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Diff for /OpenXM/src/asir-doc/parts/builtin/poly.texi between version 1.2 and 1.4

version 1.2, 1999/12/21 02:47:34 version 1.4, 2003/04/19 15:44:59
Line 1 
Line 1 
 @comment $OpenXM$  @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/poly.texi,v 1.3 2002/09/03 01:50:59 noro Exp $
 \BJP  \BJP
 @node $BB?9`<0$*$h$SM-M}<0$N1i;;(B,,, $BAH$_9~$_H!?t(B  @node $BB?9`<0$*$h$SM-M}<0$N1i;;(B,,, $BAH$_9~$_H!?t(B
 @section $BB?9`<0(B, $BM-M}<0$N1i;;(B  @section $BB?9`<0(B, $BM-M}<0$N1i;;(B
Line 63 
Line 63 
 \E  \E
 \BEG  \BEG
 @item  @item
 @xref{Types in Asir} for main variable.  See @ref{Types in Asir} for main variable.
 @item  @item
 Indeterminates (variables) are ordered by default as follows.  Indeterminates (variables) are ordered by default as follows.
   
Line 171  Lists variables according to the variable ordering.
Line 171  Lists variables according to the variable ordering.
 @code{strtov()} $B$rMQ$$$k(B.  @code{strtov()} $B$rMQ$$$k(B.
 @item  @item
 @code{uc()} $B$G@8@.$5$l$?ITDj85$NITDj85$H$7$F$N7?(B (@code{vtype}) $B$O(B 1 $B$G$"$k(B.  @code{uc()} $B$G@8@.$5$l$?ITDj85$NITDj85$H$7$F$N7?(B (@code{vtype}) $B$O(B 1 $B$G$"$k(B.
 (@xref{$BITDj85$N7?(B})  (@xref{$BITDj85$N7?(B}.)
 \E  \E
 \BEG  \BEG
 @item  @item
Line 363  Variable @var{var} must be specified.
Line 363  Variable @var{var} must be specified.
 @item  @item
 $BM-M}<0$N>l9g$O(B, $BJ,;R$HJ,Jl$N9`?t$NOB$,JV$5$l$k(B.  $BM-M}<0$N>l9g$O(B, $BJ,;R$HJ,Jl$N9`?t$NOB$,JV$5$l$k(B.
 @item  @item
 $BH!?t7A<0(B (@xref{$BITDj85$N7?(B}) $B$O(B, $B0z?t$,2?$G$"$C$F$bC19`$H$_$J$5$l$k(B. (1 $B8D$NITDj85$HF1$8(B. )  $BH!?t7A<0(B (@ref{$BITDj85$N7?(B}) $B$O(B, $B0z?t$,2?$G$"$C$F$bC19`$H$_$J$5$l$k(B. (1 $B8D$NITDj85$HF1$8(B. )
 \E  \E
 \BEG  \BEG
 @item  @item
Line 740  x^5+2*x^4+x^3+x^2+2*x+1
Line 740  x^5+2*x^4+x^3+x^2+2*x+1
 @item psubst(@var{rat}[,@var{var},@var{rat}]*)  @item psubst(@var{rat}[,@var{var},@var{rat}]*)
 \BJP  \BJP
 :: @var{rat} $B$N(B @var{varn} $B$K(B @var{ratn} $B$rBeF~(B  :: @var{rat} $B$N(B @var{varn} $B$K(B @var{ratn} $B$rBeF~(B
 (@var{n=1,2},... $B$G:8$+$i1&$K=g<!BeF~$9$k(B).  (@var{n}=1,2,... $B$G:8$+$i1&$K=g<!BeF~$9$k(B).
 \E  \E
 \BEG  \BEG
 :: Substitute @var{ratn} for @var{varn} in expression @var{rat}.  :: Substitute @var{ratn} for @var{varn} in expression @var{rat}.
 (@var{n=1,2},@dots{}.  (@var{n}=1,2,@dots{}.
 Substitution will be done successively from left to right  Substitution will be done successively from left to right
 if arguments are repeated.)  if arguments are repeated.)
 \E  \E
Line 754  if arguments are repeated.)
Line 754  if arguments are repeated.)
 @item return  @item return
 \JP $BM-M}<0(B  \JP $BM-M}<0(B
 \EG rational expression  \EG rational expression
 @item rat,ratn  @item rat ratn
 \JP $BM-M}<0(B  \JP $BM-M}<0(B
 \EG rational expression  \EG rational expression
 @item varn  @item varn
Line 913  sin(x)
Line 913  sin(x)
 @item var  @item var
 \JP $BITDj85(B  \JP $BITDj85(B
 \EG indeterminate  \EG indeterminate
 @item poly1,poly2  @item poly1 poly2
 \JP $BB?9`<0(B  \JP $BB?9`<0(B
 \EG polynomial  \EG polynomial
 @item mod  @item mod
Line 1060  multiples of @var{hint}.
Line 1060  multiples of @var{hint}.
 $B3F4{Ls0x;R$N<!?t$,(B @var{hint} $B$NG\?t$G$"$k$3$H$,$o$+$C$F$$$k>l9g$K(B  $B3F4{Ls0x;R$N<!?t$,(B @var{hint} $B$NG\?t$G$"$k$3$H$,$o$+$C$F$$$k>l9g$K(B
 @var{poly} $B$N4{Ls0x;RJ,2r$r(B @code{fctr()} $B$h$j8zN(NI$/9T$&(B.  @var{poly} $B$N4{Ls0x;RJ,2r$r(B @code{fctr()} $B$h$j8zN(NI$/9T$&(B.
 @var{poly} $B$,(B, @var{d} $B<!$N3HBgBN>e$K$*$1$k(B  @var{poly} $B$,(B, @var{d} $B<!$N3HBgBN>e$K$*$1$k(B
 $B$"$kB?9`<0$N%N%k%`(B (@xref{$BBe?tE*?t$K4X$9$k1i;;(B}) $B$GL5J?J}$G$"$k>l9g(B,  $B$"$kB?9`<0$N%N%k%`(B (@ref{$BBe?tE*?t$K4X$9$k1i;;(B}) $B$GL5J?J}$G$"$k>l9g(B,
 $B3F4{Ls0x;R$N<!?t$O(B @var{d} $B$NG\?t$H$J$k(B. $B$3$N$h$&$J>l9g$K(B  $B3F4{Ls0x;R$N<!?t$O(B @var{d} $B$NG\?t$H$J$k(B. $B$3$N$h$&$J>l9g$K(B
 $BMQ$$$i$l$k(B.  $BMQ$$$i$l$k(B.
 \E  \E
Line 1073  more efficiently by the knowledge than @code{fctr()}.
Line 1073  more efficiently by the knowledge than @code{fctr()}.
 When @var{hint} is 1, @code{ufctrhint()} is the same as @code{fctr()} for  When @var{hint} is 1, @code{ufctrhint()} is the same as @code{fctr()} for
 uni-variate polynomials.  uni-variate polynomials.
 An typical application where @code{ufctrhint()} is effective:  An typical application where @code{ufctrhint()} is effective:
 Consider the case where @var{poly} is a norm (@xref{Algebraic numbers})  Consider the case where @var{poly} is a norm (@ref{Algebraic numbers})
 of a certain polynomial over an extension field with its extension  of a certain polynomial over an extension field with its extension
 degree @var{d}, and it is square free;  Then, every irreducible factor  degree @var{d}, and it is square free;  Then, every irreducible factor
 has a degree that is a multiple of @var{d}.  has a degree that is a multiple of @var{d}.
Line 1329  y-z
Line 1329  y-z
 @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
 @item mod  @item mod
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