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Annotation of OpenXM/src/kan96xx/Doc/Old/int-d.sm1, Revision 1.1

1.1     ! maekawa     1: % int-d.sm1
        !             2: %%
        !             3: %%%
        !             4:
        !             5: (int-d.sm1: Aug 28, 1995.) message
        !             6: (      New macros  "integral-d" and "get0-d"  are added.) message
        !             7: (      Type in 3 0 demo.int-d to see a demo.) message
        !             8:
        !             9:
        !            10: %% Usage, putUsages and showKeywords
        !            11: %% The data should be automatically generated from int-d.txt
        !            12: %% int-d.sm1 = int-d.sm + int-d.txt
        !            13: [(integral-d)
        !            14: [(ff n integral-d ffi  )
        !            15:  (  ff is a list of operators,)
        !            16:  (  n  is a number to specify the degree of approximation,)
        !            17:  (  ffi is the result list that will be the input to the "groebner")
        !            18:  (  to get the "sum" of the module ff.)
        !            19:  (Example: )
        !            20:  $ [(m) ring_of_difference_operators (Em) elimination_order 0] define_ring $
        !            21:  $ [((m-e+1) Em - (m+1)).  ( (e+1) E - (m-e)).] 3 integral-d /ffi set$
        !            22:  ( [ffi] groebner 0 get get0-d ::)
        !            23:  ( )
        !            24:  (See also, groebner (option countdown) and get0-d.)
        !            25: ]] putUsages
        !            26:
        !            27: [(get0-d)
        !            28: [(ff get0 result)
        !            29:  (   ff is a list of operators. The operators in ff that does not)
        !            30:  (   contain "e" is stored in result.)
        !            31:  (   Note that "h" and "E" are set to 1.)
        !            32:  (See also integral-d)
        !            33:  (Example: )
        !            34:  $  [ (x h + E). (e+x).] get0-d :: $
        !            35:  (  [ x + 1 ] )
        !            36: ]] putUsages
        !            37:
        !            38: %% You can use it as a template.
        !            39: /demo.int-d {
        !            40: /ccc set
        !            41: /nnn set
        !            42: %%%% Define the ring
        !            43: [ (n) ring_of_difference_operators (En) elimination_order 0] define_ring
        !            44:
        !            45: %%%% Give the equations here.
        !            46: %%%% E e = e E + E and "e"  and "E" will be eliminated.
        !            47: [ ((n-e+1)^2*En - (n+e+1)^2).
        !            48:   ((e+1)^4*E - (-1)^2*(n-e)^2*(n+e+1)^2). ] /ff set
        !            49:
        !            50: %%% Let's compute
        !            51: ff nnn integral-d /ffi set
        !            52: %% Give the lower and the upper bound of the degree.
        !            53: %% /from-degree 0 def  /to-degree 5 def
        !            54: %%[ffi [(from) from-degree (to) to-degree]]
        !            55: [ffi [(countDown) ccc]]
        !            56: groebner 0 get get0-d /ans set
        !            57: (Answer is in ans. ans = )  message
        !            58: ans ::
        !            59: (This is Apery's reccurence formula.) message
        !            60: } def
        !            61:
        !            62: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            63: %%%%%%%%%%%% Don't touch below %%%%%%%%%%%%%%%%%%%%%%%%
        !            64: %%%%%%%%%%%%%% e-vectors, integral-d, get0-d %%%%%%%%%%%%%%
        !            65: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !            66: %% (Try   [f1 f2 ...] nnn integral-d /ff set) message
        !            67: %% ([ff] groebner 0 get get0-d) message
        !            68: %%  number e-vectors
        !            69: /e-vectors {
        !            70:   /arg1 set
        !            71:   [/ans] pushVariables
        !            72:   [
        !            73:   /ans [(e).] def
        !            74:   1 1  << arg1 1 sub >>
        !            75:   { pop
        !            76:     /ans
        !            77:       [(e).] ans {(e). mul} map join
        !            78:     def
        !            79:   } for
        !            80:   /arg1 ans def
        !            81:   ] pop
        !            82:   popVariables
        !            83:   arg1
        !            84: } def
        !            85:
        !            86:
        !            87: %% [f1 f2 ...] nnn integral-d
        !            88: /integral-d {
        !            89:   /arg2 set
        !            90:   /arg1 set
        !            91:   [/nnn /gens /m /ans /fff] pushVariables
        !            92:   [
        !            93:   /gens arg1 def
        !            94:   /nnn arg2 def
        !            95:   /m gens length def
        !            96:   /ans [ ] def
        !            97:   0 1 << m 1 sub >> {
        !            98:     gens 2 1 roll get /fff set
        !            99:     %%fff ::
        !           100:     /ans
        !           101:       ans [fff] join nnn e-vectors {fff mul} map join
        !           102:     def
        !           103:     %%ans ::
        !           104:   } for
        !           105:   /ans
        !           106:     ans nnn e-vectors {(E-1). 2 1 roll mul} map join
        !           107:   def
        !           108:   /ans ans {[[(h). (1).]] replace} map def
        !           109:   /ans ans {homogenize} map def
        !           110:   /arg1 ans def
        !           111:   ] pop
        !           112:   popVariables
        !           113:   arg1
        !           114: } def
        !           115:
        !           116: % [g1 g2 g3 ...] get0-d
        !           117: /get0-d {
        !           118:   /arg1 set
        !           119:   [/gb /degs /ans /n /ff] pushVariables
        !           120:   [
        !           121:   /gb arg1 def
        !           122:   /degs gb {(e). degree} map def
        !           123:   /ans [
        !           124:     0 1 << gb length 1 sub >> {
        !           125:       /n set
        !           126:       << degs n get  >>  0 eq
        !           127:       { gb n get [[(E). (1).] [(h). (1).]] replace /ff set
        !           128:         ff (0). eq
        !           129:         {  }
        !           130:         { ff } ifelse
        !           131:       }
        !           132:       {   } ifelse
        !           133:     } for
        !           134:   ] def
        !           135:   /arg1 ans def
        !           136:   ] pop
        !           137:   popVariables
        !           138:   arg1
        !           139: } def
        !           140:
        !           141: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !           142: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
        !           143:
        !           144:
        !           145: