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Diff for /OpenXM/src/asir-contrib/packages/doc/ns_twistedlog/ns_twistedlog-ja.texi between version 1.1 and 1.6

version 1.1, 2012/02/16 00:10:07

version 1.6, 2012/03/02 03:49:30

Line 10

@comment %**start of header

@comment --- GNU info ファイルの名前 ---

@setfilename man-ns_twistedlog.rr

@setfilename asir-contrib-ns_twistedlog

@comment --- タイトル ---

@settitle ns_twistedlog.rr

Line 161 dimension : 3

[3] ns_twistedlog.twisted_log_cohomology([x*z+y,x^4+y^5+x*y^4],[0,0],[x,y,z]);

-- nd_weyl_gr :0.004sec(0.0028sec)

weyl_minipoly_by_elim : b-function does not exist

stopped in weyl_minipoly_by_elim2 at line 378 in file "/usr/local/ox/OpenXM/src/asir-contrib/packages/src/nk_restriction.rr"

stopped in weyl_minipoly_by_elim2 at line 378 in file "/usr/local/ox/OpenXM/src/

378 error("weyl_minipoly_by_elim : b-function does not exist");

asir-contrib/packages/src/nk_restriction.rr"

378 error("weyl_minipoly_by_elim : b-function does not exist");

(debug)

@end example

@comment --- 参照(リンク)を書く ---

@table @t

@item 参照

@fref{ns_twistedlog.twisted_log_cohomology(option)}

ns_twistedlog.twisted_log_cohomology(option)

@end table

@node ns_twistedlog.twisted_log_cohomology(option),,, Twisted logarithmic cohomology 群の計算に関する関数

Line 217 B_{S0} length : 3

Line 218 B_{S0} length : 3

dimension : 2

[y,1]

[5] ns_twistedlog.twisted_log_cohomology([x*z+y,x^4+y^5+x*y^4],[0,0],[x,y,z]|check = 1);

[5] ns_twistedlog.twisted_log_cohomology([x*z+y,x^4+y^5+x*y^4],[0,0],[x,y,z]|ch

eck = 1);

Hilbert polynomial : 1/24*x^4+65/12*x^3-529/24*x^2+727/12*x-51

holonomic : No

-- nd_weyl_gr :0.004001sec(0.002876sec)

weyl_minipoly_by_elim : b-function does not exist

stopped in weyl_minipoly_by_elim2 at line 378 in file "/usr/local/ox/OpenXM/src/asir-contrib/packages/src/nk_restriction.rr"

stopped in weyl_minipoly_by_elim2 at line 378 in file "/usr/local/ox/OpenXM/src/

378 error("weyl_minipoly_by_elim : b-function does not exist");

asir-contrib/packages/src/nk_restriction.rr"

378 error("weyl_minipoly_by_elim : b-function does not exist");

(debug)

[6] ns_twistedlog.twisted_log_cohomology([x*z+y,x^4+y^5+x*y^4],[0,0],[x,y,z]|s0 = 1);

[6] ns_twistedlog.twisted_log_cohomology([x*z+y,x^4+y^5+x*y^4],[0,0],[x,y,z]|s0 = 1

);

dimension : 3

[y,z,1]

Line 239 dimension : 1

Line 243 dimension : 1

@end example

@table @t

@item 参照

@fref{ns_twistedlog.twisted_log_cohomology}

@end table

@node ns_twistedlog.difference_equation,,, Twisted logarithmic cohomology 群の計算に関する関数

@subsection @code{ns_twistedlog.difference_equation}

@findex ns_twistedlog.difference_equation

Line 310 Order : 1

Line 308 Order : 1

@table @t

@item 参照

@fref{ns_twistedlog.difference_equation(option)}

ns_twistedlog.difference_equation(option)

@end table

Line 362 Order : 1

Line 360 Order : 1

-- nd_weyl_gr :0sec(0.0003991sec)

-- weyl_minipoly_by_elim :0sec(0.001058sec)

Order : 1

[[(-ea+1)*b*a-ea*b^2-ea*c*b,[((y^2-y)*dy+b*x+(b+c)*y-b)*dx+(-y^2+y)*dy^2+((-a-b-c)*y+b)*dy,(-a-b-c)*x+(-b-c)*y]],[eb*a+(eb-1)*b+eb*c,[((y^2-y)*dy+b*x+(b+c)*y-b)*dx+(-y^2+y)*dy^2+((-a-b-c)*y+b)*dy,-y]],[ec*b*a+ec*b^2+(ec-1)*c*b,[((y^2-y)*dy+b*x+(b+c)*y-b)*dx+(-y^2+y)*dy^2+((-a-b-c)*y+b)*dy,(-a-b-c)*x-c*y]]]

[[(-ea+1)*b*a-ea*b^2-ea*c*b,[((y^2-y)*dy+b*x+(b+c)*y-b)*dx+(-y^2+y)*dy^2+((-a-b-

c)*y+b)*dy,(-a-b-c)*x+(-b-c)*y]],[eb*a+(eb-1)*b+eb*c,[((y^2-y)*dy+b*x+(b+c)*y-b)

*dx+(-y^2+y)*dy^2+((-a-b-c)*y+b)*dy,-y]],[ec*b*a+ec*b^2+(ec-1)*c*b,[((y^2-y)*dy+

b*x+(b+c)*y-b)*dx+(-y^2+y)*dy^2+((-a-b-c)*y+b)*dy,(-a-b-c)*x-c*y]]]

[12] ns_twistedlog.difference_equation([x,y,1-x-y],[a,b,c],[x,y]|shift = a);

-- nd_weyl_gr :0.004sec(0.0004289sec)

Line 371 Order : 1

Line 372 Order : 1

[(ea-1)*a+ea*b+ea*c]

@end example

@table @t

@item 参照

@fref{ns_twistedlog.difference_equation}

@end table

@node ns_twistedlog.differential_equation,,, Twisted logarithmic cohomology 群の計算に関する関数

@subsection @code{ns_twistedlog.differential_equation}

@findex ns_twistedlog.differential_equation

Line 413 Twisted logarithmic cohomology 群の基底を用いて, 指数�

Line 409 Twisted logarithmic cohomology 群の基底を用いて, 指数�

以下は @code{f(x_1,x_2) = \int_C exp(x1*t1+x2*t2) t1^@{a-1@}*t2^@{b-1@}dt1dt2} の満たす微分方程式系を計算した例である.

@example

[13] ns_twistedlog.differential_equation(x1*t1+x2*t2,[t1,t2],[a,b],[t1,t2],[x1,x2]);

[13] ns_twistedlog.differential_equation(x1*t1+x2*t2,[t1,t2],[a,b],[t1,t2],[x1,x2])

;

-- nd_weyl_gr :0sec(0.0004089sec)

-- weyl_minipoly_by_elim :0sec(0.000495sec)

Order : 1

Line 422 Order : 1

Line 419 Order : 1

@table @t

@item 参照

@fref{ns_twistedlog.differential_equation(option)}

ns_twistedlog.differential_equation(option)

@end table

Line 466 Order : 1

Line 463 Order : 1

@end itemize

@example

[14] ns_twistedlog.differential_equation(x1*t1+x2*t2,[t1,t2],[a,b],[t1,t2],[x1,x2]| diff = x1);

[14] ns_twistedlog.differential_equation(x1*t1+x2*t2,[t1,t2],[a,b],[t1,t2],[x1,x2]|

diff = x1);

-- nd_weyl_gr :0sec(0.0007901sec)

-- weyl_minipoly_by_elim :0sec + gc : 0.008sec(0.006175sec)

Order : 1

[x1*dx1+a]

@end example

@table @t

@item 参照

@fref{ns_twistedlog.differential_equation}

@end table

@node その他の関数,,, ns_twistedlog.rr

@section その他の関数

Line 510 Order : 1

Line 503 Order : 1

@var{P} が変数の場合, 係数体に属する整数でない不定元と見なして計算される.

従って, これらの変数に依存する generic @var{b}-関数の根は最大整数根とはならず, またグレブナ基底の計算において, これらの変数を係数に含む先頭項は0にはならない.

このような事情により, パラメータが変数の場合と整数の場合とでは出力結果が異なる場合がある.

@itemize

@end itemize

@example

[15] ns_twistedlog.twisted_deRham(x*y*(1-x-y),a,[x,y]);

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