version 1.5, 2000/01/26 01:37:33 |
version 1.9, 2002/09/03 01:50:58 |
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@comment $OpenXM: OpenXM/src/asir-doc/parts/type.texi,v 1.4 2000/01/20 03:00:34 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/type.texi,v 1.8 2001/03/12 05:01:18 noro Exp $ |
\BJP |
\BJP |
@node $B7?(B,,, Top |
@node $B7?(B,,, Top |
@chapter $B7?(B |
@chapter $B7?(B |
Line 83 x afo (2.3*x+y)^10 |
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Line 83 x afo (2.3*x+y)^10 |
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\BJP |
\BJP |
$BB?9`<0$O(B, $BA4$FE83+$5$l(B, $B$=$N;~E@$K$*$1$kJQ?t=g=x$K=>$C$F(B, $B:F5"E*$K(B |
$BB?9`<0$O(B, $BA4$FE83+$5$l(B, $B$=$N;~E@$K$*$1$kJQ?t=g=x$K=>$C$F(B, $B:F5"E*$K(B |
1 $BJQ?tB?9`<0$H$7$F9_QQ$N=g$K@0M}$5$l$k(B (@xref{$BJ,;6I=8=B?9`<0(B}). |
1 $BJQ?tB?9`<0$H$7$F9_QQ$N=g$K@0M}$5$l$k(B. (@xref{$BJ,;6I=8=B?9`<0(B}.) |
$B$3$N;~(B, $B$=$NB?9`<0$K8=$l$k=g=x:GBg$NJQ?t$r(B @b{$B<gJQ?t(B} $B$H8F$V(B. |
$B$3$N;~(B, $B$=$NB?9`<0$K8=$l$k=g=x:GBg$NJQ?t$r(B @b{$B<gJQ?t(B} $B$H8F$V(B. |
\E |
\E |
\BEG |
\BEG |
Every polynomial is maintained internally in its full expanded form, |
Every polynomial is maintained internally in its full expanded form, |
represented as a nested univariate polynomial, according to the current |
represented as a nested univariate polynomial, according to the current |
variable ordering, arranged by the descending order of exponents. |
variable ordering, arranged by the descending order of exponents. |
(@xref{Distributed polynomial}). |
(@xref{Distributed polynomial}.) |
In the representation, the indeterminate (or variable), appearing in |
In the representation, the indeterminate (or variable), appearing in |
the polynomial, with maximum ordering is called the @b{main variable}. |
the polynomial, with maximum ordering is called the @b{main variable}. |
Moreover, we call the coefficient of the maximum degree term of |
Moreover, we call the coefficient of the maximum degree term of |
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newstruct(afo) |
newstruct(afo) |
@end example |
@end example |
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\JP $B9=B$BN$K4X$7$F$O(B, $B>O$r2~$a$F2r@b$9$kM=Dj$G$"$k(B. |
\BJP |
\EG For type @b{structure}, we shall describe it in a later chapter. |
Asir $B$K$*$1$k9=B$BN$O(B, C $B$K$*$1$k9=B$BN$r4J0W2=$7$?$b$N$G$"$k(B. |
(Not written yet.) |
$B8GDjD9G[Ns$N3F@.J,$rL>A0$G%"%/%;%9$G$-$k%*%V%8%'%/%H$G(B, |
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$B9=B$BNDj5AKh$KL>A0$r$D$1$k(B. |
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\E |
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\BEG |
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The type @b{structure} is a simplified version of that in C language. |
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It is defined as a fixed length array and each entry of the array |
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is accessed by its name. A name is associated with each structure. |
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\E |
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\JP @item 9 @b{$BJ,;6I=8=B?9`<0(B} |
\JP @item 9 @b{$BJ,;6I=8=B?9`<0(B} |
\EG @item 9 @b{distributed polynomial} |
\EG @item 9 @b{distributed polynomial} |
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Line 347 This is used for basis conversion in finite fields of |
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Line 355 This is used for basis conversion in finite fields of |
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\JP quantifier elimination $B$GMQ$$$i$l$k0l3,=R8lO@M}<0(B. |
\JP quantifier elimination $B$GMQ$$$i$l$k0l3,=R8lO@M}<0(B. |
\EG This expresses a first order formula used in quantifier elimination. |
\EG This expresses a first order formula used in quantifier elimination. |
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@item 15 @b{matrix over GF(p)} |
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@* |
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\JP $B>.I8?tM-8BBN>e$N9TNs(B. |
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\EG A matrix over a small finite field. |
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@item 16 @b{byte array} |
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@* |
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\JP $BId9f$J$7(B byte $B$NG[Ns(B |
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\EG An array of unsigned bytes. |
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\JP @item -1 @b{VOID $B%*%V%8%'%/%H(B} |
\JP @item -1 @b{VOID $B%*%V%8%'%/%H(B} |
\EG @item -1 @b{VOID object} |
\EG @item -1 @b{VOID object} |
@* |
@* |
Line 474 not guarantee the accuracy of the result, |
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Line 492 not guarantee the accuracy of the result, |
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but it indicates the representation size of numbers with which internal |
but it indicates the representation size of numbers with which internal |
operations of @b{PARI} are performed. |
operations of @b{PARI} are performed. |
\E |
\E |
(@ref{eval}, @xref{pari}) |
(@xref{eval deval}, @ref{pari}.) |
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@item 4 |
@item 4 |
\JP @b{$BJ#AG?t(B} |
\JP @b{$BJ#AG?t(B} |