version 1.2, 2003/07/29 08:36:39 |
version 1.6, 2003/08/18 11:59:57 |
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%% appell.sm1, 1998, 11/8 |
%% appell.sm1, 1998, 11/8 |
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% $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 81 $appell.sm1 generates Appell hypergeometric differenti |
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Line 82 $appell.sm1 generates Appell hypergeometric differenti |
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[(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 ) |
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(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 151 $appell.sm1 generates Appell hypergeometric differenti |
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Line 153 $appell.sm1 generates Appell hypergeometric differenti |
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[(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)) |
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(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 161 $appell.sm1 generates Appell hypergeometric differenti |
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Line 164 $appell.sm1 generates Appell hypergeometric differenti |
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] |
] |
] putUsages |
] putUsages |
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/appell4r { |
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/arg1 set |
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[/in-appell4r /typev /setarg /b /n /vv /i /a /c /bb /ans /rr |
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] pushVariables |
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[(CurrentRingp) (KanGBmessage)] pushEnv %% push current global environment. |
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[ |
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/aa arg1 def |
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aa isArray { } { (array appell) message (appell4r) usage error } ifelse |
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/setarg 0 def |
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aa { tag } map /typev set |
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/rr 0 def |
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typev [ ArrayP ] eq |
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{ /b aa 0 get def |
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/setarg 1 def |
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} { } ifelse |
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typev [ ArrayP RingP] eq |
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{ /b aa 0 get def |
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/rr aa 1 get def |
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/setarg 1 def |
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} { } ifelse |
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typev [ ] eq |
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{ |
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/b appell.b def |
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/setarg 1 def |
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} { } ifelse |
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setarg { } { (Argument mismatch) message (appell4r) usage error } ifelse |
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[(KanGBmessage) appell.verbose] system_variable |
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/n b length 2 sub def %% Lauricella F_C^n |
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%% vv = [(x1) (x2)] |
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[ |
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1 1 n { |
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/i set |
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(x) i gensym |
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} for |
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] /vv set |
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rr tag 1 eq { |
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[vv from_records ring_of_differential_operators 0] define_ring |
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} { |
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rr ring_def |
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} ifelse |
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%% b = [a b c_1 ... c_n ] |
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/a b 0 get def |
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/c b 1 get def |
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/bb b rest rest def |
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[ 1 1 n { |
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/i set |
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[@@@.Dsymbol (x)] cat i gensym . |
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i i appellr.euler . bb i 1 sub get (1).. sub add |
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mul |
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1 n appellr.euler . (0).. a add add |
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1 n appellr.euler . (0).. c add add |
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mul |
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sub |
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(numerator) dc cancelCoeff dehomogenize |
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toString |
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} for |
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] /ans set |
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/arg1 [ans vv] def |
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] pop |
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popEnv |
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popVariables |
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arg1 |
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} def |
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%% [ [(1).. (2).. div -4 -2 5 6] ] appell4r |
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[(appell4r) |
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[(param appell4r c) |
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(array param; array c;) |
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(appell4r returns an annihilating ideal for ) |
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(the Lauricella function F_C(a,b, c_1, ..., c_n; x_1,...,x_n)) |
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(for the parameter << param >> = [a, b, c_1, ..., c_n].) |
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(In case of n=2, the function is called the Appell function F_4.) |
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(c = [ generators, variables ]) |
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(Example 1. [ [(1).. (2).. div -4 -2 5 6] ] appell4r rank ::) |
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$Example 2. [(a,x1,x2) ring_of_differential_operators 0] define_ring /r set $ |
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$ [ [(a). (2).. div (a). (1). (1).] r] appell4r $ |
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] |
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] putUsages |
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/appell.euler { |
/appell.euler { |
/arg2 set |
/arg2 set |
/arg1 set |
/arg1 set |
Line 177 $appell.sm1 generates Appell hypergeometric differenti |
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Line 265 $appell.sm1 generates Appell hypergeometric differenti |
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arg1 |
arg1 |
} def |
} def |
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/appellr.euler { |
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/arg2 set |
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/arg1 set |
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[/n /i /n0] pushVariables |
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[ |
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/n0 arg1 def |
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/n arg2 def |
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[ n0 1 n { /i set (x) i gensym ( ) [@@@.Dsymbol (x)] cat i gensym |
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i n eq not { ( + ) } { } ifelse } for ] cat |
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/arg1 set |
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] pop |
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popVariables |
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arg1 |
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} def |
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/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 232 $appell.sm1 generates Appell hypergeometric differenti |
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Line 335 $appell.sm1 generates Appell hypergeometric differenti |
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[(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 ) |
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(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 240 $appell.sm1 generates Appell hypergeometric differenti |
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Line 344 $appell.sm1 generates Appell hypergeometric differenti |
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] |
] |
] putUsages |
] putUsages |
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/appell2r { |
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/arg1 set |
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[/in-appell2r /typev /setarg /b /n /vv /i /a /c /bb /ans /r |
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] pushVariables |
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[(CurrentRingp) (KanGBmessage)] pushEnv %% push current global environment. |
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[ |
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/aa arg1 def |
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aa isArray { } { (array appell) message (appell2r) usage error } ifelse |
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/setarg 0 def |
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aa { tag } map /typev set |
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/r 0 def |
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typev [ ArrayP ] eq |
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{ /b aa 0 get def |
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/setarg 1 def |
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} { } ifelse |
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typev [ ArrayP RingP] eq |
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{ /b aa 0 get def |
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/setarg 1 def |
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/r aa 1 get def |
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} { } ifelse |
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typev [ ] eq |
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{ |
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/b [1 [2 3] [4 5]] def |
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/setarg 1 def |
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} { } ifelse |
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setarg { } { (Argument mismatch) message (appell2r) usage error } ifelse |
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[(KanGBmessage) appell.verbose] system_variable |
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/n b 1 get length def %% Lauricella F_A^n |
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%% vv = [(x1) (x2)] |
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[ |
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1 1 n { |
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/i set |
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(x) i gensym |
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} for |
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] /vv set |
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r tag 1 eq { |
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[vv from_records ring_of_differential_operators 0] define_ring |
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} { |
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r ring_def |
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} ifelse |
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%% b = [a [b_1 ... b_n] [c_1 ... c_n] ] |
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/a b 0 get def |
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/c b 2 get def |
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/bb b 1 get def |
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[ 1 1 n { |
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/i set |
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[@@@.Dsymbol (x)] cat i gensym . |
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i i appellr.euler . c i 1 sub get (1).. sub add |
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mul |
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1 n appellr.euler . (0).. a add add |
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i i appellr.euler . (0).. bb i 1 sub get add add |
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mul |
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sub |
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(numerator) dc cancelCoeff dehomogenize |
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toString |
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} for |
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] /ans set |
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/arg1 [ans vv] def |
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] pop |
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popEnv |
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popVariables |
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arg1 |
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} def |
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%%[[(1).. (2).. div [(1).. (2).. div (1).. (2).. div] [1 1]] ] appell2r rank :: |
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[(appell2r) |
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[(param appell2r c) |
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(array param; array c;) |
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(appell2r returns an annihilating ideal for ) |
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(the Lauricella function F_A(a,b_1, ..., b_n, c_1, ..., c_n; x_1,...,x_n)) |
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(for the parameter << param >> = [a, [b_1, ..., b_n], [c_1, ..., c_n]].) |
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(In case of n=2, the function is called the Appell function F_2.) |
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(c = [ generators, variables ]) |
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(Example 1. [ [(1).. (2).. div [-4 -2] [5 6]] ] appell2r rank ::) |
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$Example 2. [(a,x1,x2) ring_of_differential_operators 0] define_ring /r set $ |
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$ [ [(a). (2).. div [(a). (1).. (3).. div] [(1). (1).]] r] appell2r $ |
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] |
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] putUsages |
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( ) message-quiet ; |
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( ) message-quiet ; |