`asq', `af', `af_noalg'
-----------------------

asq(POLY)
     :: $BBe?tBN>e$N(B 1 $BJQ?tB?9`<0$NL5J?J}J,2r(B

af(POLY,ALGLIST)
af_noalg(POLY,DEFPOLYLIST)
     :: $BBe?tBN>e$N(B 1 $BJQ?tB?9`<0$N0x?tJ,2r(B

RETURN
     $B%j%9%H(B

POLY
     $BB?9`<0(B

ALGLIST
     `root' $B$N%j%9%H(B

DEFPOLYLIST
     `root' $B$rI=$9ITDj85$HDj5AB?9`<0$N%Z%"$N%j%9%H(B

   * $B$$$:$l$b(B `sp' $B$GDj5A$5$l$F$$$k(B.

   * `root' $B$r4^$^$J$$>l9g$O@0?t>e$NH!?t$,8F$S=P$5$l9bB.$G$"$k$,(B,
     `root' $B$r4^$`>l9g$K$O(B, `cr_gcda()' $B$,5/F0$5$l$k$?$a$7$P$7$P(B
     $B;~4V$,$+$+$k(B.

   * `af()' $B$O(B, $B4pACBN$N;XDj(B, $B$9$J$o$ABh(B 2 $B0z?t$N(B, `root' $B$N%j%9%H(B
     $B$N;XDj$,I,MW$G$"$k(B.

   * `alglist' $B$G;XDj$5$l$k(B `root' $B$O(B, $B8e$GDj5A$5$l$?$b$N$[$IA0$N(B
     $BJ}$KMh$J$1$l$P$J$i$J$$(B.

   * `af(F,AL)' $B$K$*$$$F(B, `AL' $B$OBe?tE*?t$N%j%9%H$G$"$j(B, $BM-M}?tBN$N(B
     $BBe?t3HBg$rI=$9(B. `AL=[An,...,A1]' $B$H=q$/$H$-(B, $B3F(B `Ak' $B$O(B, $B$=$l$h$j(B
     $B1&$K$"$kBe?tE*?t$r78?t$H$7$?(B,
     $B%b%K%C%/$JDj5AB?9`<0$GDj5A$5$l$F$$$J$1$l$P(B $B$J$i$J$$(B.

          [1] A1 = newalg(x^2+1);
          [2] A2 = newalg(x^2+A1);
          [3] A3 = newalg(x^2+A2*x+A1);
          [4] af(x^2+A2*x+A1,[A2,A1]);
          [[x^2+(#1)*x+(#0),1]]

     `af_noalg' $B$G$O(B, POLY $B$K4^$^$l$kBe?tE*?t(B AI $B$rITDj85(B VI
     $B$GCV$-49$($k(B. `defpolylist' $B$O(B, [[VN,DN(VN,...,V1)],...,[V1,D(V1)]]
     $B$J$k%j%9%H$G$"$k(B. $B$3$3$G(B DI(VI,...,V1) $B$O(B AI $B$NDj5AB?9`<0$K$*$$$F(B
     $BBe?tE*?t$rA4$F(B VJ $B$KCV$-49$($?$b$N$G$"$k(B.

          [1] af_noalg(x^2+a2*x+a1,[[a2,a2^2+a1],[a1,a1^2+1]]);
          [[x^2+a2*x+a1,1]]

   * $B7k2L$O(B, $BDL>o$NL5J?J}J,2r(B, $B0x?tJ,2r$HF1MM(B [$B0x;R(B, $B=EJ#EY(B]
     $B$N%j%9%H$G$"$k(B. `af_noalg' $B$N>l9g(B, $B0x;R(B $B$K8=$l$kBe?tE*?t$O(B,
     DEFPOLYLIST $B$K=>$C$FITDj85$KCV$-49$($i$l$k(B.

   * $B=EJ#EY$r9~$a$?0x;R$NA4$F$N@Q$O(B, POLY $B$HDj?tG\$N0c$$$,$"$jF@$k(B.

     [98] A = newalg(t^2-2);
     (#0)
     [99] asq(-x^4+6*x^3+(2*alg(0)-9)*x^2+(-6*alg(0))*x-2);
     [[-x^2+3*x+(#0),2]]
     [100] af(-x^2+3*x+alg(0),[alg(0)]);
     [[x+(#0-1),1],[-x+(#0+2),1]]
     [101] af_noalg(-x^2+3*x+a,[[a,x^2-2]]);
     [[x+a-1,1],[-x+a+2,1]]

$B;2>H(B
     *Note `cr_gcda': cr_gcda, *Note `fctr sqfr': fctr sqfr

