===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/dr.sm1,v
retrieving revision 1.22
retrieving revision 1.49
diff -u -p -r1.22 -r1.49
--- OpenXM/src/kan96xx/Kan/dr.sm1	2003/08/26 12:46:04	1.22
+++ OpenXM/src/kan96xx/Kan/dr.sm1	2005/06/16 06:21:21	1.49
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/src/kan96xx/Kan/dr.sm1,v 1.21 2003/08/24 05:25:58 takayama Exp $
+% $OpenXM: OpenXM/src/kan96xx/Kan/dr.sm1,v 1.48 2005/02/27 05:28:06 takayama Exp $
 %% dr.sm1 (Define Ring) 1994/9/25, 26
 %% This file is error clean.
 
@@ -50,7 +50,7 @@
           } for
      ] /dList set
 
-     [(H)] xList join [@@@.esymbol] join /xList set
+     [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
      [(h)] dList join [@@@.Esymbol] join /dList set
      [0 %% dummy characteristic
       << xList length >> << xList length >> << xList length >> 
@@ -167,7 +167,7 @@
      vars reverse /xList set         %[z y x]
      vars {@@@.Dsymbol 2 1 roll 2 cat_n} map
      reverse /dList set              %[Dz Dy Dx]
-     [(H)] xList join [@@@.esymbol] join /xList set
+     [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
      [(h)] dList join [@@@.Esymbol] join /dList set
      [0 1 1 1 << xList length >>
         1 1 1 << xList length 1 sub >> ] /param set
@@ -269,7 +269,7 @@
      vars reverse /xList set         %[z y x]
      vars {@@@.diffEsymbol 2 1 roll 2 cat_n} map
      reverse /dList set              %[Dz Dy Dx]
-     [(H)] xList join [@@@.esymbol] join /xList set
+     [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
      [(h)] dList join [@@@.Esymbol] join /dList set
      [0 1 1 << xList length >> << xList length >>
         1 1 << xList length 1 sub >> << xList length >> ] /param set
@@ -308,7 +308,7 @@
      vars2 reverse
      vars {@@@.Dsymbol 2 1 roll 2 cat_n} map
      reverse join /dList set              %[s2 s1 Dz Dy Dx]
-     [(H)] xList join [@@@.esymbol] join /xList set
+     [@@@.Hsymbol] xList join [@@@.esymbol] join /xList set
      [(h)] dList join [@@@.Esymbol] join /dList set
      [0 1 1 << vars2 length 1 add >>  << xList length >>
         1 1 << vars2 length 1 add >> << xList length 1 sub >> ] /param set
@@ -342,12 +342,14 @@
      0 1 << set0 length 1 sub >>
      {
         /i set
-        << set0 i get >> a eq
-        {
-           /flag 1 def 
-         }
-        { }
-        ifelse
+        set0 i get tag , a tag , eq {
+          << set0 i get >> a eq
+          {
+             /flag 1 def  exit
+           }
+          { }
+          ifelse
+        } {  } ifelse
      } for
   ] pop
   /arg1 flag def
@@ -361,6 +363,8 @@
   [
     /mat arg1 def
     /m mat length def
+  { 
+    m 0 eq { /ans [ ] def exit } { } ifelse
     mat 0 get isArray 
     {   }
     { (transpose: Argument must be an array of arrays.) error }
@@ -374,6 +378,8 @@
          ans [ j i ]  <<  mat i get j get >> put
       } for
     } for
+    exit
+   } loop
    /arg1 ans def
   ] pop
   popVariables
@@ -787,7 +793,7 @@
    (    Pointer to the ring. )
    (Example: [$x,y$ ring_of_q_difference_operators $Qx,Qy$ elimination_order)
    (          0] define_qring )
-   (cf. define_ring, set_up_ring@ <coefficient ring>, ring_def, << ,, >>)
+   (cf. define_ring, set_up_ring@ <coefficient ring>, ring_def, << __ >>)
   ]
 ] putUsages
 /define_qring {
@@ -839,7 +845,7 @@
   (one may use the command )
   (          f (ring) data_conversion /R set)
   (cf. define_ring, define_qring, system_variable, poly (ring) data_conversion)
-  (cf. << ,, >>)
+  (cf. << __ >>)
  ]
 ] putUsages
 
@@ -1328,6 +1334,7 @@
     /univ vars 0 get reverse
           vars 1 get reverse join
     def
+    w-vectors to_int32 /w-vectors set
     [
     0 1 << w-vectors length 1 sub >> 
     {
@@ -1350,7 +1357,8 @@
   /arg2 set  /arg1 set
   [/univ /www /k /vname /vweight /ans] pushVariables
   /univ arg1 def /www arg2 def
-  [ 
+  [
+    www to_int32 /www set 
     /ans << univ length >> -1 0 evecw def
     0  2  << www length 2 sub >>
     {
@@ -1405,7 +1413,7 @@
        gg (0). eq 
        { 0 }
        { gg (ring) data_conversion /rr set 
-         gg  << var rr ,, >> degree
+         gg  << var rr __ >> degree
        } ifelse
     } map def
   %%degs message
@@ -1520,6 +1528,13 @@
   (type?) data_conversion  RingP eq
 } def
 
+[(isByteArray)
+ [(obj isByteArray bool) ]
+] putUsages
+/isByteArray {
+  (type?) data_conversion  ByteArrayP eq
+} def
+
 /toString.tmp {
   /arg1 set
   [/obj /fname] pushVariables
@@ -1549,6 +1564,8 @@
     { obj (string) data_conversion } { } ifelse
     obj isRational
     { obj (string) data_conversion } { } ifelse
+    obj isByteArray
+    { obj (array) data_conversion toString } { } ifelse
     obj tag 0 eq
     { (null) } { } ifelse
 
@@ -1663,9 +1680,10 @@
 /RationalFunctionP 16 def
 /ClassP 17 def
 /DoubleP 18 def
+/ByteArrayP 19 def
 /@.datatypeConstant.usage [
  (IntegerP, LiteralP, StringP, ExecutableArrayP, ArrayP, PolyP, FileP, RingP,)
- (UniversalNumberP, RationalFunctionP, ClassP, DoubleP)
+ (UniversalNumberP, RationalFunctionP, ClassP, DoubleP, ByteArrayP)
  (      return data type identifiers.)
  (Example:  7 tag IntegerP eq  ---> 1)
 ] def
@@ -1680,18 +1698,19 @@
 [(RationalFunctionP) @.datatypeConstant.usage ] putUsages
 [(ClassP) @.datatypeConstant.usage ] putUsages
 [(DoubleP) @.datatypeConstant.usage ] putUsages
+[(ByteArrayP) @.datatypeConstant.usage ] putUsages
 
-[(,,)
- [( string ring ,, polynomial)
+[(__)
+ [( string ring __ polynomial)
   (Parse the <<string>> as an element in the <<ring>> and returns)
   (the polynomial.)
   (cf. define_ring, define_qring, ring_def)
   (Example: [(x,y) ring_of_polynomials [[(x) 1]] weight_vector 7]define_ring)
   (         /myring set)
-  (         ((x+y)^4) myring ,, /f set)
+  (         ((x+y)^4) myring __ /f set)
 ]] putUsages
  
-/,, {
+/__ {
   /arg2 set /arg1 set
   [/rrr] pushVariables
   [ arg1 tag StringP eq
@@ -1701,7 +1720,7 @@
       /arg1 arg1 expand def
       [(CurrentRingp) rrr] system_variable
     }
-    {(Argument Error for ,, ) error }
+    {(Argument Error for __ ) error }
     ifelse
   ] pop
   popVariables
@@ -1712,8 +1731,9 @@
  [( string .. universalNumber)
   (Parse the << string >> as a universalNumber.)
   (Example:  (123431232123123).. /n set)
+  ({ commands }..  executes the commands.  << .. >> is equivalent to exec.)
 ]] putUsages
-/.. { (universalNumber) data_conversion } def
+/.. { dup tag 3 eq { exec } { (universalNumber) data_conversion} ifelse } def
 
 [(dc) 
  [(Abbreviation of data_conversion.)
@@ -1766,7 +1786,11 @@
   /arg1 set
   [/f /k /i /ans] pushVariables
   [
-     /ans (1).. def
+   /ans (1).. def
+   [(QuoteMode)] system_variable {
+     /f arg1 def   /k arg2 def
+     [(ooPower) f k] extension /ans set
+   } {
      /f arg1 def   /k arg2 ..int def
      k 0 lt {
        1 1 << 0 k sub >> {
@@ -1779,7 +1803,8 @@
          /ans f ans {mul} sendmsg2 def
        } for
      } ifelse
-     /arg1 ans def
+   } ifelse
+   /arg1 ans def
   ] pop
   popVariables
   arg1
@@ -1918,8 +1943,8 @@ newline
 } def
 %%end of function
 
-/rest { % returns remainder of a given list
-  [ 2 1 roll  aload length -1 roll pop ]
+/rest {
+  /arg1 set [(Krest) arg1] extension 
 } def
 [(rest)
  [(array rest the-rest-of-the-array)
@@ -1942,7 +1967,7 @@ newline
         error
      } ifelse
      /myring  base 0 get (ring) dc def
-     /zero (0) myring ,, def
+     /zero (0) myring __ def
      base length 1 sub /n set
      /minbase [ 0 1 n { /i set base i get } for ] def
      0 1 n {
@@ -2251,7 +2276,7 @@ newline
         [(variableNames) M2N 0 get] system_variable
         f toString /f2 set
         [(variableNames) M2N 3 get] system_variable
-        f2 M2N 2 get ,, /f2 set
+        f2 M2N 2 get __ /f2 set
     } ifelse
     [(CurrentRingp) cp] system_variable
     /arg1 f2 def
@@ -2277,7 +2302,7 @@ newline
   $/R2 set$
   $[[(x) (Dx)] [((t-1) Dt) (z)]] /r0 set$
   $r0 R1 R2 makeRingMap /maptable set$
-  $(Dx-1) R1 ,, /ff set$
+  $(Dx-1) R1 __ /ff set$
   $ ff maptable ringmap :: $
  ]
 ] putUsages
@@ -2363,7 +2388,7 @@ newline
        /rrr set
        base { . } map /base set
      } ifelse
-     vlist { dup isPolynomial {  } { rrr ,, } ifelse } map /vlist set
+     vlist { dup isPolynomial {  } { rrr __ } ifelse } map /vlist set
 
      [(hilbert) base vlist] extension /ff set
      [(CurrentRingp) rrrorg] system_variable
@@ -2382,7 +2407,7 @@ newline
      /vv arg2 def
      /f hhh 1 get def
      f (0). eq { /ans [0] def /hilbReduce.label goto } { } ifelse
-     f vv << f (ring) dc >> ,,  degree /vv set
+     f vv << f (ring) dc >> __  degree /vv set
      hhh 0 get /d set  
      d   d  (integer) dc factorial /d set
      d << vv (universalNumber) dc vv factorial >> idiv /d set
@@ -2458,9 +2483,9 @@ newline
     { /fn (0). def }
     {
        f (ring) dc /rrr set
-       v toString (^) n toString 3 cat_n rrr ,,
+       v toString (^) n toString 3 cat_n rrr __
        f mul 
-       [[v (0).] [(h) rrr ,, (1) rrr ,,]] replace /fn set
+       [[v (0).] [(h) rrr __ (1) rrr __]] replace /fn set
      } ifelse
      fn /arg1 set
   ] pop
@@ -2517,13 +2542,14 @@ newline
   [
     /fff arg1 def
     /www arg2 def
+    www to_int32 /www set
     fff (0). eq { /ddd -intInfinity def /ord_w.LLL goto} { } ifelse
     fff (ring) dc /rrr set
     fff init /fff set
     /ddd 0 def
     0 2 www length 1 sub {
       /iii set
-      fff << www iii get rrr ,, >> degree
+      fff << www iii get rrr __ >> degree
       << www iii 1 add get >> mul
       ddd add /ddd set
     } for
@@ -2548,17 +2574,18 @@ newline
   [
     /fff arg1 def
     /www arg2 def
+    www to_int32 /www set
     fff (0). eq { /ddd -intInfinity def /ord_w_all.LLL goto} { } ifelse
     /ddd -intInfinity def
     fff (ring) dc /rrr set
-    /zzz (0) rrr ,, def
+    /zzz (0) rrr __ def
     fff init /fff-in set
     fff fff-in sub /fff set
     {
      /ddd-tmp 0 def
      0 2 www length 1 sub {
        /iii set
-       fff-in << www iii get rrr ,, >> degree
+       fff-in << www iii get rrr __ >> degree
        << www iii 1 add get >> mul
        ddd-tmp add /ddd-tmp set
      } for
@@ -2605,22 +2632,22 @@ newline
          /v0 vv ii get (string) dc def
          v0 (array) dc 0 get Dascii eq  %% If the first character is D?
          {  rule  %% Dx-->x
-            [v0 rr ,, 
-            v0 (array) dc rest { (string) dc} map aload length cat_n rr ,,]
+            [v0 rr __ 
+            v0 (array) dc rest { (string) dc} map aload length cat_n rr __]
             append /rule set
          }
          { rule   %% x --> -Dx
-           [v0 rr ,,
+           [v0 rr __
             (0). 
             [Dascii] v0 (array) dc join { (string) dc } map aload length 
-            cat_n rr ,,  sub
+            cat_n rr __  sub
            ]
            append /rule set
          } ifelse
       } ifelse
      } for
      % rule message
-     ff rule replace [[(h) rr ,, (1) rr ,,]] replace /ans1 set
+     ff rule replace [[(h) rr __ (1) rr __]] replace /ans1 set
      } ifelse
     }
    { 
@@ -2762,6 +2789,7 @@ newline
   [/in-ngcd /nlist /g.ngcd /ans] pushVariables
   [
      /nlist arg1 def
+     nlist to_univNum /nlist set
      nlist length 2 lt
      { /ans nlist 0 get def /L.ngcd goto }
      {
@@ -2977,9 +3005,9 @@ newline
      {
         /xx xx (string) dc def
         /dxx [@@@.Dsymbol xx] cat def
-        /xx xx f (ring) dc ,, def
-        /dxx dxx f (ring) dc ,, def
-        /one (1) f (ring) dc ,, def
+        /xx xx f (ring) dc __ def
+        /dxx dxx f (ring) dc __ def
+        /one (1) f (ring) dc __ def
 
         { 
           /g f init def
@@ -3056,9 +3084,9 @@ newline
     f (0). eq {  }
     {
       /rr f (ring) dc def
-      xx {toString rr ,, } map /xx set
-      dx {toString rr ,, } map /dx set
-      ss {toString rr ,, } map /ss set
+      xx {toString rr __ } map /xx set
+      dx {toString rr __ } map /dx set
+      ss {toString rr __ } map /ss set
       /n xx length  def
       0 1 n 1 sub {
          /i set
@@ -3088,7 +3116,7 @@ newline
   [
     /f arg1 def /xx arg2 def /dx arg3 def /ss arg4 def
     f (ring) dc /rr set
-    /one (1) rr ,, def %% 
+    /one (1) rr __ def %% 
     /ww [ xx toString -1 dx toString 1 ] weightv  def
     f ww init f sub (0). eq {   } 
     { [(destraction2.1 : inhomogeneous with respect to ) 
@@ -3651,6 +3679,34 @@ $ [ff ff] fromVectors :: $ 
  (         ff to_int { tag } map :: )
 ]] putUsages
 
+/to_int32 {
+  /arg1 set
+  [/to-int32 /ob /ans] pushVariables
+  [
+    /ob arg1 def
+    /ans ob def
+    ob isArray {
+      ob {to_int32} map /ans set
+      /LLL.to_int32 goto
+    } {  } ifelse
+    ob isUniversalNumber {
+      ob (integer) dc /ans set
+      /LLL.to_int32 goto
+    } {  } ifelse
+    /LLL.to_int32
+    /arg1 ans def
+  ] pop
+  popVariables
+  arg1
+} def
+[(to_int32)
+[(obj to_int32 obj2)
+ $All universalNumber in obj are changed to integer (int32).$
+ (Example: /ff [1 (2).. [(hello) (0).]] def  ff { tag } map ::)
+ (         ff to_int32 { tag } map :: )
+ (cf. to_int, to_univNum )
+]] putUsages
+
 /define_ring_variables {
   [/in-define_ring_variables /drv._v /drv._p /drv._v0] pushVariables
 %% You cannot use these names for names for polynomials.
@@ -3753,6 +3809,7 @@ $ [ff ff] fromVectors :: $ 
  ] 
 ] putUsages
 
+/ecart.debug_reduction1 0 def
 /beginEcart {
   (red@) (ecart) switch_function
   [(Ecart) 1] system_variable
@@ -3760,6 +3817,9 @@ $ [ff ff] fromVectors :: $ 
   [(ReduceLowerTerms) 0] system_variable
   [(AutoReduce) 0] system_variable
   [(EcartAutomaticHomogenization) 0] system_variable
+  ecart.debug_reduction1 {
+    (red@) (debug) switch_function
+  } {  } ifelse
 } def
 
 [(endEcart)
@@ -3824,7 +3884,562 @@ $ [ff ff] fromVectors :: $ 
   arg1
 } def
 
+/addStdoutStderr {
+  [(>) (stringOut://@@@stdout) (2>) (stringOut://@@@stderr)] join
+} def
 
+[(___)
+[(reparse a polynomial or polynomials)]
+] putUsages
+/___ {
+  /arg1 set
+  [/in-reparse /ff] pushVariables
+  [
+    /ff arg1 def
+    ff tag 6 eq {
+      ff { ___ } map /arg1 set
+    } {
+      ff toString . /arg1 set
+    } ifelse
+  ] pop
+  popVariables
+  arg1
+} def
+
+/to_univNum {
+  /arg1 set
+  [/rr  ] pushVariables
+  [
+    /rr arg1 def
+    rr isArray {
+      rr { to_univNum } map /rr set
+    } {  
+    } ifelse 
+    rr isInteger {
+      rr (universalNumber) dc /rr set
+    } {
+    } ifelse
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1 
+} def
+[(to_univNum) 
+[(obj to_univNum obj2)
+ (Example. [ 2 (3).. ] to_univNum)
+ $cf. to_int32. (to_int)$
+]] putUsages
+
+[(lcm)
+ [ ([a b c ...] lcm r)
+   (cf. polylcm, mpzext)
+ ]
+] putUsages
+/lcm {
+  /arg1 set
+  [/aa /bb /rr /pp /i] pushVariables
+  [
+    /aa arg1 def
+    /rr (1).. def
+    /pp 0 def % isPolynomial array?
+    0 1 aa length 1 sub {
+      /i set
+      aa i get  isPolynomial {
+        /pp 1 def
+        exit
+      } {  } ifelse
+    } for
+
+    0 1 aa length 1 sub {
+      /i set
+      pp {
+        [rr aa i get] polylcm /rr set
+      } {  
+        [(lcm) rr aa i get ] mpzext /rr set
+      } ifelse
+    } for
+    
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def
+[(gcd)
+ [ ([a b c ...] gcd r)
+   (cf. polygcd, mpzext)
+ ]
+] putUsages
+/gcd {
+  /arg1 set
+  [/aa /bb /rr /pp /i] pushVariables
+  [
+    /aa arg1 def
+    /rr (1).. def
+    /pp 0 def % isPolynomial array?
+    0 1 aa length 1 sub {
+      /i set
+      aa i get  isPolynomial {
+        /pp 1 def
+        /rr aa i get def
+        exit
+      } {  } ifelse
+    } for
+
+    pp {
+     0 1 aa length 1 sub {
+       /i set
+       [rr aa i get] polygcd /rr set
+     } for
+    } {
+      aa ngcd /rr set
+    } ifelse
+    
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def
+
+[(denominator)
+ [ ([a b c ...] denominator r)
+   ( a denominator r )
+   (cf. dc, numerator)
+   (Output is Z or a polynomial.)
+ ]
+] putUsages
+% test data.
+%  [(1).. (2).. div (1).. (3).. div ] denominator
+%  [(2).. (3).. (4).. ] denominator
+/denominator {
+  /arg1 set
+  [/pp /dd /ii /rr] pushVariables
+  [
+    /pp arg1 def
+    pp to_univNum /pp set
+    {
+      pp isArray {
+        pp { denominator } map /dd set        
+        /rr dd lcm def % rr = lcm(dd[0], dd[1], ... )
+        rr /dd set 
+        exit
+      } {  } ifelse
+
+      pp (denominator) dc /dd set
+      exit
+
+    } loop
+    /arg1 dd def
+  ] pop
+  popVariables
+  arg1
+} def 
+
+[(numerator)
+ [ ([a b c ...] numerator r)
+   ( a numerator r )
+   (cf. dc, denominator)
+   (Output is a list of Z or polynomials.)
+ ]
+] putUsages
+% test data.
+/numerator {
+  /arg1 set
+  [/pp /dd /ii /rr] pushVariables
+  [
+    /pp arg1 def
+    pp to_univNum /pp set
+    {
+      pp isArray {
+        pp denominator /dd set        
+        pp dd mul /rr set
+        rr cancel /rr set
+        exit
+      } {  } ifelse
+
+      pp (numerator) dc /rr set
+      exit
+
+    } loop
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def 
+
+/cancel.Q {
+  /arg1 set
+  [/aa /rr /nn /dd /gg]  pushVariables
+  [
+    /aa arg1 def
+    {
+      aa isRational {
+         [(cancel) aa] mpzext /rr set 
+         rr (denominator) dc (1).. eq {
+            /rr rr (numerator) dc def
+            exit
+         } { } ifelse
+         rr (denominator) dc (-1).. eq {
+            /rr rr (numerator) dc (-1).. mul def
+         } { } ifelse
+         exit
+      } { } ifelse
+
+      /rr aa def
+      exit 
+    } loop
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def 
+
+/cancel.one {
+  /arg1 set
+  [/aa /rr /nn /dd /gg]  pushVariables
+  [
+    /aa arg1 def
+    {
+      aa isRational {
+        aa (numerator) dc /nn set
+        aa (denominator) dc /dd set
+        nn isUniversalNumber dd isUniversalNumber and {
+          /rr aa cancel.Q def
+          exit
+        } { (cancel: not implemented) error } ifelse
+      } { } ifelse
+
+      /rr aa def
+      exit 
+    } loop
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def 
+
+[(cancel)
+ [ (obj cancel r)
+   (Cancel numerators and denominators)
+   (The implementation has not yet been completed. It works only for Q.) 
+]] putUsages
+/cancel {
+  /arg1 set
+  [/aa /rr] pushVariables
+  [ 
+    /aa arg1 def
+    aa isArray {
+      aa {cancel} map /rr set
+    } { 
+      aa cancel.one /rr set
+    } ifelse
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def
+
+/nnormalize_vec {
+  /arg1 set
+  [/pp /rr /dd ] pushVariables
+  [
+    /pp arg1 def
+    pp denominator /dd set
+    dd (0).. lt { (nnormalize_vec: internal error) error } { } ifelse
+    pp numerator dd mul cancel /pp set
+    /@@@.nnormalize_vec_c dd def
+    pp gcd /dd set
+    dd (0).. lt { (nnormalize_vec: internal error) error } { } ifelse
+    pp (1).. dd div mul cancel /rr set
+    @@@.nnormalize_vec_c dd div cancel /@@@.nnormalize_vec_c set
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def
+[(nnormalize_vec)
+[(pp nnormalize_vec npp)
+ (It normalizes a given vector of Q into a vector of Z with relatively prime)
+ (entries by multiplying a postive number.)
+]] putUsages
+
+/getNode {
+  /arg2 set
+  /arg1 set
+  [/in-getNode /ob /key /rr /tt /ii] pushVariables
+  [
+    /ob arg1 def
+    /key arg2 def
+    /rr null def
+    {
+      ob isArray {
+        ob length 1 gt {
+          ob 0 get isString {
+            ob 0 get , key eq {
+              /rr ob 1 get def exit
+            } {  } ifelse
+          } { } ifelse
+        }{ } ifelse
+        ob { key getNode , dup tag 0 eq {pop} { } ifelse }  map /tt set
+        tt length 0 gt { /rr tt 0 get def exit } 
+        {/rr null def exit } ifelse    
+      } { } ifelse
+
+      ob isClass {
+        ob (array) dc /ob set
+      } { } ifelse
+      ob isClass , ob isArray or { } { exit } ifelse 
+      ob 0 get key eq {
+        /rr ob def
+        exit
+      } {  } ifelse
+      ob 2 get /ob set
+      0 1 ob length 1 sub {
+         /ii set
+         ob ii get key getNode /rr set
+         rr tag 0 eq { } { exit } ifelse
+      } for 
+      exit
+    } loop 
+    /arg1 rr def
+  ] pop
+  popVariables
+  arg1
+} def
+[(getNode)
+[(ob key getNode node-value)
+ (ob is a class object or an array.)
+ (The operator getNode returns the node with the key in ob.)
+ (When ob is a class, the node is an array of the format [key attr-list node-list])
+ (When ob is an array, the node is a value of key-value pairs.)
+ (Example:)
+ (  /dog [(dog) [[(legs) 4] ] [ ]] [(class) (tree)] dc def)
+ (  /man [(man) [[(legs) 2] ] [ ]] [(class) (tree)] dc def)
+ (  /ma [(mammal) [ ] [man dog]] [(class) (tree)] dc def)
+ (  ma (dog) getNode )
+ (Example 2:)
+ ( [ [1 ] [2 3] [[(dog) 2]]] (dog) getNode ::)
+]] putUsages 
+
+/cons {
+  /arg2 set /arg1 set
+  [/aa /bb] pushVariables
+  [
+    /aa arg1 def /bb arg2 def
+    [aa] (list) dc bb join /arg1 set
+  ] pop
+  popVariables
+  arg1
+} def
+[(cons)
+[(obj list cons list)
+]] putUsages
+/arrayToList {
+  /arg1 set
+  [/a /r] pushVariables
+  [
+    /a arg1 def
+    {
+      a isArray {
+       a { arrayToList } map /a set
+       a (list) dc  /r set
+       exit
+      } {  } ifelse
+      /r a def
+      exit
+    } loop
+    /arg1 r def
+  ] pop
+  popVariables
+  arg1
+} def 
+[(arrayToList)
+[(a arrayToList list)
+]] putUsages
+
+/listToArray {
+  /arg1 set
+  [/a /r] pushVariables
+  [
+    /a arg1 def
+    {
+      a tag 12 eq {
+       a (array) dc  /a set
+       a { listToArray } map /r set
+       exit
+      } {  } ifelse
+      a tag 0 eq {
+       /r [ ] def
+       exit
+      } {  } ifelse
+      /r a def
+      exit
+    } loop
+    /arg1 r def
+  ] pop
+  popVariables
+  arg1
+} def 
+[(listToArray)
+[(list listToArray a)
+]] putUsages
+
+% Body is moved to smacro.sm1
+[(makeInfix)
+[(literal makeInfix)
+ (Change literal to an infix operator.)
+ (Example: /+ { add } def )
+ (  /+ makeInfix)
+ (  /s 0 def 1 1 100 { /i set s + i /s set } for s message)
+ (  [ 1 2 3 ] { /i set i + 2 } map ::)
+]] putUsages
+
+/usages {
+  /arg1 set
+  [/name /flag /n /k /slist /m /i /sss /key /ukeys] pushVariables
+  [
+    /name arg1 def
+    /flag true def
+    {  % begin loop
+
+       name isArray {
+         /ukeys @.usages { 0 get } map shell def
+         name { /key set [(regexec) key ukeys] extension
+                { 0 get } map } map /sss set
+         exit
+       } {  } ifelse
+
+ name tag 1 eq { 
+   @.usages { 0 get } map shell { (, ) nl } map /sss set
+   exit
+ } { 
+
+    /sss [ ] def
+   @.usages length /n set  
+   0 1 << n 1 sub >> 
+   {   
+      /k set
+      name << @.usages k get 0 get >> eq
+      {
+        /slist @.usages k get 1 get def
+        /m slist length def
+        0 1 << m 1 sub >> {
+          /i set
+          sss slist i get append nl append /sss set
+        } for
+        /flag false def
+      }
+      { }
+      ifelse
+   } for
+      
+   %BUG:  cannot get usages of primitives.
+   flag
+   {name Usage  /sss [(Usage of ) name ( could not obtained.) nl ] def}
+   { }
+   ifelse
+   exit
+ } ifelse
+
+} loop
+   /arg1 sss cat def
+   ] pop
+   popVariables
+   arg1
+} def
+[(usages)
+ [(key usages usages-as-a-string)
+  (num usages list-of-key-words)
+  ([key1 key2 ... ] usages list-of-key-words  : it accepts regular expressions.)
+]] putUsages
+
+/setMinus {
+  /arg2 set /arg1 set
+  [/aa /bb /i ] pushVariables
+  [
+    /aa arg1 def /bb arg2 def
+    [
+      0 1 aa length 1 sub {
+        /i set
+        aa i get bb memberQ {
+        } { aa i get } ifelse
+      } for 
+    ] /arg1 set
+  ] pop
+  popVariables
+  arg1
+} def
+[(setMinus)
+[(a b setMinus c)
+]] putUsages
+
+% Define  some infix operators
+/~add~ { add } def /~add~ makeInfix
+/~sub~ { sub } def /~sub~ makeInfix
+/~mul~ { mul } def /~mul~ makeInfix
+/~div~ { div } def /~div~ makeInfix
+/~power~ { power } def /~power~ makeInfix
+/~put~ {
+  dup tag 3 eq { exec } {  } ifelse  put
+} def
+/~put~ makeInfix
+
+/toTokensBySpace {
+  /arg1 set
+  [(cgiToTokens) arg1 [ ]] extension
+} def 
+[(toTokensBySpace)
+[
+ ( string toTokensBySpace token_array )
+]] putUsages
+
+/setAttributeList {
+  /arg2 set
+  /arg1 set
+  [
+    [(setAttributeList) arg1 arg2] extension /arg1 set
+  ] pop
+  arg1
+} def
+/getAttributeList {
+  /arg1 set
+  [(getAttributeList) arg1] extension 
+} def
+/setAttribute {
+  /arg3 set
+  /arg2 set
+  /arg1 set
+  [
+    [(setAttribute) arg1 arg2 arg3] extension /arg1 set
+  ] pop
+  arg1
+} def
+/getAttribute {
+  /arg2 set
+  /arg1 set
+  [(getAttribute) arg1 arg2] extension 
+} def
+[(setAttributeList)
+[
+ (ob attr setAttributeList new-obj )
+ (Example: [(x-1) (y-1)] [(gb) 1] setAttributeList /ff set )
+]] putUsages
+[(setAttribute)
+[
+ (ob key value setAttribute new-obj )
+ (Example: [(x-1) (y-1)] (gb) 1 setAttribute /ff set )
+]] putUsages
+[(getAttributeList)
+[
+ (ob getAttributeList attr-obj )
+ (Example: [(x-1) (y-1)] [(gb) 1] setAttributeList /ff set )
+ (         ff getAttributeList :: )
+]] putUsages
+[(getAttribute)
+[
+ (ob key getAttribute value )
+ (Example: [(x-1) (y-1)] (gb) 1 setAttribute /ff set )
+ (         ff (gb) getAttribute :: )
+]] putUsages
 ;