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Diff for /OpenXM/src/k097/lib/minimal/minimal-note-ja.txt between version 1.9 and 1.11

version 1.9, 2000/07/30 02:26:25 version 1.11, 2000/08/02 05:14:30
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 $OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.8 2000/07/26 02:21:31 takayama Exp $  $OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.10 2000/08/01 08:51:02 takayama Exp $
   
 SpairAndReduction() :  SpairAndReduction() :
    $BM?$($i$l$?(B pair $B$r(B reduction $B$9$k(B.     $BM?$($i$l$?(B pair $B$r(B reduction $B$9$k(B.
Line 698  July 30.  Removed unnecessary code.
Line 698  July 30.  Removed unnecessary code.
      test12()  ( x^3-y^2 z^2)       test12()  ( x^3-y^2 z^2)
      test15()   GKZ 1,2,3 with a check.       test15()   GKZ 1,2,3 with a check.
      test15b()   toric       test15b()   toric
      test15c()   (u,v) = (-1,1)  
   
        test15c()   (u,v) = (-1,1)
   
   August 1.
       (u,v)-minimal $B$N%F%9%H%3!<%I$r$$$l$?(B.
       IsExact_h $B$G(B $BJQ?t(B c $B$NCM$,$+$o$k(B. $B860xITL@(B.
      c=Sinit_w(b,w);
      Println("Resolution (b)----");
      sm1_pmat(b);
      Println("Initial (c)----");
      sm1_pmat(c); cc=c;
      Println("Exactness of the resolution ---");
      Println(IsExact_h(b,v));  /* IsExact_h breaks the variable c.
                                   THIS BUG SHOULD BE FIXED. */
      $B$3$N$"$H$J$<$+(B, c $B$,(B b $B$NCM$K$+$o$C$F$7$^$&(B.
      $B$J$*(B def IsExact(c,...) $B$HDj5A$5$l$F$*$j(B, $B$3$N(B c $B$rJL$NJQ?tL>$K(B
      $BJQ$($l$P$3$NLdBj$O$*$-$J$$(B.
      Println("Why is the initial c rewritten by b? (buggy) ");sm1_pmat(c[0]);
   
      ===>  complex.sm1 $B$N(B isExact_h (isExact) $B$G(B popVariables $B$rK:$l$F$?$@$1(B.
   
      betti $B?t$O(B, $B9TNs$N>C5n$r$d$k$^$G$o$+$i$J$$$N(B?
      SbettiTable().
   
      Sminimal $B$O(B [(Homogenize_vec) 0] system_variable $B$K$9$k$h$&$G(B,
      $B$3$l$,(B cohomology $B$N7W;;$K$O<YKb(B.
   
   August 2, 2000.
   
   Sminimal $B$O(B [(Homogenize_vec) 0] system_variable $B$K$9$k$h$&$G(B,
   $B$3$l$,(B cohomology $B$N7W;;$K$O<YKb(B.
   ( cf. $BBg0$5W;a$N%9%/%j%W%H(B. $B8=:_?@8M$KBZ:_Cf(B. )
   
   /restoreEnvAfterResolution {
     [(AvoidTheSameRing)] pushEnv
     [ [(AvoidTheSameRing) 0] system_variable
       [(gbListTower) [[ ]] (list) dc] system_variable
     ] pop popEnv
     setupEnvForResolution.opts restoreOptions  <=== $BJQ99(B.  opts $B$O$$$m$s$J$H$3$m$G;H$C$F$k(B.
   } def
   
   $B$3$N%^%/%m$r$h$Y$P$$$$$N$+!)(B
      sm1(" restoreEnvAfterResolution ");
   $B$r(B Sminimal $B$N$*$o$j$K8F$V$h$&$KJQ$($?(B.
   test17b(), test18() $B$O@5>oF0:n(B.
   
   
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  Added in v.1.11
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