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Diff for /OpenXM/src/kan96xx/Doc/appell.sm1 between version 1.4 and 1.5

version 1.4, 2003/08/18 06:36:49 version 1.5, 2003/08/18 11:28:15
Line 1 
Line 1 
 %% appell.sm1, 1998,  11/8  %% appell.sm1, 1998,  11/8
 % $OpenXM: OpenXM/src/kan96xx/Doc/appell.sm1,v 1.3 2003/07/29 08:37:16 takayama Exp $  % $OpenXM: OpenXM/src/kan96xx/Doc/appell.sm1,v 1.4 2003/08/18 06:36:49 takayama Exp $
 /appell.version (2.981108) def  /appell.version (2.981108) def
 appell.version [(Version)] system_variable gt  appell.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
Line 82  $appell.sm1 generates Appell hypergeometric differenti
Line 82  $appell.sm1 generates Appell hypergeometric differenti
 [(appell1)  [(appell1)
  [(param appell1 c)   [(param appell1 c)
   (array param; array c;)    (array param; array c;)
   (appell1 returns the Lauricella function F_D(a,b_1, ..., b_n,c; x_1,...,x_n))    (appell1 returns an annihilating ideal for )
     (the Lauricella function F_D(a,b_1, ..., b_n,c; x_1,...,x_n))
   (for the parameter << param >> = [a, c, b_1, ..., b_n].)    (for the parameter << param >> = [a, c, b_1, ..., b_n].)
   (In case of n=2, the function is called the Appell function F_1.)    (In case of n=2, the function is called the Appell function F_1.)
   (c = [ generators,  variables ])    (c = [ generators,  variables ])
Line 152  $appell.sm1 generates Appell hypergeometric differenti
Line 153  $appell.sm1 generates Appell hypergeometric differenti
 [(appell4)  [(appell4)
  [(param appell4 c)   [(param appell4 c)
   (array param; array c;)    (array param; array c;)
   (appell4 returns the Lauricella function F_C(a,b, c_1, ..., c_n; x_1,...,x_n))    (appell4 returns an annihilating ideal for )
   (for the parameter << param >> = [a, c, b_1, ..., b_n].)    (the Lauricella function F_C(a,b, c_1, ..., c_n; x_1,...,x_n))
     (for the parameter << param >> = [a, b, c_1, ..., c_n].)
   (In case of n=2, the function is called the Appell function F_4.)    (In case of n=2, the function is called the Appell function F_4.)
   (c = [ generators,  variables ])    (c = [ generators,  variables ])
   (Note that for a special set of parameters, the returned differential equation)    (Note that for a special set of parameters, the returned differential equation)
Line 164  $appell.sm1 generates Appell hypergeometric differenti
Line 166  $appell.sm1 generates Appell hypergeometric differenti
   
 /appell4r {  /appell4r {
   /arg1 set    /arg1 set
   [/in-appell4r /typev /setarg /b /n /vv /i /a /c /bb /ans    [/in-appell4r /typev /setarg /b /n /vv /i /a /c /bb /ans /rr
   ] pushVariables    ] pushVariables
   [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.    [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.
   [    [
Line 172  $appell.sm1 generates Appell hypergeometric differenti
Line 174  $appell.sm1 generates Appell hypergeometric differenti
     aa isArray { } { (array appell) message (appell4) usage error } ifelse      aa isArray { } { (array appell) message (appell4) usage error } ifelse
     /setarg 0 def      /setarg 0 def
     aa { tag } map /typev set      aa { tag } map /typev set
       /rr 0 def
     typev [ ArrayP ] eq      typev [ ArrayP ] eq
     {  /b aa 0 get def      {  /b aa 0 get def
        /setarg 1 def         /setarg 1 def
     } { } ifelse      } { } ifelse
       typev [ ArrayP RingP] eq
       {  /b aa 0 get def
          /rr aa 1 get def
          /setarg 1 def
       } { } ifelse
     typev [ ] eq      typev [ ] eq
     {      {
        /b appell.b def         /b appell.b def
Line 195  $appell.sm1 generates Appell hypergeometric differenti
Line 203  $appell.sm1 generates Appell hypergeometric differenti
       } for        } for
     ] /vv set      ] /vv set
   
     [vv from_records ring_of_differential_operators 0] define_ring      rr tag 1 eq {
         [vv from_records ring_of_differential_operators 0] define_ring
       } {
         rr ring_def
       } ifelse
   
     %% b = [a  b  c_1 ... c_n ]      %% b = [a  b  c_1 ... c_n ]
     /a b 0 get def      /a b 0 get def
Line 224  $appell.sm1 generates Appell hypergeometric differenti
Line 236  $appell.sm1 generates Appell hypergeometric differenti
   arg1    arg1
 } def  } def
 %% [ [(1).. (2).. div -4 -2 5 6] ] appell4r  %% [ [(1).. (2).. div -4 -2 5 6] ] appell4r
   [(appell4r)
    [(param appell4r c)
     (array param; array c;)
     (appell4r returns an annihilating ideal for )
     (the Lauricella function F_C(a,b, c_1, ..., c_n; x_1,...,x_n))
     (for the parameter << param >> = [a, b, c_1, ..., c_n].)
     (In case of n=2, the function is called the Appell function F_4.)
     (c = [ generators,  variables ])
     (Example 1. [ [(1).. (2).. div -4 -2 5 6] ] appell4r rank ::)
     $Example 2. [(a,x1,x2) ring_of_differential_operators 0] define_ring /r set $
     $           [ [(a). (2).. div (a). (1). (1).] r] appell4r $
    ]
   ] putUsages
   
   
 /appell.euler {  /appell.euler {
Line 310  $appell.sm1 generates Appell hypergeometric differenti
Line 335  $appell.sm1 generates Appell hypergeometric differenti
 [(appell2)  [(appell2)
  [(param appell2 c)   [(param appell2 c)
   (array param; array c;)    (array param; array c;)
   (appell2 returns the Lauricella function F_A(a,b_1, ..., b_n, c_1, ..., c_n; x_1,...,x_n))    (appell2 returns an annihilating ideal for )
     (the Lauricella function F_A(a,b_1, ..., b_n, c_1, ..., c_n; x_1,...,x_n))
   (for the parameter << param >> = [a, [b_1, ..., b_n],[c_1, ..., c_n]].)    (for the parameter << param >> = [a, [b_1, ..., b_n],[c_1, ..., c_n]].)
   (In case of n=2, the function is called the Appell function F_2.)    (In case of n=2, the function is called the Appell function F_2.)
   (c = [ generators,  variables ])    (c = [ generators,  variables ])
Line 320  $appell.sm1 generates Appell hypergeometric differenti
Line 346  $appell.sm1 generates Appell hypergeometric differenti
   
 /appell2r {  /appell2r {
   /arg1 set    /arg1 set
   [/in-appell2r /typev /setarg /b /n /vv /i /a /c /bb /ans    [/in-appell2r /typev /setarg /b /n /vv /i /a /c /bb /ans /r
   ] pushVariables    ] pushVariables
   [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.    [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.
   [    [
Line 328  $appell.sm1 generates Appell hypergeometric differenti
Line 354  $appell.sm1 generates Appell hypergeometric differenti
     aa isArray { } { (array appell) message (appell2) usage error } ifelse      aa isArray { } { (array appell) message (appell2) usage error } ifelse
     /setarg 0 def      /setarg 0 def
     aa { tag } map /typev set      aa { tag } map /typev set
       /r 0 def
     typev [ ArrayP ] eq      typev [ ArrayP ] eq
     {  /b aa 0 get def      {  /b aa 0 get def
        /setarg 1 def         /setarg 1 def
     } { } ifelse      } { } ifelse
       typev [ ArrayP RingP] eq
       {  /b aa 0 get def
          /setarg 1 def
          /r aa 1 get def
       } { } ifelse
     typev [ ] eq      typev [ ] eq
     {      {
        /b [1 [2 3] [4 5]] def         /b [1 [2 3] [4 5]] def
Line 351  $appell.sm1 generates Appell hypergeometric differenti
Line 383  $appell.sm1 generates Appell hypergeometric differenti
       } for        } for
     ] /vv set      ] /vv set
   
     [vv from_records ring_of_differential_operators 0] define_ring      r tag 1 eq {
         [vv from_records ring_of_differential_operators 0] define_ring
       } {
         r ring_def
       } ifelse
   
     %% b = [a  [b_1 ... b_n]  [c_1 ... c_n] ]      %% b = [a  [b_1 ... b_n]  [c_1 ... c_n] ]
     /a b 0 get def      /a b 0 get def
Line 380  $appell.sm1 generates Appell hypergeometric differenti
Line 416  $appell.sm1 generates Appell hypergeometric differenti
   arg1    arg1
 } def  } def
 %%[[(1).. (2).. div [(1).. (2).. div (1).. (2).. div] [1 1]] ] appell2r rank ::  %%[[(1).. (2).. div [(1).. (2).. div (1).. (2).. div] [1 1]] ] appell2r rank ::
   [(appell2r)
    [(param appell2r c)
     (array param; array c;)
     (appell2r returns an annihilating ideal for )
     (the Lauricella function F_A(a,b_1, ..., b_n, c_1, ..., c_n; x_1,...,x_n))
     (for the parameter << param >> = [a, [b_1, ..., b_n], [c_1, ..., c_n]].)
     (In case of n=2, the function is called the Appell function F_2.)
     (c = [ generators,  variables ])
     (Example 1. [ [(1).. (2).. div [-4 -2] [5 6]] ] appell2r rank ::)
     $Example 2. [(a,x1,x2) ring_of_differential_operators 0] define_ring /r set $
     $           [ [(a). (2).. div [(a). (1).. (3).. div] [(1). (1).]] r] appell2r $
    ]
   ] putUsages
   
 ( ) message-quiet ;  ( ) message-quiet ;
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  Added in v.1.5
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