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Diff for /OpenXM/src/kan96xx/Doc/hol.sm1 between version 1.16 and 1.21

version 1.16, 2004/05/04 08:29:35 version 1.21, 2004/07/29 08:13:42
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 % $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.15 2004/05/04 08:03:30 takayama Exp $  % $OpenXM: OpenXM/src/kan96xx/Doc/hol.sm1,v 1.20 2004/06/10 06:01:50 takayama Exp $
 %% hol.sm1, 1998, 11/8, 11/10, 11/14, 11/25, 1999, 5/18, 6/5. 2000, 6/8  %% hol.sm1, 1998, 11/8, 11/10, 11/14, 11/25, 1999, 5/18, 6/5. 2000, 6/8
 %% rank, rrank, characteristic  %% rank, rrank, characteristic
 %% This file is error clean.  %% This file is error clean.
Line 14  $hol.sm1, basic package for holonomic systems (C) N.Ta
Line 14  $hol.sm1, basic package for holonomic systems (C) N.Ta
 message-quiet  message-quiet
   
 /gb.warning 0 def  /gb.warning 0 def
   /gb.oxRingStructure [[ ] [ ]] def
 /rank.v [(x) (y) (z)] def   %% default value of v (variables).  /rank.v [(x) (y) (z)] def   %% default value of v (variables).
 /rank.ch [ ] def  %% characteristic variety.  /rank.ch [ ] def  %% characteristic variety.
 /rank.verbose 0 def  /rank.verbose 0 def
Line 415  message-quiet
Line 416  message-quiet
       /ans set        /ans set
     }{ }      }{ }
     ifelse      ifelse
       ans getRing (oxRingStructure) dc /gb.oxRingStructure set
     %%      %%
     env1 restoreOptions  %% degreeShift changes "grade"      env1 restoreOptions  %% degreeShift changes "grade"
   
Line 762  message-quiet
Line 764  message-quiet
   (                array ds; ds is the degree shift )    (                array ds; ds is the degree shift )
   (  )    (  )
   (gb.authoHomogenize 1 [default])    (gb.authoHomogenize 1 [default])
     (gb.oxRingStructure )
   ( )    ( )
   $Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) $    $Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) $
   $             [ [ (Dx) 1 ] ] ] gb pmat ; $    $             [ [ (Dx) 1 ] ] ] gb pmat ; $
Line 919  message-quiet
Line 922  message-quiet
        [vsize gtmp] toVectors /gtmp set         [vsize gtmp] toVectors /gtmp set
        ggall 0 gtmp put         ggall 0 gtmp put
     }{  } ifelse      }{  } ifelse
       /arg1 [gg dehomogenize ggall] def  
       gg getRing (oxRingStructure) dc /gb.oxRingStructure set
   
       /arg1 [gg dehomogenize ggall] def
   ] pop    ] pop
   popEnv    popEnv
   popVariables    popVariables
Line 1858  message-quiet
Line 1864  message-quiet
   arg1    arg1
 } def  } def
   
   /gb.reduction_noh {
     /arg2 set
     /arg1 set
     [/in-gb.reduction_noh /gbasis /flist /ans /gbasis2
     ] pushVariables
     [(CurrentRingp) (KanGBmessage) (Homogenize)] pushEnv
     [
        /gbasis arg2  def
        /flist  arg1  def
        gbasis 0 get tag 6 eq { }
        { (gb.reduction_noh: 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 gb 0 get getRing ring_def
          /gbasis2 gbasis 0 get ,,, def
        } ifelse
   
   
        flist ,,, /flist set
        [(Homogenize) 0] system_variable
        flist tag 6 eq {
          flist { gbasis2 reduction } map /ans set
        }{
          flist gbasis2 reduction /ans set
        } ifelse
        /arg1 ans def
   
     ] pop
     popEnv
     popVariables
     arg1
   } def
   
 /gb.reduction.test {  /gb.reduction.test {
   [    [
     [( 2*(1-x-y) Dx + 1 ) ( 2*(1-x-y) Dy + 1 )]      [( 2*(1-x-y) Dx + 1 ) ( 2*(1-x-y) Dy + 1 )]
Line 1890  message-quiet
Line 1933  message-quiet
   $ ((h-x-y)^2*Dx*Dy) ggg gb.reduction :: $    $ ((h-x-y)^2*Dx*Dy) ggg gb.reduction :: $
 ]] putUsages  ]] putUsages
   
   [(gb.reduction_noh)
   [ (f basis gb.reduction_noh r)
     (f is reduced by basis by the normal form algorithm.)
     (The first element of basis <g_1,...,g_m> must be a Grobner 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 gb.)
     (cf. gb.reduction, gb )
     $Example:$
     $ [[( 2*Dx + 1 ) ( 2*Dy + 1 )] $
     $   (x,y) [[(Dx) 1 (Dy) 1]]] /ggg set $
     $ ((1-x-y)^2*Dx*Dy) ggg gb.reduction_noh :: $
   ]] putUsages
   
 ( ) message-quiet ;  ( ) message-quiet ;
   
   /hol_loaded 1 def
   
   
   
Legend:
Removed from v.1.16  
changed lines
  Added in v.1.21
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