 0]]])
   (  ] define_ring)
   ( ecart.begin)
   ( [[1 -4 -2 5]] appell4 0 get /eqs set)
   ( eqs { . [[(x1). (x1+2).] [(x2). (x2+4).]] replace} map )
-  ( ecart.homogenize01 /eqs2 set)
+  ( {ecart.homogenize01} map /eqs2 set)
   ( [eqs2] groebner )
 ]] putUsages
 
 /ecart.homogenize01_with_shiftVector {
  /arg2.set
  /arg1 set
- [/in.ecart.homogenize01 /ll /sv] pushVariables
+ [/in.ecart.homogenize01 /ll /sv /ll0] pushVariables
  [
    /sv arg2 def
    /ll arg1 def
-   [(degreeShift) sv ll ] homogenize
-   /arg1 set
+   ll tag ArrayP eq {
+     ll 0 get tag ArrayP eq not {
+       [(degreeShift) sv ll ] homogenize   /arg1 set
+     } {
+       ll { ecart.homogenize01_with_shiftVector } map /arg1 set
+     } ifelse
+   } {
+       [(degreeShift) sv ll ] homogenize   /arg1 set
+   } ifelse
  ] pop
  popVariables
  arg1
 } def
 [(ecart.dehomogenize01_with_degreeShift)
  [(obj shift-vector ecart.dehomogenize01_with_degreeShift r)
+  (cf. homogenize)
 ]] putUsages
 
 %% Aux functions to return the default weight vectors.
@@ -157,7 +172,12 @@
   (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.)
-  (                array ds; ds is the degree shift )
+  (                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.)
+  (        array ds; ds is the degree shift for the ring. )
+  (        array hsShift is the degree shift for the homogenization. cf.homogenize )
+  $a : [f v w ds (no)]; array f; string v; array of array w; w is the weight matirx.$
+  (       No automatic homogenization.)
   (  )
   $cf. ecarth.gb (homogenized),  ecartd.gb (dehomogenize) $
   ( )
@@ -165,13 +185,17 @@
   $             [ [ (Dx) 1 ] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecart.gb pmat ; $
   (Example 2: )
   $ [ [(2 x Dx + 3 y Dy+6) (2 y Dx + 3 x^2 Dy)] (x,y) $
-  $   [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] ecart.gb  pmat ;$
+  $   [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] ecart.gb  /ff set ff pmat ;$
+  (To set the current ring to the ring in which ff belongs )
+  (      ff getRing ring_def  )
   (  )
   $Example 3: [ [( (x Dx)^2 + (y Dy)^2 -1) (  x y Dx Dy -1)] (x,y) $
   $             [ [ (Dx) 1 (Dy) 1] ] ] ecart.gb pmat ; $
+  (   This example will cause an error on order.)
   (  )
   $Example 4: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $
   $             [ [ (x) -1 (y) -1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecart.gb pmat ; $
+  (   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 ; $
@@ -185,11 +209,13 @@
 ]] putUsages
 
 /ecart.gb.verbose 1 def
+%ecarth.gb  s(H)-homogenized outputs.  GG's original version of ecart gb.
 /ecarth.gb {
   /arg1 set
   [/in-ecarth.gb /aa /typev /setarg /f /v 
    /gg /wv /vec /ans /rr /mm
    /degreeShift  /env2 /opt /ans.gb
+   /hdShift
   ] pushVariables 
   [(CurrentRingp) (KanGBmessage)] pushEnv
   [
@@ -198,6 +224,7 @@
     /setarg 0 def
     /wv 0 def
     /degreeShift 0 def
+    /hdShift 0 def 
     /opt [(weightedHomogenization) 1] def
     aa { tag } map /typev set
     typev [ ArrayP ] eq
@@ -239,6 +266,15 @@
        /degreeShift aa 3 get def
        /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
@@ -246,10 +282,31 @@
        /degreeShift aa 3 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
 
     /env1 getOptions def
 
-    setarg { } { (ecart.gb : Argument mismatch) error } ifelse
+    ecart.gb.verbose { $ecarth.gb computes std basis with h-s(H)-homogenized buchberger algorithm.$ message } {  } ifelse
+    setarg { } { (ecarth.gb : Argument mismatch) error } ifelse
     
     [(KanGBmessage) ecart.gb.verbose ] system_variable
 
@@ -325,15 +382,25 @@
 
     ecart.gb.verbose { (gb.options = ) messagen gb.options message } { } ifelse
     ecart.autoHomogenize {
-      (ecart.gb: Input polynomial or vectors are automatically h-H-homogenized.)
+      (ecarth.gb: Input polynomial or vectors are automatically h-H-homogenized.)
       message
     } { } ifelse
-    ecart.autoHomogenize {
-      f { {. ecart.dehomogenize} map} map /f set   
-      f ecart.homogenize01 /f set
-    }{
-      f { {. } map } map /f set
-    } ifelse
+
+    hdShift tag 1 eq {
+     ecart.autoHomogenize not hdShift -1 eq or {
+% No automatic h-s-homogenization.
+       f { {. } map} map /f set   
+     } {
+% Automatic h-s-homogenization without degreeShift
+       f { {. ecart.dehomogenize} map} map /f set   
+       f ecart.homogenize01 /f set
+     } ifelse
+   } {
+% Automatic h-s-homogenization with degreeShift
+       f { {. ecart.dehomogenize} map} map /f set   
+       f {/fi set [(degreeShift) hdShift fi] homogenize} map /f set
+   }ifelse
+
     ecart.needSyz {
       [f [(needSyz)] gb.options join ] groebner /gg set
     } {  
@@ -343,14 +410,18 @@
     ecart.needSyz {
       mm {
        gg 0 get { /tmp set [mm tmp] toVectors } map /ans.gb set
-      } { /ans.gb gg 0 get def } ifelse
-      /ans [gg 2 get , ans.gb , gg 1 get , f ] def
-      ans pmat ;
+       } { /ans.gb gg 0 get def } ifelse
+       /ans [gg 2 get , ans.gb , gg 1 get , f ] def
+%      ans pmat ;
     } { 
       wv isInteger {
         /ans [gg gg {init} map] def
       }{
-        /ans [gg gg {wv 0 get weightv init} map] def
+       degreeShift isInteger {
+         /ans [gg gg {wv 0 get weightv init} map] def
+       } {
+         /ans [gg gg {[wv 0 get weightv degreeShift 0 get ] init} map] def
+       } ifelse
       }ifelse
 
       %% Postprocess : recover the matrix expression.
@@ -379,8 +450,9 @@
   (array a; array b;)
   $b : [g ii];  array g; array in; g is a standard (Grobner) basis of f$
   (             in the ring of differential operators.)
-  (The computation is done by using Ecart division algorithm and )
-  (the double homogenization.)
+  (The computation is done by using Ecart division algorithm.)
+  $Buchberger algorithm is applied for double h-H(s)-homogenized elements and$
+  (they are not dehomogenized.)
   (cf. M.Granger and T.Oaku: Minimal filtered free resolutions ... 2003)
    $            ii is the initial ideal in case of w is given or <<a>> belongs$
    $            to a ring. In the other cases, it returns the initial monominal.$
@@ -415,7 +487,6 @@
   (                                                          define_ring )
 ]] putUsages
 
-%% BUG:  " f weight init " works well in case of vectors with degree shift ?
 
 /ecart.syz {
   /arg1 set
@@ -442,6 +513,8 @@
   $ ff 0 get ff 3 get mul pmat $
   $ ff 2 get  ff 3 get mul [ff 1 get ] transpose sub pmat ; $
   (  )
+  (To set the current ring to the ring in which ff belongs )
+  (      ff getRing ring_def  )
   $Example 2: [[ [(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] ]  [[0 1] [-3 1] ] ] ecart.syz pmat ; $
   (  )
@@ -618,12 +691,16 @@
        gg 0 get { /tmp set [mm tmp] toVectors } map /ans.gb set
       } { /ans.gb gg 0 get def } ifelse
       /ans [gg 2 get , ans.gb , gg 1 get , f ] def
-      ans pmat ;
+%      ans pmat ;
     } { 
       wv isInteger {
         /ans [gg gg {init} map] def
       }{
-        /ans [gg gg {wv 0 get weightv init} map] def
+       degreeShift isInteger {
+         /ans [gg gg {wv 0 get weightv init} map] def
+       } {
+         /ans [gg gg {[wv 0 get weightv degreeShift 0 get ] init} map] def
+       } ifelse
       }ifelse
 
       %% Postprocess : recover the matrix expression.
@@ -652,6 +729,7 @@
   [/in-ecart.gb /aa /typev /setarg /f /v 
    /gg /wv /vec /ans /rr /mm
    /degreeShift  /env2 /opt /ans.gb
+   /hdShift
   ] pushVariables 
   [(CurrentRingp) (KanGBmessage)] pushEnv
   [
@@ -660,6 +738,7 @@
     /setarg 0 def
     /wv 0 def
     /degreeShift 0 def
+    /hdShift 0 def
     /opt [(weightedHomogenization) 1] def
     aa { tag } map /typev set
     typev [ ArrayP ] eq
@@ -708,6 +787,34 @@
        /degreeShift aa 3 get def
        /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
 
     /env1 getOptions def
 
@@ -778,9 +885,22 @@
 
     ecart.gb.verbose { (gb.options = ) messagen gb.options message } { } ifelse
 
-    f { {. ecart.dehomogenize} map} map /f set   
-    f ecart.homogenize01 /f set
-    f { { [[(H). (1).]] replace } map } map /f set
+    hdShift tag 1 eq {
+     ecart.autoHomogenize not hdShift -1 eq  or {
+% No automatic h-homogenization.
+       f { {. } map} map /f set   
+     } {
+% Automatic h-homogenization without degreeShift
+       f { {. ecart.dehomogenize} map} map /f set   
+       f ecart.homogenize01 /f set
+       f { { [[(H). (1).]] replace } map } map /f set
+     } ifelse
+   } {
+% Automatic h-homogenization with degreeShift
+       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
+   }ifelse
 
     ecart.needSyz {
       [f [(needSyz)] gb.options join ] groebner /gg set
@@ -793,12 +913,17 @@
        gg 0 get { /tmp set [mm tmp] toVectors } map /ans.gb set
       } { /ans.gb gg 0 get def } ifelse
       /ans [gg 2 get , ans.gb , gg 1 get , f ] def
-      ans pmat ;
+%      ans pmat ;
     } { 
       wv isInteger {
         /ans [gg gg {init} map] def
       }{
-        /ans [gg gg {wv 0 get weightv init} map] def
+%% Get the initial ideal
+       degreeShift isInteger {
+         /ans [gg gg {wv 0 get weightv init} map] def
+       } {
+         /ans [gg gg {[wv 0 get weightv degreeShift 0 get ] init} map] def
+       } ifelse
       }ifelse
 
       %% Postprocess : recover the matrix expression.