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Annotation of OpenXM/src/kan96xx/Doc/Old/int.sm1, Revision 1.1.1.1

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: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%