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Diff for /OpenXM/src/kan96xx/Doc/gkz.sm1 between version 1.1 and 1.3

version 1.1, 1999/10/08 02:12:02 version 1.3, 2008/03/26 05:38:03
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 %% gkz.sm1, 1998, 11/6, 11/8  %% gkz.sm1, 1998, 11/6, 11/8,  2007-06-03
 /gkz.version (2.981108) def  /gkz.version (3.000000) def
 gkz.version [(Version)] system_variable gt  gkz.version [(Version)] system_variable gt
 { (This package requires the latest version of kan/sm1) message  { (This package requires the latest version of kan/sm1) message
   (Please get it from http://www.math.kobe-u.ac.jp/KAN) message    (Please get it from http://www.math.kobe-u.ac.jp/KAN) message
   error    error
 } { } ifelse  } { } ifelse
   
 $gkz.sm1 generates gkz systems (C) N.Takayama, 1998, 11/8, cf. rrank in hol.sm1 $ message-quiet  $gkz.sm1 generates gkz, mgkz systems (C) N.Takayama, 1998-2007, cf. rrank in hol.sm1 $ message-quiet
 /gkz.verbose 0 def  /gkz.verbose 0 def
 /gkz.A [[1 1 1 1] [0 1 2 3]] def  /gkz.A [[1 1 1 1] [0 1 2 3]] def
 /gkz.b [3 5] def  /gkz.b [3 5] def
Line 143  $gkz.sm1 generates gkz systems (C) N.Takayama, 1998, 1
Line 143  $gkz.sm1 generates gkz systems (C) N.Takayama, 1998, 1
   (Example 2: [ [[1 1 1 1] [0 1 3 4]] [0 0]] gkz rrank :: )    (Example 2: [ [[1 1 1 1] [0 1 3 4]] [0 0]] gkz rrank :: )
  ]   ]
 ] putUsages  ] putUsages
   
   
   /mgkz.A [[1 1 1 1] [0 1 2 3]] def
   /mgkz.w  [4 0 0 2] def
   /mgkz.b [3 5] def
   
   
   /mgkz {
     /arg1 set
     [/in-mgkz /aa /typev /setarg /A /b /vx /vy /vyi /w /n /k
      /vvv /www /At /i /ff /ttt /vxd /ttt2 /ttt /i /vxrule
      /w /mrulex /mruled
     ] pushVariables
     [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.
     [
       /aa arg1 def
       aa isArray { } { (array mgkz) message (mgkz) usage error } ifelse
       /setarg 0 def
       aa { tag } map /typev set
       typev [ ArrayP ArrayP ArrayP] eq
       {  /A aa 0 get def
          /w aa 1 get def
          /b aa 2 get  def
          /setarg 1 def
       } { } ifelse
       typev [ ] eq
       {
          /A mgkz.A def
          /w mgkz.w def
          /b mgkz.b def
          /setarg 1 def
       } { } ifelse
       setarg { } { (Argument mismatch) message error } ifelse
   
       b [0] join /b set
       [(KanGBmessage) gkz.verbose] system_variable
       b length /k set
       A w append /A set
       A transpose , [ 2 1 k { pop 0 } for 1] append /A set
       A transpose /A set
       A 0 get length /n set
   
      %% vy = [ (y1) (y2) (y3)] , vyi = [(yi1) (yi2) (yi3)],
      %% vx = [(x1) (x2) (x3) (x4) (x5)]
      [ 1 1 k { } for ] { (y) 2 1 roll gensym } map /vy   set
      [ 1 1 k { } for ] { (yi) 2 1 roll gensym } map /vyi set
      [ 1 1 n { } for ] { (x) 2 1 roll gensym } map /vx   set
   
      %% vvv = [(y1) (y2) (y3) (yi1) (yi2) (yi3) (x1) (x2) (x3) (x4) (x5)]
      /vvv vy vyi join vx join def
      %% www = [(y1) 1 (y2) 1 (y3) 1 (yi1) 1 (yi2) 1 (yi3) 1]
      /www vy vyi join { 1 } map def
      [ vvv from_records  ring_of_polynomials
        [www] weight_vector 0] define_ring
   
      /At A transpose def
      %% Apply an algorithm to get the toric ideal.
      %% Negative components are accepted.  yi1=y1^(-1), ...
      [
       1 1 n {
         /i set
         (x) i gensym .   vy vyi << At i 1 sub get >> gkz.prod sub
       } for
       1 1 k {
         /i set
         (1). (y) i gensym . (yi) i gensym . mul sub %% 1- y_i yi_i
       } for
      ] /ff set
      gkz.verbose { ff message } { } ifelse
      [ff] groebner_sugar 0 get
      vy vyi join eliminatev /ttt set
      ttt { toString } map /ttt set
      %%% ttt <== toric ideal
   
      [ vx from_records ring_of_differential_operators 0] define_ring
   %%D-clean  /vvv  [ 1 1 n { /i set [(x) i gensym . (Dx) i gensym . mul] } for ] def
      /vvv  [ 1 1 n { /i set [(x) i gensym . [@@@.Dsymbol (x)] cat i gensym . mul] } for ] def
      A { {(universalNumber) dc} map } map vvv mul transpose 0 get /ff set
   
      ff b {(universalNumber) dc} map sub /ff set
   
      /mrulex vx , n 1 sub , get . /mrulex set
      [[mrulex , (0). mrulex sub]] /mrulex set
      %%% [[(x5). (-x5).]] mrulex
      ff {mrulex replace} map  {toString} map /ff set
      %%% ff <== linear equations.
   
      %%% vxd = [(Dx1) ... (Dx4) (Dx5)]
      /vxd vx {@@@.Dsymbol 2 1 roll 2 cat_n} map def
   
     [[vxd , n 1 sub , get .
       vx  , n 1 sub , get .]] /mruled set
   
      %% fix 1999, 3/3 for non-homogeneous toric ideal.
      /vxrule [ 0 1 vx length 1 sub {
         /i set
         [vx i get . vxd i get .] } for
      ] def
   %%   ttt { . vx vxd join laplace0 toString } map  /ttt2 set
      ttt { . vxrule replace , mruled replace , toString } map  /ttt2 set
   
      /arg1 [ << ff ttt2 join >> vx ] def
     ] pop
     popEnv
     popVariables
     arg1
   } def
   
   [(mgkz)
    [([A w b] gkz [eq v])
     ([    ] gkz [eq v])
     (array of array of integer A; array of integer w, b;)
     (eq is the modified GKZ system defined by the matrix A, weight w, )
     (and the parameter b.)
     (v is the list of variables. The last variable is the deformation variable.)
     (Default values of A and b are in gkz.A and gkz.b)
     (For details, see the paper Modified A-hypergeometric system, N.Takayama)
     (http://arxiv.org/abs/0707.0043)
     (Example : [ [[1 2 3]] [1 2 1] [0]] mgkz rank :: )
     (Example : [ [[1 2 3]] [0]] gkz rank :: )
     (Example : [ [[1 1 1] [1 2 3]] [1 2 1] [1 0]] mgkz message )
    ]
   ] putUsages
   
   
 ( ) message-quiet ;  ( ) message-quiet ;
   
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