===================================================================
RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/dr.sm1,v
retrieving revision 1.29
retrieving revision 1.38
diff -u -p -r1.29 -r1.38
--- OpenXM/src/kan96xx/Kan/dr.sm1	2004/08/22 12:52:34	1.29
+++ OpenXM/src/kan96xx/Kan/dr.sm1	2004/09/11 01:00:42	1.38
@@ -1,4 +1,4 @@
-% $OpenXM: OpenXM/src/kan96xx/Kan/dr.sm1,v 1.28 2004/05/13 05:33:10 takayama Exp $
+% $OpenXM: OpenXM/src/kan96xx/Kan/dr.sm1,v 1.37 2004/09/10 13:20:23 takayama Exp $
 %% dr.sm1 (Define Ring) 1994/9/25, 26
 %% This file is error clean.
 
@@ -361,6 +361,8 @@
   [
     /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 +376,8 @@
          ans [ j i ]  <<  mat i get j get >> put
       } for
     } for
+    exit
+   } loop
    /arg1 ans def
   ] pop
   popVariables
@@ -787,7 +791,7 @@
    (    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 +843,7 @@
   (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 +1332,7 @@
     /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 +1355,8 @@
   /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 +1411,7 @@
        gg (0). eq 
        { 0 }
        { gg (ring) data_conversion /rr set 
-         gg  << var rr ,, >> degree
+         gg  << var rr __ >> degree
        } ifelse
     } map def
   %%degs message
@@ -1681,17 +1687,17 @@
 [(ClassP) @.datatypeConstant.usage ] putUsages
 [(DoubleP) @.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 +1707,7 @@
       /arg1 arg1 expand def
       [(CurrentRingp) rrr] system_variable
     }
-    {(Argument Error for ,, ) error }
+    {(Argument Error for __ ) error }
     ifelse
   ] pop
   popVariables
@@ -1923,8 +1929,8 @@ 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)
@@ -1947,7 +1953,7 @@ 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 {
@@ -2256,7 +2262,7 @@ 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
@@ -2282,7 +2288,7 @@ 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
@@ -2368,7 +2374,7 @@ 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
@@ -2387,7 +2393,7 @@ 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
@@ -2463,9 +2469,9 @@ 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
@@ -2522,13 +2528,14 @@ 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
@@ -2553,17 +2560,18 @@ 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
@@ -2610,22 +2618,22 @@ 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
     }
    { 
@@ -2983,9 +2991,9 @@ 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
@@ -3062,9 +3070,9 @@ 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
@@ -3094,7 +3102,7 @@ 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 ) 
@@ -3657,6 +3665,34 @@ $ [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.
@@ -3838,16 +3874,16 @@ $ [ff ff] fromVectors :: $ 
   [(>) (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 { ___ } map /arg1 set
     } {
       ff toString . /arg1 set
     } ifelse
@@ -3877,7 +3913,7 @@ $ [ff ff] fromVectors :: $ 
 [(to_univNum) 
 [(obj to_univNum obj2)
  (Example. [ 2 (3).. ] to_univNum)
- (cf. to_int)
+ $cf. to_int32. (to_int)$
 ]] putUsages
 
 [(lcm)
@@ -3954,6 +3990,7 @@ $ [ff ff] fromVectors :: $ 
  [ ([a b c ...] denominator r)
    ( a denominator r )
    (cf. dc, numerator)
+   (Output is Z or a polynomial.)
  ]
 ] putUsages
 % test data.
@@ -3964,6 +4001,7 @@ $ [ff ff] fromVectors :: $ 
   [/pp /dd /ii /rr] pushVariables
   [
     /pp arg1 def
+    pp to_univNum /pp set
     {
       pp isArray {
         pp { denominator } map /dd set        
@@ -3986,6 +4024,7 @@ $ [ff ff] fromVectors :: $ 
  [ ([a b c ...] numerator r)
    ( a numerator r )
    (cf. dc, denominator)
+   (Output is a list of Z or polynomials.)
  ]
 ] putUsages
 % test data.
@@ -3994,11 +4033,12 @@ $ [ff ff] fromVectors :: $ 
   [/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 reduce /rr set
+        rr cancel /rr set
         exit
       } {  } ifelse
 
@@ -4012,7 +4052,7 @@ $ [ff ff] fromVectors :: $ 
   arg1
 } def 
 
-/reduce.Q {
+/cancel.Q {
   /arg1 set
   [/aa /rr /nn /dd /gg]  pushVariables
   [
@@ -4039,7 +4079,7 @@ $ [ff ff] fromVectors :: $ 
   arg1
 } def 
 
-/reduce.one {
+/cancel.one {
   /arg1 set
   [/aa /rr /nn /dd /gg]  pushVariables
   [
@@ -4049,9 +4089,9 @@ $ [ff ff] fromVectors :: $ 
         aa (numerator) dc /nn set
         aa (denominator) dc /dd set
         nn isUniversalNumber dd isUniversalNumber and {
-          /rr aa reduce.Q def
+          /rr aa cancel.Q def
           exit
-        } { (reduce: not implemented) error } ifelse
+        } { (cancel: not implemented) error } ifelse
       } { } ifelse
 
       /rr aa def
@@ -4063,26 +4103,155 @@ $ [ff ff] fromVectors :: $ 
   arg1
 } def 
 
-[(reduce)
- [ (obj reduce r)
+[(cancel)
+ [ (obj cancel r)
    (Cancel numerators and denominators)
    (The implementation has not yet been completed. It works only for Q.) 
 ]] putUsages
-/reduce {
+/cancel {
   /arg1 set
   [/aa /rr] pushVariables
   [ 
     /aa arg1 def
     aa isArray {
-      aa {reduce} map /rr set
+      aa {cancel} map /rr set
     } { 
-      aa reduce.one /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 /rr /ii] pushVariables
+  [
+    /ob arg1 def
+    /key arg2 def
+    /rr null def
+    {
+      ob isClass {
+        ob (array) dc /ob set
+      } { 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)
+ (ob is a class object.)
+ (The operator getNode returns the node with the key in ob.)
+ (The node is an array of the format [key attr-list node-list])
+ (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 )
+]] 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
+
 
 /usages {
   /arg1 set