version 1.5, 2010/06/16 10:39:08 |
version 1.6, 2010/06/19 09:43:45 |
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%comment $OpenXM: OpenXM/src/asir-contrib/packages/doc/nn_ndbf/nn_ndbf.texi,v 1.4 2010/06/16 08:53:03 noro Exp $ |
%comment $OpenXM: OpenXM/src/asir-contrib/packages/doc/nn_ndbf/nn_ndbf.texi,v 1.5 2010/06/16 10:39:08 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 90 In this manual we explain about a new b-function packa |
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Line 90 In this manual we explain about a new b-function packa |
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in asir-contrib. To use this package one has to load @samp{nn_ndbf.rr}. |
in asir-contrib. To use this package one has to load @samp{nn_ndbf.rr}. |
\E |
\E |
@example |
@example |
[1518] load("nn_ndbf.rr"); |
[...] load("nn_ndbf.rr"); |
@end example |
@end example |
\BJP |
\BJP |
このパッケージの函数を呼び出すには, 全て @code{ndbf.} を先頭につける. |
このパッケージの函数を呼び出すには, 全て @code{ndbf.} を先頭につける. |
Line 202 If an option @code{vord=@var{v}} is given, a variable |
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Line 202 If an option @code{vord=@var{v}} is given, a variable |
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\E |
\E |
@end itemize |
@end itemize |
@example |
@example |
[1519] load("nn_ndbf.rr"); |
[...] load("nn_ndbf.rr"); |
[1602] ndbf.bfunction(x^3-y^2*z^2); |
[...] 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 |
[1603] ndbf.bfunction(x^3-y^2*z^2|op=1); |
[...] ndbf.bfunction(x^3-y^2*z^2|op=1); |
[-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,(108*z^3*x*dz^3+756*z^2*x*dz^2+1080*z*x*dz+216*x)*dx^4 |
-158375*s-24500,(108*z^3*x*dz^3+756*z^2*x*dz^2+1080*z*x*dz+216*x)*dx^4 |
... |
... |
+(729/8*z^3*dz^5+9477/8*z^2*dz^4+5103/2*z*dz^3+2025/2*dz^2)*dy^2] |
+(729/8*z^3*dz^5+9477/8*z^2*dz^4+5103/2*z*dz^3+2025/2*dz^2)*dy^2] |
[1604] F=256*u1^3-128*u3^2*u1^2+(144*u3*u2^2+16*u3^4)*u1-27*u2^4 |
[...] 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$ |
[1605] ndbf.bfunction(F|weight=[u3,2,u2,3,u1,4]); |
[...] ndbf.bfunction(F|weight=[u3,2,u2,3,u1,4]); |
576*s^6+3456*s^5+8588*s^4+11312*s^3+8329*s^2+3250*s+525 |
576*s^6+3456*s^5+8588*s^4+11312*s^3+8329*s^2+3250*s+525 |
@end example |
@end example |
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Line 313 If an option @code{vord=@var{v}} is given, a variable |
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Line 313 If an option @code{vord=@var{v}} is given, a variable |
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\E |
\E |
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@example |
@example |
[1527] load("nn_ndbf.rr"); |
[...] load("nn_ndbf.rr"); |
[1610] ndbf.bf_local(y*((x+1)*x^3-y^2),[x,-1,y,0]); |
[...] 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); |
[...] ndbf.bf_local(y*((x+1)*x^3-y^2),[x,-1,y,0]|op=1); |
[[[-s-1,2]],12*x^3+36*y^2*x-36*y^2,(32*y*x^2+56*y*x)*dx^2 |
[[[-s-1,2]],12*x^3+36*y^2*x-36*y^2,(32*y*x^2+56*y*x)*dx^2 |
+((-8*x^3-2*x^2+(128*y^2-6)*x+112*y^2)*dy+288*y*x+(-240*s-128)*y)*dx |
+((-8*x^3-2*x^2+(128*y^2-6)*x+112*y^2)*dy+288*y*x+(-240*s-128)*y)*dx |
+(32*y*x^2-6*y*x+128*y^3-9*y)*dy^2+(32*x^2+6*s*x+640*y^2+39*s+30)*dy |
+(32*y*x^2-6*y*x+128*y^3-9*y)*dy^2+(32*x^2+6*s*x+640*y^2+39*s+30)*dy |
Line 399 If an option @code{vord=@var{v}} is given, a variable |
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Line 399 If an option @code{vord=@var{v}} is given, a variable |
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\E |
\E |
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@example |
@example |
[1537] load("nn_ndbf.rr"); |
[...] 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 |
[...] 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); |
[...] ndbf.bf_strat(F); |
[[u3^2,-u1,-u2],[-1],[[-s-1,2],[16*s^2+32*s+15,1],[36*s^2+72*s+35,1]]] |
[[[u3^2,-u1,-u2],[-1],[[-s-1,2],[16*s^2+32*s+15,1],[36*s^2+72*s+35,1]]], |
[[-4*u1+u3^2,-u2],[96*u1^2+40*u3^2*u1-9*u3*u2^2,...],[[-s-1,2]]] |
[[-4*u1+u3^2,-u2],[96*u1^2+40*u3^2*u1-9*u3*u2^2,...],[[-s-1,2]]], |
[[...],[-u3*u2,u2*u1,...],[[-s-1,1],...]]] |
[[-2048*u1^3-...],[-u3*u2,u2*u1,...],[[-s-1,1],...]]], |
[[-256*u1^3+128*u3^2*u1^2+...],[...],[[-s-1,1]]] |
[[-256*u1^3+128*u3^2*u1^2+...],[...],[[-s-1,1]]], |
[[],[-256*u1^3+128*u3^2*u1^2+...],[]] |
[[],[-256*u1^3+128*u3^2*u1^2+...],[]]] |
@end example |
@end example |
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\JP @node ndbf.action_on_gfs,,, b 関数計算 |
\JP @node ndbf.action_on_gfs,,, b 関数計算 |
Line 417 If an option @code{vord=@var{v}} is given, a variable |
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Line 417 If an option @code{vord=@var{v}} is given, a variable |
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@table @t |
@table @t |
@item ndbf.action_on_gfs(@var{op},@var{v},@var{gfs}) |
@item ndbf.action_on_gfs(@var{op},@var{v},@var{gfs}) |
\JP :: 微分作用素 @var{op} の @var{gf^(s+1)} への作用を計算する. |
\JP :: 微分作用素 @var{op} の @var{gf^(s+a)} への作用を計算する. |
\EG :: computes the action of an operatior @var{op} on @var{gf^(s+1)} |
\EG :: computes the action of an operatior @var{op} on @var{gf^(s+a)} |
@end table |
@end table |
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@table @var |
@table @var |
Line 429 If an option @code{vord=@var{v}} is given, a variable |
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Line 429 If an option @code{vord=@var{v}} is given, a variable |
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\JP 微分作用素 |
\JP 微分作用素 |
\EG a differential operator |
\EG a differential operator |
@item gfs |
@item gfs |
\JP @var{[g,f,s-a]} なるリスト |
\JP @var{[g,f,s+a]} なるリスト |
\EG a list @var{[g,f,s-a]} |
\EG a list @var{[g,f,s+a]} |
@item v |
@item v |
\JP @var{f} の変数のリスト |
\JP @var{f} の変数のリスト (@var{v=[v1,...,vn]}) |
\EG list of variables of @var{f} |
\EG list of variables of @var{f} (@var{v=[v1,...,vn]}) |
@end table |
@end table |
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\BJP |
\BJP |
@itemize @bullet |
@itemize @bullet |
@item 微分作用素 @var{op} を @var{gf^(s+1)} に作用させた結果を計算する. |
@item 微分作用素 @var{op} を @var{gf^(s+a)} に作用させた結果を計算する. |
@item @var{g} および @var{h} は @var{v} を変数とする多項式である. |
@item @var{g} は @var{v1,...,vn} を変数とする多項式である. |
@item @var{op} は @var{[v1,...,vn,dv1,...,dvn]} を変数とする多項式で表現する. |
@item @var{op} は @var{[v1,...,vn,dv1,...,dvn]} を変数とする多項式で表現する. |
@item 入力リスト @var{[g,f,s+1]} は @var{gf^(s+1)} を表す. |
@item 入力リスト @var{[g,f,s+a]} は @var{gf^(s+a)} を表す. |
@item 結果は @var{[h,f,s-a]} なるリストで, @var{hf^(s-a)} を |
@item 結果は @var{[h,f,s+c]} なるリストで, @var{hf^(s+b)} を |
意味する. ここで @var{a} は整数で, @var{op} が |
意味する. ここで @var{c} は整数である. |
b-関数を与える作用素なら, @var{a} は 0 となり, @var{h} は b-関数となる. |
@var{op} が b-関数 @var{b(s)} を与える作用素なら, |
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@var{a=1} に対し @var{c=0} で, @var{h=b(s)} (global case) または |
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@var{h=d(v)b(s)} (local case) である. |
@end itemize |
@end itemize |
\E |
\E |
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\BEG |
\BEG |
@itemize @bullet |
@itemize @bullet |
@item This function computes the action of a differential operator |
@item This function computes the action of a differential operator |
@var{op} on @var{gf^(s+1)}. |
@var{op} on @var{gf^(s+a)}. |
@item @var{g} and @var{h} are polynomials with variables @var{v}=@var{v1,\ldots,vn}. |
@item @var{g} is a polynomial with variables @var{v1,...,vn}. |
@item @var{op} is represented by a polynonmial with @var{[v1,...,vn,dv1,...,dvn]}. |
@item @var{op} is represented by a polynonmial with @var{[v1,...,vn,dv1,...,dvn]}. |
@item The input list @var{[g,f,s+1]} represents @var{gf^(s+1)}. |
@item The input list @var{[g,f,s+a]} represents @var{gf^(s+a)}. |
@item The result is a list @var{[h,f,s-a]} and it means @var{hf^(s-a)}, |
@item The result is a list @var{[h,f,s+c]} and it means @var{hf^(s+c)}, |
where @var{a} is an integer. If @var{op} is an operator giving b-function, |
where @var{c} is an integer. If @var{op} is an operator giving b-function |
then @var{a}=0 and @var{h} is a b-functio n. |
@var{b(s)}, |
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then @var{c=0} for @var{a=1} and @var{h=b(s)} (global case) |
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or @var{h=b(s)d(v)} (local case). |
@end itemize |
@end itemize |
\E |
\E |
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@example |
@example |
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[...] load("nn_ndbf.rr"); |
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[...] F=x^5-y^2*z^2$ |
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[...] B=ndbf.bfunction(F|op=1)$ |
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[...] ndbf.action_on_gfs(B[1],[x,y,z],[1,F,s+1]); |
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[-62500000000*s^13-...-2985505717194*s-245434132944,x^5-z^2*y^2,s] |
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[...] L=ndbf.bf_local(F,[x,0,y,0,z,1]|op=1)$ |
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[...] ndbf.action_on_gfs(L[2],[x,y,z],[1,F,s+1]); |
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[(-100000*s^5-500000*s^4-990000*s^3-970000*s^2-470090*s-90090)*z^2, |
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x^5-z^2*y^2,s] |
@end example |
@end example |
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\JP @node Annihilator イデアル計算,,, 新 b 関数パッケージ nn_ndbf.rr |
\JP @node Annihilator イデアル計算,,, 新 b 関数パッケージ nn_ndbf.rr |
Line 527 This option is useful when @var{f} is weighted homogen |
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Line 539 This option is useful when @var{f} is weighted homogen |
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\E |
\E |
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@example |
@example |
[1542] load("nn_ndbf.rr"); |
[...] load("nn_ndbf.rr"); |
[1625] ndbf.ann(x*y*z*(x^3-y^2*z^2)); |
[...] 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, |
(x^4*dy-3*z^3*y*x*dz-6*z^2*y*x)*dx-4*z*x^3*dz*dy+z^4*y*dz^2+3*z^3*y*dz, |
(x^4*dy-3*z^3*y*x*dz-6*z^2*y*x)*dx-4*z*x^3*dz*dy+z^4*y*dz^2+3*z^3*y*dz, |