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Diff for /OpenXM/src/asir-doc/parts/algnum.texi between version 1.2 and 1.3

version 1.2, 1999/12/21 02:47:30 version 1.3, 2000/03/10 07:18:40
Line 1 
Line 1 
 @comment $OpenXM$  @comment $OpenXM: OpenXM/src/asir-doc/parts/algnum.texi,v 1.2 1999/12/21 02:47:30 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 502  where the ground field is a multiple extension.
Line 502  where the ground field is a multiple extension.
 [65] P1=75*x^2+(150*B+10*A^7-175*A^4-395*A)*x+(75*B^2+(10*A^7-175*A^4-395*A)*B  [65] P1=75*x^2+(150*B+10*A^7-175*A^4-395*A)*x+(75*B^2+(10*A^7-175*A^4-395*A)*B
 +13*A^8-220*A^5-581*A^2)$  +13*A^8-220*A^5-581*A^2)$
 [66] P2=x^2+A*x+A^2$  [66] P2=x^2+A*x+A^2$
 [67] cr_gcda(P1,P2,[B,A]);  [67] cr_gcda(P1,P2);
 27*x+((#0^6-19*#0^3-65)*#1-#0^7+19*#0^4+38*#0)  27*x+((#0^6-19*#0^3-65)*#1-#0^7+19*#0^4+38*#0)
 @end example  @end example
   
Line 1074  substitutes a @b{root} for the associated indeterminat
Line 1074  substitutes a @b{root} for the associated indeterminat
 @findex cr_gcda  @findex cr_gcda
   
 @table @t  @table @t
 @item cr_gcda(@var{poly1},@var{poly2},@var{alist})  @item cr_gcda(@var{poly1},@var{poly2})
 \JP :: $BBe?tBN>e$N(B 1 $BJQ?tB?9`<0$N(B GCD  \JP :: $BBe?tBN>e$N(B 1 $BJQ?tB?9`<0$N(B GCD
 \EG :: GCD of two uni-variate polynomials over an algebraic number field.  \EG :: GCD of two uni-variate polynomials over an algebraic number field.
 @end table  @end table
Line 1086  substitutes a @b{root} for the associated indeterminat
Line 1086  substitutes a @b{root} for the associated indeterminat
 @item poly1, poly2  @item poly1, poly2
 \JP $BB?9`<0(B  \JP $BB?9`<0(B
 \EG polynomial  \EG polynomial
 @item alist  
 \JP $B%j%9%H(B  
 \EG list  
 @end table  @end table
   
 @itemize @bullet  @itemize @bullet
Line 1098  substitutes a @b{root} for the associated indeterminat
Line 1095  substitutes a @b{root} for the associated indeterminat
 @item  @item
 \JP 2 $B$D$N(B 1 $BJQ?tB?9`<0$N(B GCD $B$r5a$a$k(B.  \JP 2 $B$D$N(B 1 $BJQ?tB?9`<0$N(B GCD $B$r5a$a$k(B.
 \EG Finds the GCD of two uni-variate polynomials.  \EG Finds the GCD of two uni-variate polynomials.
 @item  
 \BJP  
 @var{alist} $B$OF~NO$K8=$l$k(B @code{root} $B$*$h$S(B, $B$=$l$i$NDj5A$K4^$^$l$k(B  
 @code{root} $B$r:F5"E*$K<h$j=P$7$FJB$Y$?%j%9%H(B. @var{a} $B$,(B @var{b} $B$N(B  
 $BDj5A$K4^$^$l$F$$$k>l9g(B, @var{a} $B$O(B @var{b} $B$h$j8e(B ($B1&(B) $B$KJB$P$J$1$l$P(B  
 $B$J$i$J$$(B.  
 \E  
 \BEG  
 @var{alist} is a list of @b{root}'s.  
 All the @b{root}'s appearing in the input and those required to define  
 the @b{root}'s in the list  must appear in the list. In the list  
 ,if the defining polynomial of @var{a} contains @var{b}  
 then @var{a} must come first.  
 \E  
 @end itemize  @end itemize
   
 @example  @example
Line 1119  then @var{a} must come first.
Line 1102  then @var{a} must come first.
 [77] Y=x^6+6*x^5+24*x^4+8*x^3-48*x^2+384*x+1024$  [77] Y=x^6+6*x^5+24*x^4+8*x^3-48*x^2+384*x+1024$
 [78] A=newalg(X);  [78] A=newalg(X);
 (#0)  (#0)
 [79] cr_gcda(X,subst(Y,x,x+A),[A]);  [79] cr_gcda(X,subst(Y,x,x+A));
 x+(-#0)  x+(-#0)
 @end example  @end example
   
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