version 1.1, 2009/12/02 02:55:29 |
version 1.2, 2009/12/02 04:38:47 |
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%comment $OpenXM$ |
%comment $OpenXM: OpenXM/src/asir-contrib/packages/doc/nn_ndbf/nn_ndbf.texi,v 1.1 2009/12/02 02:55:29 noro Exp $ |
%comment --- おまじない --- |
%comment --- おまじない --- |
\input ../../../../asir-doc/texinfo |
\input ../../../../asir-doc/texinfo |
@iftex |
@iftex |
Line 149 In this manual we also explain about some related buil |
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Line 149 In this manual we also explain about some related buil |
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@itemize @bullet |
@itemize @bullet |
\BJP |
\BJP |
@item |
@item |
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この関数は asir-contrib のパッケージ @samp{nn_ndbf.rr} で定義されている. |
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@item |
多項式 @var{f} の大域 b 関数 (global b-function) を計算する. 出力は |
多項式 @var{f} の大域 b 関数 (global b-function) を計算する. 出力は |
変数 @var{s} の多項式である. |
変数 @var{s} の多項式である. |
@item |
@item |
Line 166 In this manual we also explain about some related buil |
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Line 168 In this manual we also explain about some related buil |
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\E |
\E |
\BEG |
\BEG |
@item |
@item |
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This function is defined in an asir-contrib package @samp{nn_ndbf.rr}. |
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@item |
This function computes the global b-function of a polynomial @var{f}. |
This function computes the global b-function of a polynomial @var{f}. |
The output is a polynomial in @var{s}. |
The output is a polynomial in @var{s}. |
@item |
@item |
Line 182 If an option @code{vord=@var{v}} is given, a variable |
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Line 186 If an option @code{vord=@var{v}} is given, a variable |
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\E |
\E |
@end itemize |
@end itemize |
@example |
@example |
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[1519] load("nn_ndbf.rr"); |
[1602] ndbf.bfunction(x^3-y^2*z^2); |
[1602] ndbf.bfunction(x^3-y^2*z^2); |
-11664*s^7-93312*s^6-316872*s^5-592272*s^4-658233*s^3-435060*s^2 |
-11664*s^7-93312*s^6-316872*s^5-592272*s^4-658233*s^3-435060*s^2 |
-158375*s-24500 |
-158375*s-24500 |
Line 210 If an option @code{vord=@var{v}} is given, a variable |
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Line 215 If an option @code{vord=@var{v}} is given, a variable |
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\EG a polynomail |
\EG a polynomail |
@item p |
@item p |
\JP @code{[@var{v1,a1,...,vn,an}]} なるリスト |
\JP @code{[@var{v1,a1,...,vn,an}]} なるリスト |
\JP a list @code{[@var{v1,a1,...,vn,an}]} |
\EG a list @code{[@var{v1,a1,...,vn,an}]} |
@item w |
@item w |
\JP @code{[@var{v1,w1,...,vn,wn}]} なるリスト |
\JP @code{[@var{v1,w1,...,vn,wn}]} なるリスト |
\EG a list @code{[@var{v1,w1,...,vn,wn}]} |
\EG a list @code{[@var{v1,w1,...,vn,wn}]} |
Line 225 If an option @code{vord=@var{v}} is given, a variable |
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Line 230 If an option @code{vord=@var{v}} is given, a variable |
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\BJP |
\BJP |
@itemize @bullet |
@itemize @bullet |
@item |
@item |
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この関数は asir-contrib のパッケージ @samp{nn_ndbf.rr} で定義されている. |
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@item |
多項式 @var{f} の @var{(v1,...,vn)=(a1,...,an)} における |
多項式 @var{f} の @var{(v1,...,vn)=(a1,...,an)} における |
局所 b 関数 (local b-function) を計算する. 出力は局所 $b$ 関数の因子, 重複度のペアのリストである. |
局所 b 関数 (local b-function) を計算する. 出力は局所 $b$ 関数の因子, 重複度のペアのリストである. |
@item |
@item |
Line 255 If an option @code{vord=@var{v}} is given, a variable |
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Line 262 If an option @code{vord=@var{v}} is given, a variable |
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\BEG |
\BEG |
@itemize @bullet |
@itemize @bullet |
@item |
@item |
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This function is defined in an asir-contrib package @samp{nn_ndbf.rr}. |
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@item |
This function computes the local b-function of a polynomial @var{f} at a point @var{(v1,...,vn)=(a1,...,an)}. |
This function computes the local b-function of a polynomial @var{f} at a point @var{(v1,...,vn)=(a1,...,an)}. |
The output is a list of pairs of each factor of the local b-function and its multiplicity. |
The output is a list of pairs of each factor of the local b-function and its multiplicity. |
@item |
@item |
Line 281 If an option @code{vord=@var{v}} is given, a variable |
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Line 290 If an option @code{vord=@var{v}} is given, a variable |
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\E |
\E |
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@example |
@example |
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[1527] load("nn_ndbf.rr"); |
[1610] ndbf.bf_local(y*((x+1)*x^3-y^2),[x,-1,y,0]); |
[1610] ndbf.bf_local(y*((x+1)*x^3-y^2),[x,-1,y,0]); |
[[-s-1,2]] |
[[-s-1,2]] |
[1611] ndbf.bf_local(y*((x+1)*x^3-y^2),[x,-1,y,0]|op=1); |
[1611] ndbf.bf_local(y*((x+1)*x^3-y^2),[x,-1,y,0]|op=1); |
Line 322 If an option @code{vord=@var{v}} is given, a variable |
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Line 332 If an option @code{vord=@var{v}} is given, a variable |
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\BJP |
\BJP |
@itemize @bullet |
@itemize @bullet |
@item |
@item |
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この関数は asir-contrib のパッケージ @samp{nn_ndbf.rr} で定義されている. |
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@item |
多項式 @var{f} の大域 b 関数 (global b-function) を計算する. 出力は |
多項式 @var{f} の大域 b 関数 (global b-function) を計算する. 出力は |
変数 @var{s} の多項式である. |
変数 @var{s} の多項式である. |
@item |
@item |
Line 342 If an option @code{vord=@var{v}} is given, a variable |
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Line 354 If an option @code{vord=@var{v}} is given, a variable |
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\BEG |
\BEG |
@itemize @bullet |
@itemize @bullet |
@item |
@item |
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This function is defined in an asir-contrib package @samp{nn_ndbf.rr}. |
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@item |
This function computes a stratification assoficated with local b-function of a polynomial @var{f}. |
This function computes a stratification assoficated with local b-function of a polynomial @var{f}. |
The output is a list @var{[s1,...sl]} where each @var{si} is a list @var{[l1,l2,bi]}. |
The output is a list @var{[s1,...sl]} where each @var{si} is a list @var{[l1,l2,bi]}. |
In this list, @var{l1} and @var{l2} is generators of ideals and they represents |
In this list, @var{l1} and @var{l2} is generators of ideals and they represents |
Line 362 If an option @code{vord=@var{v}} is given, a variable |
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Line 376 If an option @code{vord=@var{v}} is given, a variable |
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\E |
\E |
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@example |
@example |
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[1537] load("nn_ndbf.rr"); |
[1620] F=256*u1^3-128*u3^2*u1^2+(144*u3*u2^2+16*u3^4)*u1-27*u2^4 |
[1620] F=256*u1^3-128*u3^2*u1^2+(144*u3*u2^2+16*u3^4)*u1-27*u2^4 |
-4*u3^3*u2^2$ |
-4*u3^3*u2^2$ |
[1621] ndbf.bf_strat(F); |
[1621] ndbf.bf_strat(F); |
Line 406 If an option @code{vord=@var{v}} is given, a variable |
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Line 421 If an option @code{vord=@var{v}} is given, a variable |
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\BJP |
\BJP |
@itemize @bullet |
@itemize @bullet |
@item |
@item |
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この関数は asir-contrib のパッケージ @samp{nn_ndbf.rr} で定義されている. |
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@item |
多項式 @var{f} に対し, @var{f^s} の annihilator ideal を計算する. |
多項式 @var{f} に対し, @var{f^s} の annihilator ideal を計算する. |
出力は, @var{s} を係数に含む微分作用素のリストである. 微分作用素の |
出力は, @var{s} を係数に含む微分作用素のリストである. 微分作用素の |
表現方法は, @code{ndbf.bf_local} と同様である. |
表現方法は, @code{ndbf.bf_local} と同様である. |
Line 419 If an option @code{vord=@var{v}} is given, a variable |
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Line 436 If an option @code{vord=@var{v}} is given, a variable |
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\BEG |
\BEG |
@itemize @bullet |
@itemize @bullet |
@item |
@item |
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This function is defined in an asir-contrib package @samp{nn_ndbf.rr}. |
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@item |
This function computes the annihilator ideal of @var{f^s} for @var{f}. |
This function computes the annihilator ideal of @var{f^s} for @var{f}. |
The output is a list of defferential operators containing @var{s} in thier coefficients. |
The output is a list of defferential operators containing @var{s} in thier coefficients. |
The differential operators are represented in the same manner as @code{ndbf.bf_local}. |
The differential operators are represented in the same manner as @code{ndbf.bf_local}. |
Line 430 This option is useful when @var{f} is weighted homogen |
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Line 449 This option is useful when @var{f} is weighted homogen |
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\E |
\E |
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@example |
@example |
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[1542] load("nn_ndbf.rr"); |
[1625] ndbf.ann(x*y*z*(x^3-y^2*z^2)); |
[1625] ndbf.ann(x*y*z*(x^3-y^2*z^2)); |
[(-x^4*dy^2+3*z^4*x*dz^2+12*z^3*x*dz+6*z^2*x)*dx+4*z*x^3*dz*dy^2 |
[(-x^4*dy^2+3*z^4*x*dz^2+12*z^3*x*dz+6*z^2*x)*dx+4*z*x^3*dz*dy^2 |
-z^5*dz^3-6*z^4*dz^2-6*z^3*dz, |
-z^5*dz^3-6*z^4*dz^2-6*z^3*dz, |