version 1.12, 2003/04/20 08:01:27 |
version 1.13, 2007/02/15 02:41:38 |
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@comment $OpenXM: OpenXM/src/asir-doc/parts/type.texi,v 1.11 2003/04/19 15:44:57 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/type.texi,v 1.12 2003/04/20 08:01:27 noro Exp $ |
\BJP |
\BJP |
@node $B7?(B,,, Top |
@node $B7?(B,,, Top |
@chapter $B7?(B |
@chapter $B7?(B |
Line 667 GF(@var{p^n}) $B$N>hK!72$N@8@.85$r8GDj$9$k$3$H(B |
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Line 667 GF(@var{p^n}) $B$N>hK!72$N@8@.85$r8GDj$9$k$3$H(B |
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\BEG |
\BEG |
A finite field of order @var{p^n}, where @var{p^n} must be less than |
A finite field of order @var{p^n}, where @var{p^n} must be less than |
@var{2^29} and @var{n} must be equal to 1 if @var{p} is greater or |
@var{2^29} and @var{n} must be equal to 1 if @var{p} is greater or |
equal to @var{2^14}@, |
equal to @var{2^14}, |
is set by @code{setmod_ff} |
is set by @code{setmod_ff} |
by specifying its characteristic @var{p} the extension degree |
by specifying its characteristic @var{p} the extension degree |
@var{n}. If @var{p} is less than @var{2^14}, each non-zero element |
@var{n}. If @var{p} is less than @var{2^14}, each non-zero element |
Line 679 This specification is useful for treating both cases i |
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Line 679 This specification is useful for treating both cases i |
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program. |
program. |
\E |
\E |
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@item 10 |
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\JP @b{$B0L?t(B @var{p^n} $B$N>.0L?tM-8BBN$NBe?t3HBg$N85(B} |
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\EG @b{element of a finite field which is an algebraic extension of a small finite field of characteristic @var{p^n}} |
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\BJP |
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$BA09`$N(B, $B0L?t$,(B @var{p^n} $B$N>.0L?tM-8BBN$N(B @var{m} $B<!3HBg$N85$G$"$k(B. |
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$BI8?t(B @var{p} $B$*$h$S3HBg<!?t(B @var{n}, @var{m} |
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$B$r(B @code{setmod_ff} $B$K$h$j;XDj$9$k$3$H$K$h$j@_Dj$9$k(B. $B4pACBN>e$N(B @var{m} |
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$B<!4{LsB?9`<0$,<+F0@8@.$5$l(B, $B$=$NBe?t3HBg$N@8@.85$NDj5AB?9`<0$H$7$FMQ$$$i$l$k(B. |
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$B@8@.85$O(B @code{@@s} $B$G$"$k(B. |
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\E |
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\BEG |
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An extension field @var{K} of the small finite field @var{F} of order @var{p^n} |
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is set by @code{setmod_ff} |
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by specifying its characteristic @var{p} the extension degree |
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@var{n} and @var{m}=[@var{K}:@var{F}]. An irreducible polynomial of degree @var{m} |
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over @var{K} is automatically generated and used as the defining polynomial of |
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the generator of the extension @var{K/F}. The generator is denoted by @code{@@s}. |
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\E |
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@item 11 |
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\JP @b{$BJ,;6I=8=$NBe?tE*?t(B} |
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\EG @b{algebraic number represented by a distributed polynomial} |
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@* |
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\JP @xref{$BBe?tE*?t$K4X$9$k1i;;(B}. |
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\EG @xref{Algebraic numbers}. |
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\BJP |
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\E |
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\BEG |
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\E |
@end table |
@end table |
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\BJP |
\BJP |