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Diff for /OpenXM/src/asir-contrib/packages/sample/noro_matrix-ja.txt between version 1.1 and 1.2

version 1.1, 2007/04/23 23:16:05 version 1.2, 2007/04/26 03:04:30
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    $B0J2<F~NO9T$O(B tab $B$+$i;O$^$k(B.     $B0J2<F~NO9T$O(B tab $B$+$i;O$^$k(B.
 */  */
   
 $BNc(B1.   $B9TNs(BA$B$N(BJordan $BI8=`7A$r7W;;$9$k(B.  /*********************/
   
   $BNc(B1.   $B%W%m%0%i%`$N%m!<%I(B
   
         load("noro_matrix.rr");          load("noro_matrix.rr");
         A=newmat(2,2,[[2,1],[0,2]]);  
   $B7k2L(B.
   
   $B$J$7(B
   
   $B7k2L$N@bL@(B.
   
           $B0J2<$N4X?t$rMQ$$$k:]$KI,MW(B.
   
   /*********************/
   
   $BNc(B2.   $BC10L9TNs$r@8@.$9$k(B.
   
           E=linalg.unit_mat(3);
   
   $B7k2L(B.
   
           [ 1 0 0 0 0 ]
           [ 0 1 0 0 0 ]
           [ 0 0 1 0 0 ]
           [ 0 0 0 1 0 ]
           [ 0 0 0 0 1 ]
   
   $B7k2L$N@bL@(B.
   
           $B;XDj$5$l$?%5%$%:$NC10L9TNs$rJV$9(B.
   
   
   /*********************/
   
   $BNc(B3.   $B9TNs$r%i%s%@%`$K@8@.$9$k(B.
   
           R=linalg.random_rmat(3,4,5);
   
   $B7k2L(B.
   
           [ -4 -3 2 0 ]
           [ -4 -2 -3 0 ]
           [ -2 3 -3 3 ]
   
   $B7k2L$N@bL@(B.
   
           $BBh0l(B, $BBhFs0z?t$O%5%$%:(B, $B3FMWAG$O@dBPCM$,(B($BBh;00z?t(B-1)$B$N@0?t$G$"$k(B.
   
   /*********************/
   
   $BNc(B4. $B5U9TNs$r7W;;$9$k(B.
   
           A=linalg.random_mat(3,3,5);
           Inv=invmat(A);
           AI=Inv[0]/Inv[1];
           M=A*AI;
   
   $B7k2L(B.
   
           A=      [ 2 0 0 0 ]
                   [ 3 5 1 0 ]
                   [ -9 -9 -1 0 ]
                   [ -5 0 0 1 ]
   
           Inv=[
                   [ 4 0 0 0 ]
           [ -6 -2 -2 0 ]
           [ 18 18 10 0 ]
           [ 20 0 0 8 ],8]
   
   
           AI=     [ 1/2 0 0 0 ]
                   [ -3/4 -1/4 -1/4 0 ]
                   [ 9/4 9/4 5/4 0 ]
                   [ 5/2 0 0 1 ]
   
           M=      [ 1 0 0 0 ]
                   [ 0 1 0 0 ]
                   [ 0 0 1 0 ]
                   [ 0 0 0 1 ]
   
   $B7k2L$N@bL@(B.
   
           $B7k2L$O(B [Num,Den] $B$N7A$N%j%9%H$G(B, Num $B$O@0?t9TNs(B, Den $B$O@0?t$G$"$k(B.
           Num/Den $B$,5U9TNs$rI=$9(B.
   
   /*********************/
   
   $BNc(B5.  $B9TNs$N:G>.B?9`<0$r7W;;$9$k(B.
   
           A=linalg.random_rmat(3,3,5);
           M=linalg.minipoly_mat(A);
   
   $B7k2L(B.
   
           A=      [ -4 3 3 ]
                   [ 1 2 3 ]
                   [ 0 4 -3 ]
   
           M=x^3+5*x^2-17*x-93
   
   $B7k2L$N@bL@(B.
   
           f(A)=0 $B$H$J$k:G>.<!?t$NB?9`<0(B f(x) $B$rJV$9(B. deg(f) $B$,(B A $B$N%5%$%:(B
           $B$h$j>.$5$$$3$H$b$"$jF@$k(B.
   
   /*********************/
   
   $BNc(B6.   $B9TNs(BA$B$N3K$r7W;;$9$k(B.
   
           A=linalg.random_rmat(3,5,5);
           Ker=linalg.compute_kernel(A);
   
   $B7k2L(B.
   
           A=      [ 4 -3 -4 -4 -4 ]
                   [ 3 3 0 -1 3 ]
                   [ -3 -3 0 1 -3 ]
   
           Ker=[[[ 2 0 0 3 -1 ],0],[[ 0 16 0 3 -15 ],1],[[ 0 0 4 -3 -1 ],2]]
   
   $B7k2L$N@bL@(B.
   
           [[v1,p1],[v2,p2],...] $B$N7A$N%j%9%H$,JV$k(B. vi $B$O%5%$%:$,(B A $B$NNs?t$HEy$7(B
           $B$$%Y%/%H%k$G(B, [v1,v2,...] $B$,(B Ker(A) $B$N0lAH$N4pDl$G$"$k(B. pi $B$O(B vi $B$NMWAG(B
           $B$r:8$+$i$_$F(B, $B:G=i$N(B 0 $B$G$J$$MWAG$N0LCV$r<($9(B. $B:G$b:8$r(B 0 $B$H$9$k(B.
   
   /*********************/
   
   $BNc(B7.   $B9TNs$NA|$r7W;;$9$k(B.
   
           A=linalg.random_rmat(3,5,5);
           Im=linalg.compute_image(A);
   
   $B7k2L(B.
   
           A=      [ 1 1 1 -1 4 ]
                   [ -3 3 2 -4 -3 ]
                   [ 3 3 0 1 4 ]
   
           Im=[[[ 1 -3 3 ],0,(1)*<<0>>],
           [[ 0 6 0 ],1,(1)*<<1>>+(-1)*<<0>>],
           [[ 0 0 -18 ],2,(6)*<<2>>+(-5)*<<1>>+(-1)*<<0>>]]
   
   $B7k2L$N@bL@(B.
   
           [[v1,p1,g1],[v2,p2,g2],...] $B$N7A$N%j%9%H$rJV$9(B. vi $B$O%Y%/%H%k$G(B
           [v1,v2,...] $B$,(B Im(A) $B$N0lAH$N4pDl$G$"$k(B.  pi $B$O(B vi $B$NMWAG$r:8$+$i$_$F(B,
           $B:G=i$N(B 0 $B$G$J$$MWAG$N0LCV$r<($9(B. $B:G$b:8$r(B 0 $B$H$9$k(B. gi $B$O(B, vi $B$,(B
           $B$b$H$N9TNs$NNs$+$i$I$N$h$&$K@8@.$5$l$F$$$k$+$r<($9J,;6B?9`<0$G$"$k(B.
           $BNc$($P>e$NNc$G$O(B, [0 6 0] $B$O(B ($BBh(B 1 $BNs(B-$BBh(B 0 $BNs(B) $B$KEy$7$$$3$H$,J,$+$k(B.
   
   /*********************/
   
   $BNc(B8.   $B9TNs(BA$B$N(BJordan $BI8=`7A$r7W;;$9$k(B.
   
           A=newmat(4,4,[[2,0,0,0],[3,5,1,0],[-9,-9,-1,0],[-5,0,0,1]]);
         B=linalg.jordan_canonical_form(A);          B=linalg.jordan_canonical_form(A);
           P=B[0];
           L=invmat(P); PI=L[0]/L[1];
           S=PI*A*P;
   
 $B7k2L(B.  $B7k2L(B.
   
           B=[
                   [ 0 1 1 0 ]
                   [ 3 0 0 0 ]
                   [ -9 0 -3 0 ]
                   [ 0 -5 -5 1 ],
                   [[2,2,1],[2,1,1],[1,1,1]],[]]
   
           S=      [ 2 1 0 0 ]
                   [ 0 2 0 0 ]
                   [ 0 0 2 0 ]
                   [ 0 0 0 1 ]
   
 $B7k2L$N@bL@(B.  $B7k2L$N@bL@(B.
   
           $B7k2L$O(B [P,[[e1,m1,j1],[e2,m2,j2],...],DefiningIdeal] $B$N7A$N%j%9%H$G$"$k(B.
           P $B$OJQ499TNs(B, $B$9$J$o$A(B P^(-1)AP $B$,(B Jordan $BI8=`7A$K$J$k9TNs$rI=$9(B.
           $B<!$NMWAG$O(B Jordan $BI8=`7A$r9=@.$9$k(B Jordan $B%V%m%C%/$N%j%9%H$G$"$k(B.
           [ei,mi,ji] $B$O(B, $B8GM-CM(B ei, $B%5%$%:(B mi $B$N(B Jordan $B%V%m%C%/$,(B ji $B8D$"$k$3$H(B
           $B$r<($9(B. $BF@$i$l$?(B P $B$K$h$j7W;;$9$k$H(B, $B3N$+$K$=$&$J$C$F$$$k$3$H$,>e$N(B
           $BNc$GJ,$+$k(B. $B0lHL$K$O(B, $B8GM-CM$OBe?tE*?t$H$J$k(B. $B$3$N>l9g(B, $B8GM-CM$r(B
           $BI=$9ITDj85$,I,MW$J$@$1@8@.$5$l(B, $B0lHL8GM-%Y%/%H%k(B (P $B$NNs%Y%/%H%k(B)
           $B$O$=$l$i$GI=8=$5$l$k(B. DefiningIdeal $B$O$=$l$i$NITDj85$rDj5A$9$k(B
           $B%$%G%"%k$G$"$k(B.
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