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Diff for /OpenXM/src/asir-doc/parts/algnum.texi between version 1.6 and 1.7

version 1.6, 2003/04/19 15:44:55 version 1.7, 2003/04/20 08:01:24
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/algnum.texi,v 1.5 2000/09/23 07:53:24 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/algnum.texi,v 1.6 2003/04/19 15:44:55 noro Exp $
 \BJP  \BJP
 @node 代数的数に関する演算,,, Top  @node 代数的数に関する演算,,, Top
 @chapter 代数的数に関する演算  @chapter 代数的数に関する演算
Line 410  into the @b{root} by @code{rattoalgp()} function.
Line 410  into the @b{root} by @code{rattoalgp()} function.
   
 @example  @example
 [88] rattoalgp(S,[alg(0)]);  [88] rattoalgp(S,[alg(0)]);
 (((#0+2)/(#0+2))*t#1^2+((#0^2+2*#0)/(#0+2))*t#1+((2*#0^2+4*#0)/(#0+2)))*x  (((#0+2)/(#0+2))*t#1^2+((#0^2+2*#0)/(#0+2))*t#1
 +((1)/(#0+2))*t#1+((1)/(#0+2))  +((2*#0^2+4*#0)/(#0+2)))*x+((1)/(#0+2))*t#1+((1)/(#0+2))
 [89] rattoalgp(S,[alg(0),alg(1)]);  [89] rattoalgp(S,[alg(0),alg(1)]);
 (((#0^3+6*#0^2+12*#0+8)*#1^2+(#0^4+6*#0^3+12*#0^2+8*#0)*#1+2*#0^4+12*#0^3  (((#0^3+6*#0^2+12*#0+8)*#1^2+(#0^4+6*#0^3+12*#0^2+8*#0)*#1
 +24*#0^2+16*#0)/(#0^3+6*#0^2+12*#0+8))*x+(((#0+2)*#1+#0+2)/(#0^2+4*#0+4))  +2*#0^4+12*#0^3+24*#0^2+16*#0)/(#0^3+6*#0^2+12*#0+8))*x
   +(((#0+2)*#1+#0+2)/(#0^2+4*#0+4))
 [90] rattoalgp(S,[alg(1),alg(0)]);  [90] rattoalgp(S,[alg(1),alg(0)]);
 (((#0+2)*#1^2+(#0^2+2*#0)*#1+2*#0^2+4*#0)/(#0+2))*x+((#1+1)/(#0+2))  (((#0+2)*#1^2+(#0^2+2*#0)*#1+2*#0^2+4*#0)/(#0+2))*x
   +((#1+1)/(#0+2))
 [91] simpalg(@@89);  [91] simpalg(@@89);
 (#1^2+#0*#1+2*#0)*x+((-1/5*#0+2/5)*#1-1/5*#0+2/5)  (#1^2+#0*#1+2*#0)*x+((-1/5*#0+2/5)*#1-1/5*#0+2/5)
 [92] simpalg(@@90);  [92] simpalg(@@90);
Line 499  where the ground field is a multiple extension.
Line 501  where the ground field is a multiple extension.
 (#0)  (#0)
 [64] B=newalg(75*s^2+(10*A^7-175*A^4-470*A)*s+3*A^8-45*A^5-261*A^2);  [64] B=newalg(75*s^2+(10*A^7-175*A^4-470*A)*s+3*A^8-45*A^5-261*A^2);
 (#1)  (#1)
 [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
 +13*A^8-220*A^5-581*A^2)$  +(75*B^2+(10*A^7-175*A^4-395*A)*B+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);  [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)
Line 531  The function to do this factorization is @code{asq()}.
Line 533  The function to do this factorization is @code{asq()}.
 [116] A=newalg(x^2+x+1);  [116] A=newalg(x^2+x+1);
 (#4)  (#4)
 [117] T=simpalg((x+A+1)*(x^2-2*A-3)^2*(x^3-x-A)^2);  [117] T=simpalg((x+A+1)*(x^2-2*A-3)^2*(x^3-x-A)^2);
 x^11+(#4+1)*x^10+(-4*#4-8)*x^9+(-10*#4-4)*x^8+(16*#4+20)*x^7+(24*#4-6)*x^6  x^11+(#4+1)*x^10+(-4*#4-8)*x^9+(-10*#4-4)*x^8+(16*#4+20)*x^7
 +(-29*#4-31)*x^5+(-15*#4+28)*x^4+(38*#4+29)*x^3+(#4-23)*x^2+(-21*#4-7)*x  +(24*#4-6)*x^6+(-29*#4-31)*x^5+(-15*#4+28)*x^4+(38*#4+29)*x^3
 +(3*#4+8)  +(#4-23)*x^2+(-21*#4-7)*x+(3*#4+8)
 [118] asq(T);  [118] asq(T);
 [[x^5+(-2*#4-4)*x^3+(-#4)*x^2+(2*#4+3)*x+(#4-2),2],[x+(#4+1),1]]  [[x^5+(-2*#4-4)*x^3+(-#4)*x^2+(2*#4+3)*x+(#4-2),2],[x+(#4+1),1]]
 @end example  @end example
Line 641  The function is @code{sp()}.
Line 643  The function is @code{sp()}.
   
 @example  @example
 [103] sp(x^5-2);  [103] sp(x^5-2);
 [[x+(-#1),2*x+(#0^3*#1^3+#0^4*#1^2+2*#1+2*#0),2*x+(-#0^4*#1^2),2*x  [[x+(-#1),2*x+(#0^3*#1^3+#0^4*#1^2+2*#1+2*#0),2*x+(-#0^4*#1^2),
 +(-#0^3*#1^3),x+(-#0)],[[(#1),t#1^4+t#0*t#1^3+t#0^2*t#1^2+t#0^3*t#1+t#0^4],  2*x+(-#0^3*#1^3),x+(-#0)],
 [(#0),t#0^5-2]]]  [[(#1),t#1^4+t#0*t#1^3+t#0^2*t#1^2+t#0^3*t#1+t#0^4],[(#0),t#0^5-2]]]
 @end example  @end example
   
 @noindent  @noindent
Line 1405  is a list containing only integral polynomials.
Line 1407  is a list containing only integral polynomials.
 \E  \E
 \BEG  \BEG
 The splitting field is represented as a list of pairs of form  The splitting field is represented as a list of pairs of form
 @code{[root,algptorat(defpoly(root))]}.  @code{[root,} @code{algptorat(defpoly(root))]}.
 In more detail, the list is interpreted as a representation  In more detail, the list is interpreted as a representation
 of successive extension obtained by adjoining @b{root}'s  of successive extension obtained by adjoining @b{root}'s
 to the rational number field.  Adjoining is performed from the right  to the rational number field.  Adjoining is performed from the right
Line 1432  the builtin function @code{res()} is always used.
Line 1434  the builtin function @code{res()} is always used.
   
 @example  @example
 [101] L=sp(x^9-54);  [101] L=sp(x^9-54);
 [[x+(-#2),-54*x+(#1^6*#2^4),54*x+(#1^6*#2^4+54*#2),54*x+(-#1^8*#2^2),  [[x+(-#2),-54*x+(#1^6*#2^4),54*x+(#1^6*#2^4+54*#2),
 -54*x+(#1^5*#2^5),54*x+(#1^5*#2^5+#1^8*#2^2),-54*x+(-#1^7*#2^3-54*#1),  54*x+(-#1^8*#2^2),-54*x+(#1^5*#2^5),54*x+(#1^5*#2^5+#1^8*#2^2),
 54*x+(-#1^7*#2^3),x+(-#1)],[[(#2),t#2^6+t#1^3*t#2^3+t#1^6],[(#1),t#1^9-54]]]  -54*x+(-#1^7*#2^3-54*#1),54*x+(-#1^7*#2^3),x+(-#1)],
   [[(#2),t#2^6+t#1^3*t#2^3+t#1^6],[(#1),t#1^9-54]]]
 [102] for(I=0,M=1;I<9;I++)M*=L[0][I];  [102] for(I=0,M=1;I<9;I++)M*=L[0][I];
 [111] M=simpalg(M);  [111] M=simpalg(M);
 -1338925209984*x^9+72301961339136  -1338925209984*x^9+72301961339136
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