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

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