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Diff for /OpenXM/src/asir-doc/parts/ff.texi between version 1.7 and 1.8

version 1.7, 2003/04/21 03:07:32 version 1.8, 2005/09/08 07:40:49
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/ff.texi,v 1.6 2003/04/20 08:01:25 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/ff.texi,v 1.7 2003/04/21 03:07:32 noro Exp $
 \BJP  \BJP
 @node $BM-8BBN$K4X$9$k1i;;(B,,, Top  @node $BM-8BBN$K4X$9$k1i;;(B,,, Top
 @chapter $BM-8BBN$K4X$9$k1i;;(B  @chapter $BM-8BBN$K4X$9$k1i;;(B
Line 346  one to obtain the affine coordinate.
Line 346  one to obtain the affine coordinate.
 @findex setmod_ff  @findex setmod_ff
   
 @table @t  @table @t
 @item setmod_ff([@var{prime}|@var{poly}])  @item setmod_ff([@var{p}|@var{defpoly2}])
 @itemx setmod_ff(@var{prime},@var{n}])  @itemx setmod_ff([@var{defpolyp},@var{p}])
   @itemx setmod_ff([@var{p},@var{n}])
 \JP :: $BM-8BBN$N@_Dj(B, $B@_Dj$5$l$F$$$kM-8BBN$NK!(B, $BDj5AB?9`<0$NI=<((B  \JP :: $BM-8BBN$N@_Dj(B, $B@_Dj$5$l$F$$$kM-8BBN$NK!(B, $BDj5AB?9`<0$NI=<((B
 \EG :: Sets/Gets the current base fields.  \EG :: Sets/Gets the current base fields.
 @end table  @end table
Line 356  one to obtain the affine coordinate.
Line 357  one to obtain the affine coordinate.
 @item return  @item return
 \JP $B?t$^$?$OB?9`<0(B  \JP $B?t$^$?$OB?9`<0(B
 \EG number or polynomial  \EG number or polynomial
 @item prime  @item p
 \JP $BAG?t(B  \JP $BAG?t(B
 \EG prime  \EG prime
 @item poly  @item defpoly2
 \JP GF(2) $B>e4{Ls$J(B 1 $BJQ?tB?9`<0(B  \JP GF(2) $B>e4{Ls$J(B 1 $BJQ?tB?9`<0(B
 \EG univariate polynomial irreducible over GF(2)  \EG univariate polynomial irreducible over GF(2)
   @item defpolyp
   \JP GF(@var{p}) $B>e4{Ls$J(B 1 $BJQ?tB?9`<0(B
   \EG univariate polynomial irreducible over GF(@var{p})
 @item n  @item n
 \JP $B3HBg<!?t(B  \JP $B3HBg<!?t(B
 \EG the extension degree  \EG the extension degree
Line 370  one to obtain the affine coordinate.
Line 374  one to obtain the affine coordinate.
 @itemize @bullet  @itemize @bullet
 \BJP  \BJP
 @item  @item
 $B0z?t$,@5@0?t(B @var{prime} $B$N;~(B, GF(@var{prime}) $B$r4pACBN$H$7$F@_Dj$9$k(B.  $B0z?t$,@5@0?t(B @var{p} $B$N;~(B, GF(@var{p}) $B$r4pACBN$H$7$F@_Dj$9$k(B.
 @item  @item
 $B0z?t$,B?9`<0(B @var{poly} $B$N;~(B,  $B0z?t$,B?9`<0(B @var{defpoly2} $B$N;~(B,
 GF(2^deg(@var{poly} mod 2)) = GF(2)[t]/(@var{poly}(t) mod 2)  GF(2^deg(@var{defpoly2} mod 2)) = GF(2)[t]/(@var{defpoly2}(t) mod 2)
 $B$r4pACBN$H$7$F@_Dj$9$k(B.  $B$r4pACBN$H$7$F@_Dj$9$k(B.
 @item  @item
   $B0z?t$,(B @var{defpolyp} $B$H(B @var{p} $B$N;~(B,
   GF(@var{p^deg(defpolyp)}) $B$r4pACBN$H$7$F@_Dj$9$k(B.
   @item
 $B0z?t$,(B @var{p} $B$H(B @var{n} $B$N;~(B,  $B0z?t$,(B @var{p} $B$H(B @var{n} $B$N;~(B,
 GF(@var{p^n}) $B$r4pACBN$H$7$F@_Dj$9$k(B. @var{p^n} $B$O(B @var{2^29} $BL$K~$G(B  GF(@var{p^n}) $B$r4pACBN$H$7$F@_Dj$9$k(B. @var{p^n} $B$O(B @var{2^29} $BL$K~$G(B
 $B$J$1$l$P$J$i$J$$(B. $B$^$?(B, @var{p} $B$,(B @var{2^14} $B0J>e$N$H$-(B,  $B$J$1$l$P$J$i$J$$(B. $B$^$?(B, @var{p} $B$,(B @var{2^14} $B0J>e$N$H$-(B,
 @var{n} $B$O(B 1 $B$G$J$1$l$P$J$i$J$$(B.  @var{n} $B$O(B 1 $B$G$J$1$l$P$J$i$J$$(B.
 @item  @item
 $BL50z?t$N;~(B, $B@_Dj$5$l$F$$$k4pACBN$,(B GF(@var{prime})$B$N>l9g(B @var{prime},  $BL50z?t$N;~(B, $B@_Dj$5$l$F$$$k4pACBN$,(B GF(@var{p})$B$N>l9g(B @var{p},
 GF(2^@var{n}) $B$N>l9gDj5AB?9`<0$rJV$9(B.  GF(2^@var{n}) $B$N>l9gDj5AB?9`<0$rJV$9(B.
 $B4pACBN$,(B GF(p^@var{n})  $B4pACBN$,(B @code{setmod_ff(@var{defpoly},@var{p})} $B$GDj5A$5$l$?(B
 (@var{p^n} $B$,(B @var{2^14} $BL$K~(B) $B$N>l9g(B,  GF(@var{p}^@var{n}) $B$N>l9g(B, [@var{defpoly},@var{p}] $B$rJV$9(B.
   $B4pACBN$,(B @code{setmod_ff(@var{p},@var{n})} $B$GDj5A$5$l$?(B
   GF(p^@var{n}) $B$N>l9g(B,
 [@var{p},@var{defpoly},@var{prim_elem}] $B$rJV$9(B. $B$3$3$G(B, @var{defpoly}  [@var{p},@var{defpoly},@var{prim_elem}] $B$rJV$9(B. $B$3$3$G(B, @var{defpoly}
 $B$O(B, @var{n} $B<!3HBg$NDj5AB?9`<0(B, @var{prim_elem} $B$O(B, GF(@var{p^n})  $B$O(B, @var{n} $B<!3HBg$NDj5AB?9`<0(B, @var{prim_elem} $B$O(B, GF(@var{p^n})$B$N(B
 $B>hK!72$N@8@.85$r0UL#$9$k(B.  $B>hK!72$N@8@.85$r0UL#$9$k(B.
 @item  @item
 GF(2^@var{n}) $B$NDj5AB?9`<0$O(B, GF(2) $B>e(B n $B<!4{Ls$J$i$J$s$G$bNI$$$,(B, $B8zN($K(B  GF(2^@var{n}) $B$NDj5AB?9`<0$O(B, GF(2) $B>e(B n $B<!4{Ls$J$i$J$s$G$bNI$$$,(B, $B8zN($K(B
Line 394  GF(2^@var{n}) $B$NDj5AB?9`<0$O(B, GF(2) $B>e(B n 
Line 403  GF(2^@var{n}) $B$NDj5AB?9`<0$O(B, GF(2) $B>e(B n 
 \E  \E
 \BEG  \BEG
 @item  @item
 If the argument is a non-negative integer @var{prime}, GF(@var{prime})  If the argument is a non-negative integer @var{p}, GF(@var{p})
 is set as the current base field.  is set as the current base field.
 @item  @item
 If the argument is a polynomial @var{poly},  If the argument is a polynomial @var{defpoly2},
 GF(2^deg(@var{poly} mod 2)) = GF(2)[t]/(@var{poly}(t) mod2)  GF(2^deg(@var{defpoly2} mod 2)) = GF(2)[t]/(@var{defpoly2}(t) mod2)
 is set as the current base field.  is set as the current base field.
 @item  @item
   If the arguments are a polynomial @var{defpolyp} and a prime @var{p},
   GF(@var{p}^deg(@var{defpolyp})) = GF(@var{p})[t]/(@var{defpolyp}(t))
   is set as the current base field.
   @item
 If the arguments are a prime @var{p} and an extension degree @var{n},  If the arguments are a prime @var{p} and an extension degree @var{n},
 GF(@var{p^n}) is set as the current base field. @var{p^n} must be  GF(@var{p^n}) is set as the current base field. @var{p^n} must be
 less than @var{2^29} and if @var{p} is greater than or equal to @var{2^14},  less than @var{2^29} and if @var{p} is greater than or equal to @var{2^14},
 then @var{n} must be equal to 1.  then @var{n} must be equal to 1.
 @item  @item
 If no argument is specified, the modulus indicating the current base field  If no argument is specified, the modulus indicating the current base field
 is returned. If the current base field is GF(@var{prime}), @var{prime} is  is returned. If the current base field is GF(@var{p}), @var{p} is
 returned. If it is GF(2^@var{n}), the defining polynomial is returned.  returned. If it is GF(2^@var{n}), the defining polynomial is returned.
 If it is GF(@var{p^n}), where @var{p^n} is less than @var{2^14},  If it is GF(@var{p^n}) defined by @code{setmod_ff(@var{defpoly},@var{p})},
   [@var{defpolyp},@var{p}] is returned.
   If it is GF(@var{p^n}) defined by @code{setmod_ff(@var{p},@var{n})},
 [@var{p},@var{defpoly},@var{prim_elem}] is returned. Here, @var{defpoly}  [@var{p},@var{defpoly},@var{prim_elem}] is returned. Here, @var{defpoly}
 is the defining polynomial of the @var{n}-th extension,  is the defining polynomial of the @var{n}-th extension,
 and @var{prim_elem} is the generator of the multiplicative group  and @var{prim_elem} is the generator of the multiplicative group
Line 428  x^100+x^15+1
Line 443  x^100+x^15+1
 x^100+x^15+1  x^100+x^15+1
 [176] setmod_ff();  [176] setmod_ff();
 x^100+x^15+1  x^100+x^15+1
 [177] setmod_ff(2,5);  [177] setmod_ff(x^4+x+1,547);
   [1*x^4+1*x+1,547]
   [178] setmod_ff(2,5);
 [2,x^5+x^2+1,x]  [2,x^5+x^2+1,x]
 @end example  @end example
   
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