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Diff for /OpenXM/src/kan96xx/Doc/ecart.sm1 between version 1.25 and 1.29

version 1.25, 2004/05/13 05:52:53 version 1.29, 2004/05/28 08:11:31
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 % $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.24 2004/05/13 05:33:10 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) (hol.sm1) pushfile] extension
 %[(parse) (appell.sm1) pushfile] extension  %[(parse) (appell.sm1) pushfile] extension
   
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 /ecart.end   { endEcart } def  /ecart.end   { endEcart } def
 /ecart.autoHomogenize 1 def  /ecart.autoHomogenize 1 def
 /ecart.needSyz 0 def  /ecart.needSyz 0 def
 /ecartd.gb.oxRingStructure [ ] def  /ecartd.gb.oxRingStructure [[ ] [ ] ] def
   
 /ecartd.begin {  /ecartd.begin {
   ecart.begin    ecart.begin
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       (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set        (x,y) [[(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]]] /ggg set
    (Dx) ggg ecartd.reduction /gg4 set     (Dx) ggg ecartd.reduction /gg4 set
    gg4 message     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  } def
   
 /ecarth.reduction {  /ecarth.reduction {
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   $ (Dx+Dy) ggg ecartd.reduction :: $    $ (Dx+Dy) ggg ecartd.reduction :: $
 ]] putUsages  ]] 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 <g_1,...,g_m> 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 {  /ecart.stdOrder {
   /arg1 set    /arg1 set
   [/in-ecart.stdOrder /vv /tt /dvv /wv1 /wv2    [/in-ecart.stdOrder /vv /tt /dvv /wv1 /wv2
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 } def  } def
 /ecart.homogenize01Ideal {  /ecart.homogenize01Ideal {
  /arg1 set   /arg1 set
  [/in.ecart.homogenize01Ideal /ll /vv /wv] pushVariables   [/in.ecart.homogenize01Ideal /ll /vv /wv /ans] pushVariables
  [   [
    /ll arg1 0 get def     /ll arg1 0 get def
    /vv arg1 1 get def     /vv arg1 1 get def
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    [vv ring_of_differential_operators     [vv ring_of_differential_operators
     vv ecart.stdOrder weight_vector 0      vv ecart.stdOrder weight_vector 0
     [(weightedHomogenization) 1]] define_ring      [(weightedHomogenization) 1]] define_ring
    ll ,,, {ecart.homogenize01 ecart.dehomogenizeH} map /arg1 set     ll ,,, {ecart.homogenize01 ecart.dehomogenizeH} map /ans set
      ecart.end
      /arg1 ans def
  ] pop   ] pop
  popVariables   popVariables
  arg1   arg1
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  Added in v.1.29
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