| version 1.6, 2003/04/20 09:55:18 |
version 1.7, 2003/04/21 03:07:32 |
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| @comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.5 2003/04/20 08:01:25 noro Exp $ |
@comment $OpenXM: OpenXM/src/asir-doc/parts/groebner.texi,v 1.6 2003/04/20 09:55:18 noro Exp $ |
| \BJP |
\BJP |
| @node $B%0%l%V%J4pDl$N7W;;(B,,, Top |
@node $B%0%l%V%J4pDl$N7W;;(B,,, Top |
| @chapter $B%0%l%V%J4pDl$N7W;;(B |
@chapter $B%0%l%V%J4pDl$N7W;;(B |
| Line 449 If `on', various informations during a Groebner basis |
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| Line 449 If `on', various informations during a Groebner basis |
|
| displayed. |
displayed. |
| \E |
\E |
| |
|
| |
@item PrintShort |
| |
\JP on $B$G!"(BPrint $B$,(B off $B$N>l9g(B, $B%0%l%V%J4pDl7W;;$NESCf$N>pJs$rC;=L7A$GI=<($9$k(B. |
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\BEG |
| |
If `on' and Print is `off', short information during a Groebner basis computation is |
| |
displayed. |
| |
\E |
| |
|
| @item Stat |
@item Stat |
| \BJP |
\BJP |
| on $B$G(B @code{Print} $B$,(B off $B$J$i$P(B, @code{Print} $B$,(B on $B$N$H$-I=<($5(B |
on $B$G(B @code{Print} $B$,(B off $B$J$i$P(B, @code{Print} $B$,(B on $B$N$H$-I=<($5(B |
| Line 471 is shown after every normal computation. After comlet |
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| Line 478 is shown after every normal computation. After comlet |
|
| computation the maximal value among the sums is shown. |
computation the maximal value among the sums is shown. |
| \E |
\E |
| |
|
| @item Multiple |
@item Content |
| |
@itemx Multiple |
| \BJP |
\BJP |
| 0 $B$G$J$$@0?t$N;~(B, $BM-M}?t>e$N@55,7A7W;;$K$*$$$F(B, $B78?t$N%S%C%HD9$NOB$,(B |
0 $B$G$J$$M-M}?t$N;~(B, $BM-M}?t>e$N@55,7A7W;;$K$*$$$F(B, $B78?t$N%S%C%HD9$NOB$,(B |
| @code{Multiple} $BG\$K$J$k$4$H$K78?tA4BN$N(B GCD $B$,7W;;$5$l(B, $B$=$N(B GCD $B$G(B |
@code{Content} $BG\$K$J$k$4$H$K78?tA4BN$N(B GCD $B$,7W;;$5$l(B, $B$=$N(B GCD $B$G(B |
| $B3d$C$?B?9`<0$r4JLs$9$k(B. @code{Multiple} $B$,(B 1 $B$J$i$P(B, $B4JLs$9$k$4$H$K(B |
$B3d$C$?B?9`<0$r4JLs$9$k(B. @code{Content} $B$,(B 1 $B$J$i$P(B, $B4JLs$9$k$4$H$K(B |
| GCD $B7W;;$,9T$o$l0lHL$K$O8zN($,0-$/$J$k$,(B, @code{Multiple} $B$r(B 2 $BDxEY(B |
GCD $B7W;;$,9T$o$l0lHL$K$O8zN($,0-$/$J$k$,(B, @code{Content} $B$r(B 2 $BDxEY(B |
| $B$H$9$k$H(B, $B5pBg$J@0?t$,78?t$K8=$l$k>l9g(B, $B8zN($,NI$/$J$k>l9g$,$"$k(B. |
$B$H$9$k$H(B, $B5pBg$J@0?t$,78?t$K8=$l$k>l9g(B, $B8zN($,NI$/$J$k>l9g$,$"$k(B. |
| |
backward compatibility $B$N$?$a!"(B@code{Multiple} $B$G@0?tCM$r;XDj$G$-$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| If a non-zero integer, in a normal form computation |
If a non-zero rational number, in a normal form computation |
| over the rationals, the integer content of the polynomial being |
over the rationals, the integer content of the polynomial being |
| reduced is removed when its magnitude becomes @code{Multiple} times |
reduced is removed when its magnitude becomes @code{Content} times |
| larger than a registered value, which is set to the magnitude of the |
larger than a registered value, which is set to the magnitude of the |
| input polynomial. After each content removal the registered value is |
input polynomial. After each content removal the registered value is |
| set to the magnitude of the resulting polynomial. @code{Multiple} is |
set to the magnitude of the resulting polynomial. @code{Content} is |
| equal to 1, the simiplification is done after every normal form computation. |
equal to 1, the simiplification is done after every normal form computation. |
| It is empirically known that it is often efficient to set @code{Multiple} to 2 |
It is empirically known that it is often efficient to set @code{Content} to 2 |
| for the case where large integers appear during the computation. |
for the case where large integers appear during the computation. |
| |
An integer value can be set by the keyword @code{Multiple} for |
| |
backward compatibility. |
| \E |
\E |
| |
|
| @item Demand |
@item Demand |
| Line 2150 except for lack of the argument for controlling homoge |
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| Line 2161 except for lack of the argument for controlling homoge |
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| |
|
| @table @t |
@table @t |
| @item dp_gr_flags([@var{list}]) |
@item dp_gr_flags([@var{list}]) |
| @itemx dp_gr_print([@var{0|1}]) |
@itemx dp_gr_print([@var{i}]) |
| \JP :: $B7W;;$*$h$SI=<(MQ%Q%i%a%?$N@_Dj(B, $B;2>H(B |
\JP :: $B7W;;$*$h$SI=<(MQ%Q%i%a%?$N@_Dj(B, $B;2>H(B |
| \BEG :: Set and show various parameters for cotrolling computations |
\BEG :: Set and show various parameters for cotrolling computations |
| and showing informations. |
and showing informations. |
| Line 2164 and showing informations. |
|
| Line 2175 and showing informations. |
|
| @item list |
@item list |
| \JP $B%j%9%H(B |
\JP $B%j%9%H(B |
| \EG list |
\EG list |
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@item i |
| |
\JP $B@0?t(B |
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\EG integer |
| @end table |
@end table |
| |
|
| @itemize @bullet |
@itemize @bullet |
| Line 2177 and showing informations. |
|
| Line 2191 and showing informations. |
|
| $B0z?t$O(B, @code{["Print",1,"NoSugar",1,...]} $B$J$k7A$N%j%9%H$G(B, $B:8$+$i=g$K(B |
$B0z?t$O(B, @code{["Print",1,"NoSugar",1,...]} $B$J$k7A$N%j%9%H$G(B, $B:8$+$i=g$K(B |
| $B@_Dj$5$l$k(B. $B%Q%i%a%?L>$OJ8;zNs$GM?$($kI,MW$,$"$k(B. |
$B@_Dj$5$l$k(B. $B%Q%i%a%?L>$OJ8;zNs$GM?$($kI,MW$,$"$k(B. |
| @item |
@item |
| @code{dp_gr_print()} $B$O(B, $BFC$K%Q%i%a%?(B @code{Print} $B$NCM$rD>@\@_Dj(B, $B;2>H(B |
@code{dp_gr_print()} $B$O(B, $BFC$K%Q%i%a%?(B @code{Print}, @code{PrintShort} $B$NCM$rD>@\@_Dj(B, $B;2>H(B |
| $B$G$-$k(B. $B$3$l$O(B, @code{dp_gr_main()} $B$J$I$r%5%V%k!<%A%s$H$7$FMQ$$$k%f!<%6(B |
$B$G$-$k(B. $B@_Dj$5$l$kCM$O<!$NDL$j$G$"$k!#(B |
| $BH!?t$K$*$$$F(B, @code{Print} $B$NCM$r8+$F(B, $B$=$N%5%V%k!<%A%s$,Cf4V>pJs$NI=<((B |
@table @var |
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@item i=0 |
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@code{Print=0}, @code{PrintShort=0} |
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@item i=1 |
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@code{Print=1}, @code{PrintShort=0} |
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@item i=2 |
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@code{Print=0}, @code{PrintShort=1} |
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@end table |
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$B$3$l$O(B, @code{dp_gr_main()} $B$J$I$r%5%V%k!<%A%s$H$7$FMQ$$$k%f!<%6(B |
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$BH!?t$K$*$$$F(B, $B$=$N%5%V%k!<%A%s$,Cf4V>pJs$NI=<((B |
| $B$r9T$&:]$K(B, $B?WB.$K%U%i%0$r8+$k$3$H$,$G$-$k$h$&$KMQ0U$5$l$F$$$k(B. |
$B$r9T$&:]$K(B, $B?WB.$K%U%i%0$r8+$k$3$H$,$G$-$k$h$&$KMQ0U$5$l$F$$$k(B. |
| \E |
\E |
| \BEG |
\BEG |
| Line 2194 Arguments must be specified as a list such as |
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| Line 2217 Arguments must be specified as a list such as |
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| strings. |
strings. |
| @item |
@item |
| @code{dp_gr_print()} is used to set and show the value of a parameter |
@code{dp_gr_print()} is used to set and show the value of a parameter |
| @code{Print}. This functions is prepared to get quickly the value of |
@code{Print} and @code{PrintShort}. |
| @code{Print} when a user defined function calling @code{dp_gr_main()} etc. |
@table @var |
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@item i=0 |
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@code{Print=0}, @code{PrintShort=0} |
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@item i=1 |
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@code{Print=1}, @code{PrintShort=0} |
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@item i=2 |
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@code{Print=0}, @code{PrintShort=1} |
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@end table |
| |
This functions is prepared to get quickly the value |
| |
when a user defined function calling @code{dp_gr_main()} etc. |
| uses the value as a flag for showing intermediate informations. |
uses the value as a flag for showing intermediate informations. |
| \E |
\E |
| @end itemize |
@end itemize |
| Line 3831 if an input ideal is not radical. |
|
| Line 3863 if an input ideal is not radical. |
|
| $BItJ,$r7W;;$9$k$3$H$K$h$k(B early termination $B$r9T$&(B. $B0lHL$K(B, |
$BItJ,$r7W;;$9$k$3$H$K$h$k(B early termination $B$r9T$&(B. $B0lHL$K(B, |
| $B%$%G%"%k$N<!85$,9b$$>l9g$KM-8z$@$,(B, 0 $B<!85$N>l9g$J$I(B, $B<!85$,>.$5$$(B |
$B%$%G%"%k$N<!85$,9b$$>l9g$KM-8z$@$,(B, 0 $B<!85$N>l9g$J$I(B, $B<!85$,>.$5$$(B |
| $B>l9g$K$O(B overhead $B$,Bg$-$$>l9g$,$"$k(B. |
$B>l9g$K$O(B overhead $B$,Bg$-$$>l9g$,$"$k(B. |
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@item |
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$B7W;;ESCf$GFbIt>pJs$r8+$?$$>l9g$K$O!"(B |
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$BA0$b$C$F(B @code{dp_gr_print(2)} $B$r<B9T$7$F$*$1$P$h$$(B. |
| \E |
\E |
| \BEG |
\BEG |
| @item |
@item |
| Line 3855 is tried by computing the intersection of obtained com |
|
| Line 3890 is tried by computing the intersection of obtained com |
|
| incrementally. In general, this strategy is useful when the krull |
incrementally. In general, this strategy is useful when the krull |
| dimension of the ideal is high, but it may add some overhead |
dimension of the ideal is high, but it may add some overhead |
| if the dimension is small. |
if the dimension is small. |
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@item |
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If you want to see internal information during the computation, |
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execute @code{dp_gr_print(2)} in advance. |
| \E |
\E |
| @end itemize |
@end itemize |
| |
|
| Line 3876 if the dimension is small. |
|
| Line 3914 if the dimension is small. |
|
| @fref{modfctr}, |
@fref{modfctr}, |
| @fref{dp_gr_main dp_gr_mod_main dp_gr_f_main dp_weyl_gr_main dp_weyl_gr_mod_main dp_weyl_gr_f_main}, |
@fref{dp_gr_main dp_gr_mod_main dp_gr_f_main dp_weyl_gr_main dp_weyl_gr_mod_main dp_weyl_gr_f_main}, |
| \JP @fref{$B9`=g=x$N@_Dj(B}. |
\JP @fref{$B9`=g=x$N@_Dj(B}. |
| \EG @fref{Setting term orderings}. |
\EG @fref{Setting term orderings}, |
| |
@fref{dp_gr_flags dp_gr_print}. |
| @end table |
@end table |
| |
|
| \JP @node bfunction generic_bfct,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B |
\JP @node bfunction generic_bfct,,, $B%0%l%V%J4pDl$K4X$9$kH!?t(B |
| Line 3916 if the dimension is small. |
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| Line 3955 if the dimension is small. |
|
| $B%&%'%$%H(B @var{weight} $B$K4X$9$k(B global b $B4X?t$r7W;;$9$k(B. |
$B%&%'%$%H(B @var{weight} $B$K4X$9$k(B global b $B4X?t$r7W;;$9$k(B. |
| @var{vlist} $B$O(B @code{x}-$BJQ?t(B, @var{vlist} $B$OBP1~$9$k(B @code{D}-$BJQ?t(B |
@var{vlist} $B$O(B @code{x}-$BJQ?t(B, @var{vlist} $B$OBP1~$9$k(B @code{D}-$BJQ?t(B |
| $B$r=g$KJB$Y$k(B. |
$B$r=g$KJB$Y$k(B. |
| @item $B>\:Y$K$D$$$F$O(B, [SST] $B$r8+$h(B. |
@item $B>\:Y$K$D$$$F$O(B, [Saito,Sturmfels,Takayama] $B$r8+$h(B. |
| \E |
\E |
| \BEG |
\BEG |
| @item These functions are defined in @samp{bfct}. |
@item These functions are defined in @samp{bfct}. |
| Line 3930 computes the global b-function of a left ideal @code{I |
|
| Line 3969 computes the global b-function of a left ideal @code{I |
|
| generated by @var{plist}, with respect to @var{weight}. |
generated by @var{plist}, with respect to @var{weight}. |
| @var{vlist} is the list of @code{x}-variables, |
@var{vlist} is the list of @code{x}-variables, |
| @var{vlist} is the list of corresponding @code{D}-variables. |
@var{vlist} is the list of corresponding @code{D}-variables. |
| @item See [SST] for the details. |
@item See [Saito,Sturmfels,Takayama] for the details. |
| \E |
\E |
| @end itemize |
@end itemize |
| |
|
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