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Diff for /OpenXM/src/asir-doc/parts/builtin/poly.texi between version 1.6 and 1.8

version 1.6, 2003/11/27 15:56:08 version 1.8, 2004/05/15 08:25:12
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 @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/poly.texi,v 1.5 2003/04/20 08:01:29 noro Exp $  @comment $OpenXM: OpenXM/src/asir-doc/parts/builtin/poly.texi,v 1.7 2003/12/23 10:41:10 ohara 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
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 * %::  * %::
 * subst psubst::  * subst psubst::
 * diff::  * diff::
   * ediff::
 * res::  * res::
 * fctr sqfr::  * fctr sqfr::
 * modfctr::  * modfctr::
Line 903  from left to right.
Line 904  from left to right.
 sin(x)  sin(x)
 @end example  @end example
   
   \JP @node ediff,,, $BB?9`<0$*$h$SM-M}<0$N1i;;(B
   \EG @node ediff,,, Polynomials and rational expressions
   @subsection @code{ediff}
   @findex ediff
   
   @table @t
   @item ediff(@var{poly}[,@var{varn}]*)
   @item ediff(@var{poly},@var{varlist})
   \JP :: @var{poly} $B$r(B @var{varn} $B$"$k$$$O(B @var{varlist} $B$NCf$NJQ?t$G=g<!%*%$%i!<HyJ,$9$k(B.
   \BEG
   :: Differentiate @var{poly} successively by Euler operators of @var{var}'s for the first
   form, or by Euler operators of variables in @var{varlist} for the second form.
   \E
   @end table
   
   @table @var
   @item return
   \JP $BB?9`<0(B
   \EG polynomial
   @item poly
   \JP $BB?9`<0(B
   \EG polynomial
   @item varn
   \JP $BITDj85(B
   \EG indeterminate
   @item varlist
   \JP $BITDj85$N%j%9%H(B
   \EG list of indeterminates
   @end table
   
   @itemize @bullet
   \BJP
   @item
   $B:8B&$NITDj85$h$j(B, $B=g$K%*%$%i!<HyJ,$7$F$$$/(B. $B$D$^$j(B, @t{ediff}(@var{poly},@t{x,y}) $B$O(B,
   @t{ediff}(@t{ediff}(@var{poly},@t{x}),@t{y}) $B$HF1$8$G$"$k(B.
   \E
   \BEG
   @item
   differentiation is performed by the specified indeterminates (variables)
   from left to right.
   @t{ediff}(@var{poly},@t{x,y}) is the same as
   @t{ediff}(@t{ediff}(@var{poly},@t{x}),@t{y}).
   \E
   @end itemize
   
   @example
   [0] ediff((x+2*y)^2,x);
   2*x^2+4*y*x
   [1] ediff((x+2*y)^2,x,y);
   4*y*x
   @end example
   
 \JP @node res,,, $BB?9`<0$*$h$SM-M}<0$N1i;;(B  \JP @node res,,, $BB?9`<0$*$h$SM-M}<0$N1i;;(B
 \EG @node res,,, Polynomials and rational expressions  \EG @node res,,, Polynomials and rational expressions
 @subsection @code{res}  @subsection @code{res}
Line 1240  an integral polynomial such that GCD of all its coeffi
Line 1293  an integral polynomial such that GCD of all its coeffi
 $BJ,;RB?9`<0$N78?t$OM-M}?t$N$^$^$G$"$j(B, $BM-M}<0$NJ,;R$r5a$a$k(B  $BJ,;RB?9`<0$N78?t$OM-M}?t$N$^$^$G$"$j(B, $BM-M}<0$NJ,;R$r5a$a$k(B
 @code{nm()} $B$G$O(B, $BJ,?t78?tB?9`<0$O(B, $BJ,?t78?t$N$^$^$N7A$G=PNO$5$l$k$?$a(B,  @code{nm()} $B$G$O(B, $BJ,?t78?tB?9`<0$O(B, $BJ,?t78?t$N$^$^$N7A$G=PNO$5$l$k$?$a(B,
 $BD>$A$K@0?t78?tB?9`<0$rF@$k;v$O=PMh$J$$(B.  $BD>$A$K@0?t78?tB?9`<0$rF@$k;v$O=PMh$J$$(B.
   @item $B%*%W%7%g%s(B factor $B$,@_Dj$5$l$?>l9g$NLa$jCM$O%j%9%H(B [g,c] $B$G$"$k(B.
   $B$3$3$G(B c $B$OM-M}?t$G$"$j(B, g $B$,%*%W%7%g%s$N$J$$>l9g$NLa$jCM$G$"$j(B,
    @var{poly} = c*g $B$H$J$k(B.
 \E  \E
 \BEG  \BEG
 @item  @item
Line 1257  You cannot obtain an integral polynomial by direct use
Line 1313  You cannot obtain an integral polynomial by direct use
 @code{nm()}.  The function @code{nm()} returns the numerator of its  @code{nm()}.  The function @code{nm()} returns the numerator of its
 argument, and a polynomial with rational coefficients is  argument, and a polynomial with rational coefficients is
 the numerator of itself and will be returned as it is.  the numerator of itself and will be returned as it is.
   @item When the option factor is set, the return value is a list [g,c].
   Here, c is a rational number, g is an integral polynomial
   and @var{poly} = c*g holds.
 \E  \E
 @end itemize  @end itemize
   
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