[BACK]Return to debug-note.txt CVS log [TXT][DIR] Up to [local] / OpenXM / src / k097 / lib / minimal

Diff for /OpenXM/src/k097/lib/minimal/debug-note.txt between version 1.1 and 1.2

version 1.1, 2000/05/06 07:58:37 version 1.2, 2000/05/07 02:10:44
Line 1 
Line 1 
 $OpenXM$  $OpenXM: OpenXM/src/k097/lib/minimal/debug-note.txt,v 1.1 2000/05/06 07:58:37 takayama Exp $
   
   minimal.k $B$O(B V-minimal free resolution $B$r9=@.$9$k(B
   $B%W%m%0%i%`$G(B openxm version 1.1.2 $B0J>e$GF0:n(B.
   ( $BI,MW$J(B component $B$O(B  k0, ox_asir )
   openxm $B$K$D$$$F$O(B, http://www.openxm.org $B$r;2>H(B.
   
   $B8=:_(B, $B$$$A$*$&(B error $B$J$/$H$^$j(B, V-minimal free resolution
   $B$i$7$-$b$N$r9=@.$9$k$H$$$&$@$1$G(B, $B?t3XE*$J@5$7$5$N%A%'%C%/$O(B
   $B$^$@(B.
   
   $B;H$$J}(B
   
      k0    (  k0 $B%$%s%?%W%j%?$r%9%?!<%H(B )
     load["minimal.k"];;    (minimal.k $B$r%m!<%I(B)
   
   $BNc(B 1: Sminimal_v $B$O(B, V-minimal free resolution $B$r(B, Schreyer resolution
         $B$rJQ7A$7$F$$$C$F5a$a$k(B. (Sminimal $B$O(B LaScala-Stillman's algorithm
         $B$r;H$&(B: $B$^$@(B negative weight vector $B$G$-$A$s$H$&$4$+$J$$(B.)
   
     Sweyl("x,y",[["x",-1,"y",-1,"Dx",1,"Dy",1]]);
             v=[[2*x*Dx + 3*y*Dy+6, 0],
                [3*x^2*Dy + 2*y*Dx, 0],
                [0,  x^2+y^2],
                [0,  x*y]];
            a=Sminimal_v(v);
            sm1_pmat(a[0]); b=a[0]; b[1]*b[0]:
   
   $B%N!<%H(B:  a[0] is the V-minimal resolution. a[3] is the Schreyer resolution.
   
   $BNc(B 2:
            a=Sannfs3("x^3-y^2*z^2");
            b=a[0]; sm1_pmat(b);
            b[1]*b[0]: b[2]*b[1]:    ===> complex $B$G$"$k$3$H$N$?$7$+$a(B.
   
   x^3-y^2*z^2 $B$N(B annihilating ideal $B$N(B laplace $BJQ49$N(B V-minimal free resolution.
   Weight $B$O(B (-1,-1,-1,1,1,1).
   
   $B$A$J$_$K(B,
   Map(a[3],"Length"): $B$O(B  8, 17, 13, 3  (Schreyer resolution $B$N(B betti $B?t(B).
   Map(a[0],"Length"): $B$O(B  4, 6, 2  (V-minimal resolution $B$N(B betti $B?t(B).
   
   
   
   -------  $B%F%9%H%G!<%?=8(B
   
 a=Sannfs2("x*y*(x-y)*(x+y)");  a=Sannfs2("x*y*(x-y)*(x+y)");
   
 Correct answer by check.sm1  foo3;  a=testAnnfs3("x*y*z*(x+y+z-1)");
  es^2*x^2*Dx*Dy+es^3*y*Dx^2-es*y^3*Dy^2+4*x^2*y*Dy^4-es^3*y*Dy^2+8*x*y*Dx*Dy^2*h^2+2*es*y^2*Dy*h^2+4*x^2*Dy^3*h^2-24*y^2*Dy^3*h^2-2*es*y*h^4-8*y*Dy^2*h^4    V-minimal $B$K$b(B 1 $B$,@.J,$H$7$F$N$3$k$b$N$"$j(B.
 by g=[    es^2*x^2*Dy+es^3*y*Dx-es^2*y^2*Dy+es^3*x*Dy+8*x*y*Dy^2*h^2+2*es^2*y*h^2 , es*y*Dy-es^2*Dx-4*y*Dy^3-es*h^2 , -4*y^2*Dy^2-es^2*x-es^3 , -es*x^2*Dy^2-es^3*Dx^2+es*y^2*Dy^2+es^3*Dy^2-8*x*Dx*Dy^2*h^2-2*es*y*Dy*h^2+24*y*Dy^3*h^2+2*es*h^4+8*Dy^2*h^4 , 4*y*Dx*Dy+es*x+es^2 , 4*x*y*Dy^3-es^3*Dx+es^2*y*Dy-2*es^2*h^2 ]  
   
 Two bases are wrong.  a=testAnnfs2("x^3-y^2-x-1");
 In(15)=g2[4]:  
 -4*y*Dx*Dy-es*x+es^2  a=testAnnfs3("x^3+y^3+z^3");
 In(16)=g3[4]:    Schreyer $B$N(B betti $B$O(B max 100 $BDxEY(B.
 4*y*Dx*Dy+es*x+es^2    incompatible ... $B$J$k(B error $B$,$G$k$1$I$$$$$+!)(B
 In(17)=g2[5]:       Warning in order.c: mmLarger_tower3(): incompatible input and gbList.
 4*x*y*Dy^3-es^3*Dx-es^2*y*Dy+2*es^2*h^2  
 In(18)=g3[5]:       Length of gb is 6, f is es, g is -es^6*Dy^2
 4*x*y*Dy^3-es^3*Dx+es^2*y*Dy-2*es^2*h^2       Warning in order.c: mmLarger_tower3(): incompatible input and gbList.
 In(19)=    20 $BJ,8e(B segmentation fault $B$G=*N;(B.
   
   
   
   
 -------- successful construction  x^3-y^2-x  -------- successful construction  x^3-y^2-x
Legend:
Removed from v.1.1  
changed lines
  Added in v.1.2
FreeBSD-CVSweb <freebsd-cvsweb@FreeBSD.org>