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Diff for /OpenXM/src/k097/lib/minimal/minimal-note-ja.txt between version 1.4 and 1.10

version 1.4, 2000/06/09 08:04:54 version 1.10, 2000/08/01 08:51:02
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 $OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.3 2000/06/08 08:37:53 takayama Exp $  $OpenXM: OpenXM/src/k097/lib/minimal/minimal-note-ja.txt,v 1.9 2000/07/30 02:26:25 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 544  In(10)=reductionTable :
Line 544  In(10)=reductionTable :
 In(11)=bases:  In(11)=bases:
 [    %[null] , [    0 , y^2 , -x ]  , [    -y , x , 1 ]  ]  [    %[null] , [    0 , y^2 , -x ]  , [    -y , x , 1 ]  ]
 In(12)=  $B$3$l$O(B, [3, 2, 1]  $B$N85$N$&$A(B, 2,1 $B$,$b$H$^$C$F$$$k(B.  In(12)=  $B$3$l$O(B, [3, 2, 1]  $B$N85$N$&$A(B, 2,1 $B$,$b$H$^$C$F$$$k(B.
 [ 2 ] $B$N7W;;$K(B 0 $BHVL\$,I,MW$G$3$l$,$^$@$J$$(B.  $B:G8e$N(B [ 2 ] $B$N7W;;$K(B 0 $BHVL\$,I,MW$G$3$l$,$^$@$J$$(B.
   $BMW$9$k$K(B 1 $BHVL\$H(B 3 $BHVL\$r>C$9(B operator [1, 0, -y^2]
        [    y^3 , 0 , -x^2 ]
        [    0 , y^2 , -x ]
        [    y , -x , 0 ]
   $B$N(B reduction $B$,I,MW(B.
   
   -----------------------------------------
   June 11, 2000 (Tue),  20:05
   V-strict $B$+$I$&$+$r%A%'%C%/$9$k4X?t$r=q$-$?$$(B.
   $B0BA4$K(B ring (schreyer order) $B$rDj5A$9$k4X?t$,M_$7$$(B.
   $B0BA4$K(B parse $B$9$k4X?t$bM_$7$$(B.
   $B%Y%/%H%k$H(B es $BI=8=$NJQ494X?t$b$$$k(B.
   
   AvoidTheSameRing == 1 $B$J$i(B, schreyer $B$N(B gbList $B$bJQ99$G$-$J$$$h$&$K(B
   $B$9$Y$-$+!)(B
   $B4XO"JQ?t(B:
   needWarningForAvoidTheSameRing
   isTheSameRing() :  ring $B$,F1$8$+(B check. pointer $B$G$J$/Cf?H$^$G$_$k(B.
   see poly4.c.  $B$3$3$N%3%a%s%H$O;29M$K$J$k(B.
   3.If Schreyer = 1, then the system always generates a new ring.
   
   define_ring $B$K(B gbList $B$bEO$;$k$N(B?
   ==> set_up_ring@ $B$r8+$k(B. grep set_up_ring ==>
   primitive.c  KsetUpRing() grep KsetUpRing ==>
   keyword gbListTower $B$,;H$($k$,(B, list $B$GM?$($J$$$H$$$1$J$$(B.
   list $B$KJQ49$9$k$N$O(B, (list) dc.
   
   tparse $B$NI,MW$J$o$1(B?
   ?? $B$*$b$$$@$;$J$$(B.
   
   ring_def $B$G(B ring (schreyer order) $B$rDj5A$9$k$H(B, $B7W;;$N$H$-$N(B
   order $B$b(B tower $B$G$d$C$F$/$l$k$N(B?
   $BB?J,(B NO.
   grep ppAdd *.c ==>
   poly2.c
     checkRing(f,g);
   
     while (f != POLYNULL && g != POLYNULL) {
       /*printf("%s + %s\n",POLYToString(f,'*',1),POLYToString(g,'*',1));*/
       checkRing2(f,g); /* for debug */
       gt = (*mmLarger)(f,g);
   
      mmLarger $B$OJQ$($F$J$$$h$&$K8+$($k(B.  checkRing $B$O%^%/%m(B.
   
   mmLarger_tower $B$O(B
     if (!(f->m->ringp->schreyer) || !(g->m->ringp->schreyer))
       return(mmLarger_matrix(f,g));
   $B$H$J$C$F$k$N$G(B mmLarger_tower $B$r(B default $B$K$7$F$*$1$P?4G[$J$$$h$&$K8+$($k(B.
   
   ring_def $B$O@5$7$/F0$/(B?
   
   TODO:
   $B4X?t$N;EMM(B:   ( new.sm1 $B$^$?$O(B complex.sm1 $B$K$*$$$H$/(B )
     mmLarger $B$O(B tower $B$KJQ$($F$7$^$&(B.
     $BJQ?tL>(B, weight vector, $B%7%U%H%Y%/%H%k(B m $B$rM?$($k$H(B ring (with schreyer order)
     $B$r:n$k(B.   ==> weyl<m>,  weyl
     parser $B$O$H$/$K:n$kI,MW$,$J$$$h$&$K8+$($k$,(B...(tparse) ==> name
     $B%Y%/%H%k(B <---> es $BI=8=(B  cf. toVectors, [(toe_)  f] gbext ==> name
     $BE,@Z$J(B homogenization $B4X?t(B ==> homogenize<m>
     ord_w $B$N(B schreyer $BHG(B       ==> ord_w<m>
     init  $B$N(B schreyer $BHG(B       ==> init<m>
     gb_h, syz_h $B$NBP1~HG(B       ==> [ ii vv ww m] syz_h
     resolution $B$+$i(B shift vector $B$r7W;;$9$k4X?t(B.
   
     $B7k2L$N(B check $B$r$9$k(B assert $B4X?t$bI,MW(B.
   
   $B>e$N(B $B%7%U%H%Y%/%H%kBP1~HG$N4X?t$OEvJ,(B new.sm1 $B$X(B. $B$=$N$"$H(B complex.sm1 $B$X(B.
   
   cohom.sm1 $B$N(B interface $B4X?t$O(B cohom.k $B$X(B.
   Help key word $B$O(B (Cohom.deRham) $B$_$?$$$K(B, . $B$G$/$.$C$F=q$/(B.
   
   ----------------------
   $B%(%i!<$N860x$,$h$&$d$/$o$+$k(B:  June 14, 19:00
   Schreyer frame $B$NCJ3,$G(B syz $B$K(B 1 $B$,$"$k$H(B strategy $B$,(B
   $B$O$?$i$+$J$$(B.
   
   test13()  GKZ $B$N(B minimal free resolution.  2 $BEY<B9T$9$k$HJQ(B.
   grade $B$,JQ99$5$l$k$H(B, $BJQ$J$3$H$,$*$-$k$N$G(B,
   ScheckIfSchreyer() $B4X?t$G(B, $B$3$l$r(B scheck $B$9$k$3$H$K$7$?(B.
     sm1(" (report) (mmLarger) switch_function /ss set ");
   $B$O$^$@$d$a$H$/(B. matrix $B$K$J$C$F$k$N$G(B.
   
   ------------------------------------------
   June 15, 2000
   TODO:
   1.if (IdenfityIntegerAndUniversalNumber)  $B$N$H$-(B --- default
     lt, gt, eq $B$G(B integer $B$H(B universalNumber $B$NHf3S$,$G$-$k$h$&$K$9$k(B.
     rational $B$H$NHf3S$b2DG=$K$9$k(B.
   
   2. sm1_push_int0 $B$KBP1~$9$k$3$H$r(B, sm1 $B$NB&$G$d$k(B.
        $B%^%/%mL>(B  obj to_int --> Done.
        weight_vector $B$N(B universalNumber ==> $B$^$@(B. $B%(%i!<$r$@$5$J$$$N$,$3$o$$(B.
        s_weight_vector
        weightv
        ord_w
        toVectors
        define_ring
        init
        gkz
   
   -------------
   Schreyer skelton $B$,$I$&$7$F(B 1 $B$rMWAG$K$b$D$+$7$i$Y$k(B.
   
   June 24 (Sat), 22:30 at Posthouse (Heathrow) www.posthouse-hotels.com
   Sevilla $BBZ:_(B, Mega $B$b$h$&$d$/$*$o$j(B minimal resolution $B$N(B check $B$KLa$k(B.
   resol1.c $B$K<!$N(B line $B$r2C$($?(B.
             /* If isConstant(sv.a) is added, (x^3 - y^2 z^2) deRham stops
            with an error. I've not yet understood the reason.
            At Posthouse at Heathrow. June 24, 2000 */
             if (isConstant(sv.b)) {
                   s->deleted = 1;
             }
     ===> $B$*$+$7$$$N$G:o=|(B.
   
   isConstant(sv.a) $B$,$J$$$H(B, $B$3$s$I$O(B,
   Sminimal([x^2+y^2,x*y]); $B$,%(%i!<$G$H$^$k(B.
   (x,y $B$N(B weight $B$O(B -1).
   LaScala-Stillman $B$NO@J8$r$b$&0lEY$J$,$a$h$&(B.
   
   commit $B$9$Y$-(B:  misc/mega2000 (cvs-misc add) Done.
                   OpenXM/src/kan96xx           Done.
                   OpenXM/src/k097/lib/minimal  Done.
   
   July 26.
      resol.c $B$N(B schreyerSkelton0 $B$G(B, skelton $B$,(B minimal $B$K$J$k$h$&$K(B
      $B%3!<%I$rA^F~(B.
      $B%F%9%H$O(B
        cd src/k097/lib/minimal
        k0
        load["minimal.k"];;
        Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
        Sminimal([x^2+y^2,x*y]);
      $B$G(B.
   
      LaScala-Stillman $B$NO@J85U$G(B  i<j $B$J$i(B e_i > e_j $B$H$J$k(B.
      (order.c   mmLarger_tower())
   
      $B%F%9%H(B 2.
        cd src/k097/lib/minimal
        k0
        load["minimal-test.k"];;
        v:
        Sminimal(v);
   
        test11();    /* a = test_ann3("x^3-y^2*z^2"); */
        test14();    /* gkz (1,2,3) */
   
   July 30.  Removed unnecessary code.
       $BNc(B:
        Sminimal("x^3-y^2");
        test12()  ( x^3-y^2 z^2)
        test15()   GKZ 1,2,3 with a check.
        test15b()   toric
        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.
   
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