%% int.sm1,   Aug 16, 1995.
%% demo.int is a template file to get integral of D-modules.
%%
(int.sm1: Aug 26, 1995.) message
(      New macros  "integral" and "get0"  are added.) message
(      Type in demo.int to see a demo.) message

%% Usage, putUsages and showKeywords
%% The data should be automatically generated from int.txt
%% int.sm1 = int.sm + int.txt
[(integral)
[(ff n integral ffi  )
 (  ff is a list of operators,)
 (  n  is a number to specify the degree of approximation,)
 (  ffi is the result list that will be the input to the "groebner")
 (  to get the integral of the module ff.)
 (Example: )
 $ [(x) ring_of_differential_operators ( ) elimination_order 0] define_ring $
 $ [(Dx h +e^2).  (E h + 2 x e).] 3 integral /ffi set$
 ( [ffi] groebner 0 get get0 ::)
 ( )
 (See also, groebner (option countdown) and get0.)
]] putUsages

[(get0)
[(ff get0 result)
 (   ff is a list of operators. The operators in ff that does not)
 (   contain "e" is stored in result.)
 (   Note that  "E" is set to zero and "h" is set to 1.)
 (See also integral)
 (Example: )
 $  [ (x h + 1). (e+x).] get0 :: $
 (  [ x + 1 ] )
]] putUsages

/demo.int {
%%%% Define the ring
[(x) ring_of_differential_operators ( ) elimination_order 0] define_ring

%%%% Give the equations here.
%%%% E e = e E + 1 and "e"  and "E" will be eliminated.
[(Dx h +e^2). 
 (E h + 2 x e). 
] /ff set

%%%% Give a number. If you can't get the integral, increase the number.
/nnn  3 def

%%% Let's compute
ff nnn integral /ffi set
%% Give the lower and the upper bound of the degree.
%% /from-degree 0 def  /to-degree 5 def
%%[ffi [(from) from-degree (to) to-degree]] 
[ffi]
groebner 0 get get0 /ans set
(Answer is in ans. ans = )  message
ans ::
} def

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%% Don't touch below %%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%% e-vectors, integral, get0 %%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% (Try   [f1 f2 ...] nnn integral /ff set) message
%% ([ff] groebner 0 get get0) message
%%  number e-vectors
/e-vectors {
  /arg1 set
  [/ans] pushVariables
  [
  /ans [(e).] def
  1 1  << arg1 1 sub >>
  { pop
    /ans
      [(e).] ans {(e). mul} map join
    def
  } for
  /arg1 ans def
  ] pop
  popVariables
  arg1
} def


%% [f1 f2 ...] nnn integral
/integral {
  /arg2 set
  /arg1 set
  [/nnn /gens /m /ans /fff] pushVariables
  [
  /gens arg1 def
  /nnn arg2 def
  /m gens length def
  /ans [ ] def
  0 1 << m 1 sub >> {
    gens 2 1 roll get /fff set
    %%fff ::
    /ans
      ans [fff] join nnn e-vectors {fff mul} map join 
    def
    %%ans ::
  } for
  /ans
    ans nnn e-vectors {(E). 2 1 roll mul} map join 
  def
  /ans ans {[[(h). (1).]] replace} map def
  /ans ans {homogenize} map def
  /arg1 ans def
  ] pop
  popVariables
  arg1
} def
   
% [g1 g2 g3 ...] get0
/get0 {
  /arg1 set
  [/gb /degs /ans /n /ff] pushVariables
  [
  /gb arg1 def
  /degs gb {(e). degree} map def
  /ans [
    0 1 << gb length 1 sub >> {
      /n set
      << degs n get  >>  0 eq
      { gb n get [[(E). (0).] [(h). (1).]] replace /ff set
        ff (0). eq
        {  }
        { ff } ifelse
      }
      {   } ifelse
    } for
  ] def
  /arg1 ans def
  ] pop
  popVariables
  arg1
} def

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