%% lib/resol0.sm1,  1998, 11/8, 11/14, 1999, 05/18
%%     cf. r-interface.sm1, tower.sm1, tower-sugar.sm1
%%
%% It must contain one-line command for resolution.
/resol0.verbose 0  def
/resol0.parse 0 def %% If 1, 
                  %%Output of resol1 will be in a regular (non-schreyer) ring.
%% tower or tower-sugar will be chosen by the global variable
%% resol0.cp --- resol0 context pointer.
/resol0.version (2.981114) def
resol0.version [(Version)] system_variable gt
{ (This package requires the latest version of kan/sm1) message
  (Please get it from http://www.math.kobe-u.ac.jp/KAN) message
  error
} { } ifelse

$resol0.sm1, package to construct schreyer resolutions -- not minimal $ message-quiet
$                               (C) N.Takayama, 1999, 5/18. resol0, resol1 $ 
message-quiet

resol0.verbose {
  (Loading tower.sm1 in the context Tower and) message
  (loading tower-sugar.sm1 in the context Tower-sugar.) message
} {  } ifelse

(Tower) StandardContextp newcontext /cp.Tower set
cp.Tower setcontext
[(parse) (tower.sm1) pushfile] extension pop
StandardContextp setcontext

(Tower-sugar) StandardContextp newcontext /cp.Tower-sugar set
cp.Tower-sugar setcontext
[(parse) (tower-sugar.sm1) pushfile] extension pop
StandardContextp setcontext

/resol0.cp cp.Tower def
/resol0.v [(x) (y) (z)] def
/resol0 {
  /arg1 set
  [/in-resol0 /aa /typev /setarg /f /v 
   /gg /wv /vec /ans /depth
  ] pushVariables 
  [(CurrentRingp) (KanGBmessage)] pushEnv
  [
    /aa arg1 def
    aa isArray { } { (array gb) message (resol0) usage error } ifelse
    aa length 0 { (resol0) usage error } {  } ifelse
    aa 0 get isInteger {
      aa 0 get /depth set
      aa rest /aa set
    } 
    { /depth [ ] def } ifelse
  
    /setarg 0 def
    /wv [ ] def
    aa { tag } map /typev set
    typev [ ArrayP ] eq
    {  /f aa 0 get def
       /v resol0.v def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP StringP] eq
    {  /f aa 0 get def
       /v aa 1 get def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP ArrayP] eq
    {  /f aa 0 get def
       /v aa 1 get from_records def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP StringP ArrayP] eq
    {  /f aa 0 get def
       /v aa 1 get def
       /wv aa 2 get def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP ArrayP ArrayP] eq
    {  /f aa 0 get def
       /v aa 1 get from_records def
       /wv aa 2 get def
       /setarg 1 def
    } { } ifelse

    setarg { } { (resol0 : Argument mismatch) message error } ifelse
    
    [(KanGBmessage) resol0.verbose ] system_variable
    f 0 get isArray {
       [v ring_of_differential_operators 0] define_ring
        f { {toString .} map } map /f set
    }{
      f {toString} map /f set
    } ifelse

    [resol0.cp v wv ] {tower.define_sring} sendmsg
    [resol0.cp f ] {tower.tparse-vec} sendmsg /gg set
    [resol0.cp depth gg] {tower.sResolution} sendmsg /ans set
    /arg1 ans def
  ] pop
  popEnv
  popVariables
  arg1
} def
[(resol0)
 [( [ ii v] resol0 r )
  (array of poly ii; string v;)
  (<< vv >> is a string of variables separated by ,)
  (  )
  ( [ ii v] resol0 r )
  (array of poly ii; array of strings v;)
  (<< vv >> is an array of variable names. )
  (  )
  ( [ ii v w] resol0 r )
  (array of poly ii; string v; array w;)
  (<< w >> is a weight vector.)
  (  )
  (You can also give a parameter << d >> to specify the truncation depth)
  (of the resolution: [ d ii v] resol0, [d ii v w] resol0)
  (  )
  (resol0 constructs a resolution which is adapted (strict))
  (to a filtration. So, it is not minimal.)
  ( r = [starting Groebner basis g, [ s1, s2 , s3, ...], order-def].)
  (g is the reduced Groebner basis for f, )
  ( s1 is the syzygy of g,)
  ( s2 is the syzygy of s1,)
  ( s3 is the syzygy of s2 and so on.)
  (For details, see math.AG/9805006)
  (cf. sResolution, tparse, s_ring_..., resol0.cp)
  (Example:  [ [( x^3-y^2 )  ( 2 x Dx + 3 y Dy + 6 )  ( 2 y Dx + 3 x^2 Dy) ] )
  (             (x,y) ] resol0 :: )
]] putUsages

/resol1 {
  /arg1 set
  [/in-resol1 /aa /typev /setarg /f /v 
   /gg /wv /vec /ans /depth /vectorInput
   /vsize /eVector /ii /syzlist /syzlist1 /syz0 /i
  ] pushVariables 
  [(CurrentRingp) (KanGBmessage)] pushEnv
  [
    /aa arg1 def
    aa isArray { } { (array gb) message (resol1) usage error } ifelse
    aa length 0 { (resol1) usage error } {  } ifelse
    aa 0 get isInteger {
      aa 0 get /depth set
      aa rest /aa set
    } 
    { /depth [ ] def } ifelse
  
    /setarg 0 def
    /wv [ ] def
    aa { tag } map /typev set
    typev [ ArrayP ] eq
    {  /f aa 0 get def
       /v resol0.v def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP StringP] eq
    {  /f aa 0 get def
       /v aa 1 get def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP ArrayP] eq
    {  /f aa 0 get def
       /v aa 1 get from_records def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP StringP ArrayP] eq
    {  /f aa 0 get def
       /v aa 1 get def
       /wv aa 2 get def
       /setarg 1 def
    } { } ifelse
    typev [ArrayP ArrayP ArrayP] eq
    {  /f aa 0 get def
       /v aa 1 get from_records def
       /wv aa 2 get def
       /setarg 1 def
    } { } ifelse

    setarg { } { (resol1 : Argument mismatch) message error } ifelse
    
    [(KanGBmessage) resol0.verbose ] system_variable
    f 0 get isArray {
       /vectorInput  1 def
       /vsize f 0 get length def
    } {
       /vsize 1 def
       /vectorInput 0 def
    }ifelse
  
    vectorInput {
       [v ring_of_differential_operators 0] define_ring
%%      /eVector [0 1 vsize 1 sub { /ii set @@@.esymbol . ii npower } for ] def
%%      f { {toString .} map eVector mul toString } map /f set
%%Now,  sResolution in tower.sm1 accept vector input, 1999, 5/18.
        f { {toString .} map } map /f set
    }{
      f {toString} map /f set
    } ifelse

    [resol0.cp v wv ] {tower.define_sring} sendmsg
    [resol0.cp f ] {tower.tparse-vec} sendmsg /gg set
    resol0.verbose { gg message } {  } ifelse
    [resol0.cp depth gg] {tower.sResolution} sendmsg /syzlist set

    /resol1.syzlist  syzlist def  %% save in the global variable.
%% From  restall_s.sm1
%% Reformatting the free resolution:  
%%  [[f1,f2,..],[syz1,...]] --> [[[f1],[f2],...],[syz,...]] 
%% (to be modified for the case with more than one unknowns.)
      [v ring_of_differential_operators 0] define_ring
      /degmax syzlist 1 get length def
      /syzlist1 [
        syzlist 0 get /syz0 set
        %% start N.T.
        resol0.parse {
            [vsize syz0 { toString . } map]
        } { [vsize syz0 ] } ifelse
        toVectors2 
        %% end N.T.
        1 1 degmax {/i set
          resol0.parse {
             syzlist 1 get i 1 sub get {{toString .} map } map 
          }{ syzlist 1 get i 1 sub get  } ifelse 
        } for
      ] def
      syzlist1      
      /syzlist set  

    /arg1 syzlist def
  ] pop
  popEnv
  popVariables
  arg1
} def
[(resol1)
 [( [ ii v] resol1 r )
  (array of poly ii; string v;)
  (<< vv >> is a string of variables separated by ,)
  (  )
  ( [ ii v] resol1 r )
  (array of poly ii; array of strings v;)
  (<< vv >> is an array of variable names. )
  (  )
  ( [ ii v w] resol1 r )
  (array of poly ii; string v; array w;)
  (<< w >> is a weight vector.)
  (  )
  ( ii may be array of array of poly.)
  (You can also give a parameter << d >> to specify the truncation depth)
  (of the resolution: [ d ii v] resol1, [d ii v w] resol1)
  (  )
  (resol1 constructs a resolution which is adapted (strict))
  (to a filtration. So, it is not minimal in general.)
  ( r = [s0, s1, s2 , s3, ...].)
  ( s0 is the groebner basis of ii,)
  ( s1 is the syzygy of s0,)
  ( s2 is the syzygy of s1,)
  ( s3 is the syzygy of s2 and so on.)
  ( s1 s0 mul ==> 0, s2 s1 mul ==>0, ...)
  (For details, see math.AG/9805006)
  (cf. sResolution, tparse, s_ring_..., resol0.cp)
  (resol1.withZeroMap returns a resolution with zero maps of the both sides)
  (   of the resolution.)
  (cf. resol1.zeroMapL, resol1.zeroMapR, resol1.withZeroMap.aux)
  (resol1.syzlist : global variable to keep the raw output of sResolution.)
  (   )
  (Example 1: [ [( x^3-y^2 )  ( 2 x Dx + 3 y Dy + 6 )  ( 2 y Dx + 3 x^2 Dy) ] )
  (             (x,y) ] resol1 pmat ; )
  (Example 2: [ [( x^3-y^2 )  ( 2 x Dx + 3 y Dy + 6 )  ( 2 y Dx + 3 x^2 Dy) ] )
  (             (x,y) [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 pmat ; )
  (Example 3: [ [[(2 x Dx + 3 y Dy +6) (0)] )
  (              [(3 x^2 Dy + 2 y Dx) (0)] )
  (              [(0) (x^2+y^2)] )
  (              [(0) (x y )] ] )
  (             (x,y) [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 pmat ; )
  (Example 4:  /resol0.verbose 1 def)
  $          [ [[(x^2+y^2+ x y) (x+y)] [(x y ) ( x^2 + x y^3)] ] (x,y) $
  $            [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 pmat ; $
]] putUsages

/resol1.withZeroMap {
     resol1 resol1.withZeroMap.aux
} def
/resol1.withZeroMap.aux {
   /arg1 set
   [/in-resol1.withZeroMap.aux /ss /nn /mm] pushVariables
   [
     /ss arg1 def
     ss 0 get length /mm set
     ss 0 get 0 get isArray {
         /nn ss 0 get 0 get length def
     } { /nn 1 def } ifelse
     [ [nn mm] resol1.zeroMapR]
      ss join
     /ss set

     ss ss length 1 sub get [ ] eq {
       ss << ss length 1 sub >>
         << ss << ss length 2 sub >> get >> length resol1.zeroMapL put
     } { } ifelse
     /arg1 ss def
   ] pop
   popVariables
   arg1
} def

/resol1.zeroMapR {
  %% [[0,0],
  %%  [0,0],
  %%  [0,0]]
  /arg1 set
  [/in-resol1.zeroMapR /mm /nn] pushVariables
  [
    /mm arg1 0 get def
    /nn arg1 1 get def
    [ 1 1 mm { pop [1 1 nn { pop (0).} for] } for ]
    /arg1 set
  ] pop
  popVariables
  arg1
} def
/resol1.zeroMapL {
  %% [[0,0,0]]
  /arg1 set
  [/in-resol1.zeroMapL /mm ] pushVariables
  [
    /mm arg1 def
    [ [1 1 mm { pop (0). } for ]]
    /arg1 set
  ] pop
  popVariables
  arg1
} def

/pres1 {
  /arg1 set
  [/in-pres1 /rr /i /nn] pushVariables
  [
    /rr arg1 def
    /nn rr length 1 sub def
    0 1 nn {
      /i set
      rr i get [ ] eq { /pres1.LLL goto } { } ifelse
      (k^) messagen rr i get 0 get length message
      (^) message
      (|) message
      rr i get pmat
      (|) message
    } for
    /pres1.LLL
  ] pop
  popVariables
  arg1
} def
[(pres1)
[(rr pres1)
 (print resolution rr.)
  $Example $
  $          [ [[(x^2+y^2+ x y) (x+y)] [(x y ) ( x^2 + x y^3)] ] (x,y) $
  $            [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1.withZeroMap pres1 ; $
]] putUsages



%% It is included to work on the older version. It may removed.
%% toVectors2 is already in dr.sm1
(2.990500) [(Version)] system_variable gt
{
/toVectors2 {
  /arg1 set
  [/in-toVectors2 /gg /ans /n /tmp] pushVariables
  [
    /gg arg1 def
    /ans gg 1 get toVectors def
    /n   gg 0 get def
    ans { 
      /tmp set
      tmp length n lt {
        tmp
        [1 1 n tmp length sub { pop (0). } for ]
        join /tmp set
      } {  } ifelse
      tmp
    } map
    /ans set
    /arg1 ans def
  ] pop
  popVariables
  arg1
} def
} {  } ifelse

resol0.cp setcontext
/tower.define_sring {
  /arg1  set
  [/in-tower.define_sring /vv /ww /r] pushVariables
  [
     /vv arg1 1 get def
     /ww arg1 2 get def
     ww [ ] eq {
       [vv s_ring_of_differential_operators 0 [(schreyer) 1]] define_ring
     } {
       [vv s_ring_of_differential_operators ww s_weight_vector 
        0 [(schreyer) 1]] define_ring
     } ifelse
     /r set
    /arg1 r def
  ] pop
  popVariables
  arg1
} def
 
/tower.tparse-vec {
  /arg1  set
  [/in-tower.tparse-vec /ff ] pushVariables
  [
     arg1 1 get /ff set
     ff 0 get isArray {
       ff {{tparse} map} map /ff set
     } {     
       ff {tparse} map /ff set
     } ifelse
     /arg1 ff def
  ] pop
  popVariables
  arg1
} def

/tower.sResolution {
   resol0.verbose {  
    /tower.verbose 1 def
  } { } ifelse
  rest aload pop sResolution
} def
StandardContextp setcontext

/test00 {
  /resol0.verbose 1 def
   [ [[(x^2+y^2+ x y) (x+y)] [(x y ) ( x^2 + x y^3)] ] (x,y) [[(x) -1 (Dx) 1 (y) -1 (Dy) 1]]] resol1 /ff  set 
} def