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Diff for /OpenXM/src/asir-doc/parts/algnum.texi between version 1.4 and 1.6

version 1.4, 2000/03/17 02:17:03 version 1.6, 2003/04/19 15:44:55
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/algnum.texi,v 1.3 2000/03/10 07:18:40 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/algnum.texi,v 1.5 2000/09/23 07:53:24 noro Exp $
 \BJP  \BJP
 @node $BBe?tE*?t$K4X$9$k1i;;(B,,, Top  @node $BBe?tE*?t$K4X$9$k1i;;(B,,, Top
 @chapter $BBe?tE*?t$K4X$9$k1i;;(B  @chapter $BBe?tE*?t$K4X$9$k1i;;(B
Line 1083  substitutes a @b{root} for the associated indeterminat
Line 1083  substitutes a @b{root} for the associated indeterminat
 @item return  @item return
 \JP $BB?9`<0(B  \JP $BB?9`<0(B
 \EG polynomial  \EG polynomial
 @item poly1, poly2  @item poly1  poly2
 \JP $BB?9`<0(B  \JP $BB?9`<0(B
 \EG polynomial  \EG polynomial
 @end table  @end table
Line 1269  first.
Line 1269  first.
 \E  \E
 @item  @item
 \BJP  \BJP
 @code{sp_noalg} $B$G$O(B, @var{poly} $B$K4^$^$l$kBe?tE*?t(B @var{ai} $B$rITDj85(B @var{vi}  @code{af(F,AL)} $B$K$*$$$F(B, @code{AL} $B$OBe?tE*?t$N%j%9%H$G$"$j(B, $BM-M}?tBN$N(B
 $B$GCV$-49$($k(B. @code{defpolylist} $B$O(B, @var{[[vn,dn(vn,...,v1)],...,[v1,d(v1)]]}  $BBe?t3HBg$rI=$9(B. @code{AL=[An,...,A1]} $B$H=q$/$H$-(B, $B3F(B @code{Ak} $B$O(B, $B$=$l$h$j(B
 $B$J$k%j%9%H$G$"$k(B. $B$3$3$G(B @var{di(vi,...,v1)} $B$O(B @var{ai} $B$NDj5AB?9`<0$K$*$$$F(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.
   \E
   \BEG
   In @code{af(F,AL)}, @code{AL} denotes a list of @code{roots} and it
   represents an algebraic number field. In @code{AL=[An,...,A1]} each
   @code{Ak} should be defined as a root of a defining polynomial
   whose coefficients are in @code{Q(A(k+1),...,An)}.
   \E
   
   @example
   [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]]
   @end example
   
   \BJP
   @code{af_noalg} $B$G$O(B, @var{poly} $B$K4^$^$l$kBe?tE*?t(B @var{ai} $B$rITDj85(B @var{vi}
   $B$GCV$-49$($k(B. @code{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 @var{di}(vi,...,v1) $B$O(B @var{ai} $B$NDj5AB?9`<0$K$*$$$F(B
 $BBe?tE*?t$rA4$F(B @var{vj} $B$KCV$-49$($?$b$N$G$"$k(B.  $BBe?tE*?t$rA4$F(B @var{vj} $B$KCV$-49$($?$b$N$G$"$k(B.
 \E  \E
 \BEG  \BEG
 To call @code{sp_noalg}, one should replace each algebraic number  To call @code{sp_noalg}, one should replace each algebraic number
 @var{ai} in @var{poly} with an indeterminate @var{vi}. @code{defpolylist}  @var{ai} in @var{poly} with an indeterminate @var{vi}. @code{defpolylist}
 is a list @var{[[vn,dn(vn,...,v1)],...,[v1,d(v1)]]}. In this expression  is a list [[vn,dn(vn,...,v1)],...,[v1,d(v1)]]. In this expression
 @var{di(vi,...,v1)} is a defining polynomial of @var{ai} represented  @var{di}(vi,...,v1) is a defining polynomial of @var{ai} represented
 as a multivariate polynomial.  as a multivariate polynomial.
 \E  \E
   
   @example
   [1] af_noalg(x^2+a2*x+a1,[[a2,a2^2+a1],[a1,a1^2+1]]);
   [[x^2+a2*x+a1,1]]
   @end example
   
 @item  @item
 \BJP  \BJP
 $B7k2L$O(B, $BDL>o$NL5J?J}J,2r(B, $B0x?tJ,2r$HF1MM(B [@b{$B0x;R(B}, @b{$B=EJ#EY(B}]  $B7k2L$O(B, $BDL>o$NL5J?J}J,2r(B, $B0x?tJ,2r$HF1MM(B [@b{$B0x;R(B}, @b{$B=EJ#EY(B}]
Line 1302  the input polynomial by a constant.
Line 1329  the input polynomial by a constant.
 @end itemize  @end itemize
   
 @example  @example
   [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);  [99] asq(-x^4+6*x^3+(2*alg(0)-9)*x^2+(-6*alg(0))*x-2);
 [[-x^2+3*x+(#0),2]]  [[-x^2+3*x+(#0),2]]
 [100] af(-x^2+3*x+alg(0),[alg(0)]);  [100] af(-x^2+3*x+alg(0),[alg(0)]);
 [[x+(#0-1),1],[-x+(#0+2),1]]  [[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]]
 @end example  @end example
   
 @table @t  @table @t
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