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Diff for /OpenXM/src/kan96xx/Doc/appell.sm1 between version 1.3 and 1.6

version 1.3, 2003/07/29 08:37:16 version 1.6, 2003/08/18 11:59:57
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 %% appell.sm1, 1998,  11/8  %% appell.sm1, 1998,  11/8
 % $OpenXM$  % $OpenXM: OpenXM/src/kan96xx/Doc/appell.sm1,v 1.5 2003/08/18 11:28:15 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 162  $appell.sm1 generates Appell hypergeometric differenti
Line 164  $appell.sm1 generates Appell hypergeometric differenti
  ]   ]
 ] putUsages  ] putUsages
   
   /appell4r {
     /arg1 set
     [/in-appell4r /typev /setarg /b /n /vv /i /a /c /bb /ans /rr
     ] pushVariables
     [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.
     [
       /aa arg1 def
       aa isArray { } { (array appell) message (appell4r) usage error } ifelse
       /setarg 0 def
       aa { tag } map /typev set
       /rr 0 def
       typev [ ArrayP ] eq
       {  /b aa 0 get def
          /setarg 1 def
       } { } ifelse
       typev [ ArrayP RingP] eq
       {  /b aa 0 get def
          /rr aa 1 get def
          /setarg 1 def
       } { } ifelse
       typev [ ] eq
       {
          /b appell.b def
          /setarg 1 def
       } { } ifelse
       setarg { } { (Argument mismatch) message (appell4r) usage error } ifelse
   
       [(KanGBmessage) appell.verbose] system_variable
   
       /n b length 2 sub def   %% Lauricella F_C^n
   
       %% vv = [(x1) (x2)]
       [
         1 1 n {
           /i set
           (x) i gensym
         } for
       ] /vv set
   
       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 ]
       /a b 0 get def
       /c b 1 get def
       /bb b rest rest def
   
       [ 1 1 n {
           /i set
              [@@@.Dsymbol (x)] cat i gensym  .
              i i appellr.euler . bb i 1 sub get (1)..  sub add
              mul
   
              1 n appellr.euler . (0).. a add add
              1 n appellr.euler . (0).. c add add
              mul
   
              sub
              (numerator) dc cancelCoeff dehomogenize
              toString
         } for
       ] /ans set
       /arg1 [ans vv] def
     ] pop
     popEnv
     popVariables
     arg1
   } def
   %% [ [(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 {
   /arg2 set    /arg2 set
   /arg1 set    /arg1 set
Line 178  $appell.sm1 generates Appell hypergeometric differenti
Line 265  $appell.sm1 generates Appell hypergeometric differenti
   arg1    arg1
 } def  } def
   
   /appellr.euler {
     /arg2 set
     /arg1 set
     [/n /i /n0] pushVariables
     [
       /n0 arg1 def
       /n arg2 def
       [ n0 1 n { /i set (x) i gensym  ( ) [@@@.Dsymbol (x)] cat i gensym
                  i n eq not { ( + ) } {  } ifelse } for ]  cat
       /arg1 set
     ] pop
     popVariables
     arg1
   } def
   
 /appell2 {  /appell2 {
   /arg1 set    /arg1 set
   [/in-appell2 /typev /setarg /b /n /vv /i /a /c /bb /ans    [/in-appell2 /typev /setarg /b /n /vv /i /a /c /bb /ans
Line 233  $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 241  $appell.sm1 generates Appell hypergeometric differenti
Line 344  $appell.sm1 generates Appell hypergeometric differenti
  ]   ]
 ] putUsages  ] putUsages
   
   /appell2r {
     /arg1 set
     [/in-appell2r /typev /setarg /b /n /vv /i /a /c /bb /ans /r
     ] pushVariables
     [(CurrentRingp) (KanGBmessage)] pushEnv  %% push current global environment.
     [
       /aa arg1 def
       aa isArray { } { (array appell) message (appell2r) usage error } ifelse
       /setarg 0 def
       aa { tag } map /typev set
       /r 0 def
       typev [ ArrayP ] eq
       {  /b aa 0 get def
          /setarg 1 def
       } { } ifelse
       typev [ ArrayP RingP] eq
       {  /b aa 0 get def
          /setarg 1 def
          /r aa 1 get def
       } { } ifelse
       typev [ ] eq
       {
          /b [1 [2 3] [4 5]] def
          /setarg 1 def
       } { } ifelse
       setarg { } { (Argument mismatch) message (appell2r) usage error } ifelse
   
       [(KanGBmessage) appell.verbose] system_variable
   
       /n b 1 get length def   %% Lauricella F_A^n
   
       %% vv = [(x1) (x2)]
       [
         1 1 n {
           /i set
           (x) i gensym
         } for
       ] /vv set
   
       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] ]
       /a b 0 get def
       /c b 2 get def
       /bb b 1 get def
   
       [ 1 1 n {
           /i set
              [@@@.Dsymbol (x)] cat i gensym .
              i i appellr.euler . c i 1 sub get (1).. sub add
              mul
   
              1 n appellr.euler . (0).. a add add
              i i appellr.euler . (0).. bb i 1 sub get add add
              mul
   
              sub
              (numerator) dc cancelCoeff dehomogenize
              toString
         } for
       ] /ans set
       /arg1 [ans vv] def
     ] pop
     popEnv
     popVariables
     arg1
   } def
   %%[[(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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Removed from v.1.3  
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  Added in v.1.6
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