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Diff for /OpenXM/src/asir-doc/parts/ff.texi between version 1.5 and 1.7

-version 1.5, 2003/04/19 15:44:56
+version 1.7, 2003/04/21 03:07:32
 Line 1
 Line 1
 Line 1
- @comment $OpenXM: OpenXM/src/asir-doc/parts/ff.texi,v 1.4 2003/04/19 10:36:30 noro Exp $
+ @comment $OpenXM: OpenXM/src/asir-doc/parts/ff.texi,v 1.6 2003/04/20 08:01:25 noro Exp $
  \BJP
  @node $BM-8BBN$K4X$9$k1i;;(B,,, Top
  @chapter $BM-8BBN$K4X$9$k1i;;(B
 Line 332  one to obtain the affine coordinate.
 Line 332  one to obtain the affine coordinate.
 Line 332  one to obtain the affine coordinate.
  * gf2ntop::
  * ptosfp sfptop::
  * defpoly_mod2::
+ * sffctr::
  * fctr_ff::
  * irredcheck_ff::
  * randpoly_ff::
-Line 828  whose value is @var{r}.
+Line 829  whose value is @var{r}.
 Line 828  whose value is @var{r}.
 Line 829  whose value is @var{r}.
  [2] setmod_ff(547);
  [3] F=simp_ff((x-1)^10);
-*x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+427*x^3+45*x^2+537*x+1
+*x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+427*x^3
+ +45*x^2+537*x+1
  [4] lmptop(F);
- x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+427*x^3+45*x^2+537*x+1
+ x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+427*x^3
+ +45*x^2+537*x+1
  [5] lmptop(coef(F,1));
  [6] ntype(@@@@);
-Line 878  x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+42
+Line 881  x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+42
 Line 878  x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+42
 Line 881  x^10+537*x^9+45*x^8+427*x^7+210*x^6+295*x^5+210*x^4+42
  Let @var{m} be a non-negative integer.
  @var{m} has the binary representation
  @var{m}=@var{m0}+@var{m1}*2+...+@var{mk}*2^k.
- This function returns an element of  GF(2^@var{n})=GF(2)[t]/(g(t)),
+ This function returns an element of  GF(2^@var{n}) = GF(2)[t]/(g(t)),
  @var{m0}+@var{m1}*t+...+@var{mk}*t^k mod g(t).
  @item
  Apply @code{simp_ff()} to reduce the result.
-Line 1186  Then fix @var{m3} as small as possible.
+Line 1189  Then fix @var{m3} as small as possible.
 Line 1186  Then fix @var{m3} as small as possible.
 Line 1189  Then fix @var{m3} as small as possible.
  \JP @item $B;2>H(B
  \EG @item References
  @fref{setmod_ff}
+ @end table
+ \JP @node sffctr,,, $BM-8BBN$K4X$9$kH!?t$N$^$H$a(B
+ \EG @node sffctr,,, Functions for Finite fields
+ @subsection @code{sffctr}
+ @findex sffctr
+ @table @t
+ @item sffctr(@var{poly})
+ \JP :: $BB?9`<0$N>.I8?tM-8BBN>e$G$N4{LsJ,2r(B
+ \EG :: Irreducible factorization over a small finite field.
+ @end table
+ @table @var
+ @item return
+ \JP $B%j%9%H(B
+ \EG list
+ @item poly
+ \JP $BM-8BBN>e$N(B $BB?9`<0(B
+ \EG polynomial over a finite field
+ @end table
+ @itemize @bullet
+ \BJP
+ @item
+ $BB?9`<0$r(B, $B8=:_@_Dj$5$l$F$$$k>.I8?tM-8BBN>e$G4{LsJ,2r$9$k(B.
+ @item
+ $B7k2L$O(B, [[@var{f1},@var{m1}],[@var{f2},@var{m2}],...] $B$J$k(B
+ $B%j%9%H$G$"$k(B. $B$3$3$G(B, @var{fi} $B$O(B monic $B$J4{Ls0x;R(B, @var{mi} $B$O$=$N(B
+ $B=EJ#EY$G$"$k(B.
+ \E
+ \BEG
+ @item
+ Factorize @var{poly} into irreducible factors over
+ a small finite field currently set.
+ @item
+ The result is a list [[@var{f1},@var{m1}],[@var{f2},@var{m2}],...],
+ where @var{fi} is a monic irreducible factor and @var{mi} is its
+ multiplicity.
+ \E
+ @end itemize
+ @example
+ [0] setmod_ff(2,10);
+ [2,x^10+x^3+1,x]
+ [1] sffctr((z*y^3+z*y)*x^3+(y^5+y^3+z*y^2+z)*x^2+z^11*y*x+z^10*y^3+z^11);
+ [[@@_0,1],[@@_0*z*y*x+@@_0*y^3+@@_0*z,1],[(@@_0*y+@@_0)*x+@@_0*z^5,2]]
+ @end example
+ @table @t
+ \JP @item $B;2>H(B
+ \EG @item References
+ @fref{setmod_ff},
+ @fref{modfctr}
  @end table
  \JP @node fctr_ff,,, $BM-8BBN$K4X$9$kH!?t$N$^$H$a(B

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