=================================================================== RCS file: /home/cvs/OpenXM/src/k097/Doc/complex.texi,v retrieving revision 1.2 retrieving revision 1.4 diff -u -p -r1.2 -r1.4 --- OpenXM/src/k097/Doc/complex.texi 2001/01/05 11:14:26 1.2 +++ OpenXM/src/k097/Doc/complex.texi 2001/01/13 01:17:36 1.4 @@ -1,4 +1,4 @@ -%% $OpenXM: OpenXM/src/k097/Doc/complex.texi,v 1.1 2001/01/04 12:29:32 takayama Exp $ +%% $OpenXM: OpenXM/src/k097/Doc/complex.texi,v 1.3 2001/01/08 05:26:50 takayama Exp $ /*&C \input texinfo @iftex @@ -92,7 +92,7 @@ @findex Res_solv @table @t @item Res_solv(@var{m},@var{d}) -:: 一次不定方程式 u @var{m} =@var{d} の解をもとめる. +:: 一次不定方程式 u @var{m} =@var{d} の解をもとめる. @item Res_solv(@var{m},@var{d},@var{r}) :: 一次不定方程式 u @var{m} =@var{d} の解をもとめる. @var{r} は ring. @end table @@ -218,14 +218,18 @@ In(5)= Res_solv([[1,2],[3,4]],[5,0],r): @table @t @item 参照 @code{Res_solv_h}, @code{Kernel}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Res_solv %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also @code{Res_solv_h}, @code{Kernel}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Res_solv %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -240,7 +244,7 @@ In(5)= Res_solv([[1,2],[3,4]],[5,0],r): @findex Res_solv2 @table @t @item Res_solv2(@var{m},@var{v},@var{j}) -:: 一次不定方程式 u @var{m} =@var{v} mod @var{j} の解をもとめる. +:: 一次不定方程式 u @var{m} =@var{v} mod @var{j} の解をもとめる. @item Res_solv2(@var{m},@var{v},@var{j},@var{r}) :: 一次不定方程式 u @var{m} =@var{v} mod @var{j} の解をもとめる. @var{r} は ring. @@ -258,7 +262,7 @@ In(5)= Res_solv([[1,2],[3,4]],[5,0],r): @table @t @item Res_solv2(@var{m},@var{v},@var{j}) :: Find a solution u of the linear indefinite equation u @var{m} =@var{v} - mod @var{j}. + mod @var{j}. @item Res_solv2(@var{m},@var{v},@var{j},@var{r}) :: Find a solution u of the linear indefinite equation u @var{m} =@var{v} mod @var{j}. @@ -363,14 +367,18 @@ The output implies that @table @t @item 参照 @code{Res_solv2_h}, @code{Kernel2}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Res_solv2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also @code{Res_solv2_h}, @code{Kernel2}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Res_solv2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -502,14 +510,18 @@ In(5)= k=Kernel([[1,2],[2,4]],r); k[0]: @table @t @item 参照 @code{Kernel_h}, @code{Res_solv}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Kernel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also @code{Kernel_h}, @code{Res_solv}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Kernel %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -614,15 +626,19 @@ In(43)=Kernel2([[0,0,0],[0,0,0]],[],r): @item 参照 @code{Kernel2_h}, @code{Res_solv2}, @code{GetRing}, @code{SetRing}, @code{Kernel}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Kernel2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also @code{Kernel2_h}, @code{Res_solv2}, @code{GetRing}, @code{SetRing}, @code{Kernel} +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Kernel2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -743,15 +759,19 @@ In(13)= Gb(m,r): @item 参照 @code{Gb_h}, @code{Kernel}, @code{Res_solv}, @code{RingD}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Gb %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also @code{Gb_h}, @code{Kernel}, @code{Res_solv}, @code{RingD}, @code{GetRing}, @code{SetRing}. +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Gb %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -865,14 +885,18 @@ In(19)=Pmat(Substitute(k2[0],t,1)); @table @t @item 参照 @code{Gb}, (m,(u,v))-グレブナ基底 +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Res_shiftMatrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also @code{Gb}, (m,(u,v))-Grobner basis +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Res_shiftMatrix %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -895,8 +919,6 @@ In(19)=Pmat(Substitute(k2[0],t,1)); /*&C @menu * ChangeRing:: -* GetRing:: -* SetRing:: * Intersection:: * Getxvars:: * Firstn:: @@ -925,85 +947,15 @@ true か false RingD("p,q,r"); ChangeRing(f); @end example -@c %%%%%%%%%%%%%%%%%%%% end of ChangeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*/ -/*&ja -@c %%%%%%%%%%%%%%%%%%%% start of GetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -@menu -* GetRing:: -@end menu -@node GetRing,,, 基本 函数 -@subsection @code{GetRing} -@findex GetRing @table @t -@item GetRing(@var{f}) -:: @var{f} の要素の属する環を戻す. +@item Files + @code{lib/restriction/complex.k} @end table - -@table @var -@item return -環 -@item f -オブジェクト -@end table - -@itemize @bullet -@item @var{f} の要素または @var{f} 自身の属する環を戻す. -環がないときは null を戻す. -@end itemize - -@example -In(16)= RingD("x,y"); -In(17)= r = GetRing([x^2,0,1]); -@end example - -@table @t -@item 参照 - @code{SetRing}, @code{ChangeRing}. -@end table -@c %%%%%%%%%%%%%%%%%%%% end of GetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +@c %%%%%%%%%%%%%%%%%%%% end of ChangeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ -/*&ja -@c %%%%%%%%%%%%%%%%%%%% start of SetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -@menu -* SetRing:: -@end menu -@node SetRing,,, 基本 函数 -@subsection @code{SetRing} -@findex SetRing -@table @t -@item SetRing(@var{r}) -:: Current ring を @var{r} に変更する. -@end table -@table @var -@item return -なし -@item r -環 -@end table - -@itemize @bullet -@item Current ring を @var{r} に変更する. -@end itemize - -@example -In(16)= RingD("x,y"); -In(17)= f=[x^2,0,1]; r = GetRing(f); -In(19)= RingD("p,q"); -In(20)= SetRing(r); -In(21)= f = DC(f,"polynomial"); -@end example - -@table @t -@item 参照 - @code{GetRing}, @code{ChangeRing}, @code{DC}. -@end table -@c %%%%%%%%%%%%%%%%%%%% end of SetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -*/ - /*&ja @c %%%%%%%%%%%%%%%%%%%% start of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @menu @@ -1043,7 +995,8 @@ In(33)=Intersection(mm,nn): @table @t @item 参照 - +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -1108,15 +1061,17 @@ In(5)=Getxvars(): @table @t @item 参照 - +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Getxvars %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference - +@item See also +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Getxvars %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ @@ -1197,17 +1152,113 @@ In(17)= Firstn(mm,2): @table @t @item 参照 - +@item Files + @code{lib/restriction/complex.k} @end table @c %%%%%%%%%%%%%%%%%%%% end of Firstn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&en @table @t -@item Reference +@item See also +@item Files + @code{lib/restriction/complex.k} + @end table @c %%%%%%%%%%%%%%%%%%%% end of Firstn %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +*/ + +/*&ja +@c %%%%%%%%%%%%%%%%%%%% start of GKZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +@menu +* GKZ:: +@end menu +@node GKZ,,, 基本 函数 +@subsection @code{GKZ} +@findex GKZ +@table @t +@item GKZ(@var{a},@var{b}) +:: 行列 @var{a} と ベクトル @var{b} で定まる, GKZ hypergeometric system を戻す. +@end table + +@table @var +@item return +D のイデアルの生成元 +@item a +整数行列 +@item b +整数ベクトル +@end table + +@itemize @bullet +@item 行列 @var{a} と ベクトル @var{b} で定まる, GKZ hypergeometric system を戻す. +@item Gelfand, Kapranov, Zelevinski の超幾何微分方程式を戻す. +@end itemize + +@example +In(3)= GKZ([[1,1,1,1],[0,1,2,3]],[-1,-2]): +[ x1*Dx1+x2*Dx2+x3*Dx3+x4*Dx4+1 , x2*Dx2+2*x3*Dx3+3*x4*Dx4+2 , Dx2^2-Dx1*Dx3 , -Dx3^2+Dx2*Dx4 , Dx2*Dx3-Dx1*Dx4 ] +@end example + +@table @t +@item 参照 +@item Files + @code{lib/restriction/demo2.k} +@end table +@c %%%%%%%%%%%%%%%%%%%% end of GKZ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +*/ + +/*&ja +@c %%%%%%%%%%%%%%%%%%%% start of Slope %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +@menu +* Slope:: +@end menu +@node Slope,,, 基本 函数 +@subsection @code{Slope} +@findex Slope +@table @t +@item Slope(@var{i},@var{v},@var{f},@var{v}) +:: 微分方程式系 @var{i} の slope の集合をもとめる. +@end table + +@table @var +@item return +Slope の集合とそれを与える, weight vectors. +@item i +D のイデアルの生成元 +@item v +空間変数 +@item f +F-filtration を与える weight vector (0,...,0,1,...,1). +@item v +V-filtration を与える weight vector. +たとえば (0,...,0,-1,0,...,0,1). +@end table + +@itemize @bullet +@item @var{i} の x_i = 0 にそった, 原点での slope の全体をもとめる. +@item 計算には Assi, Castro, Granger のアルゴリズムを用いる. +@item Geometric slope を計算するため, radical の計算をおこなっている. +これには ox_asir を用いている. +@end itemize + +@example +In(13)= a=GKZ([[1,3,7]],[-30]); +In(14)= a: +[ x1*Dx1+3*x2*Dx2+7*x3*Dx3+30 , -Dx1^3+Dx2 , -Dx1*Dx2^2+Dx3 , -Dx2^3+Dx1^2*Dx3 ] +In(15)= Slope(a,[x1,x2,x3],[0,0,0,1,1,1],[0,0,-1,0,0,1]): +[ [ (3)/(4) , [ 0 , 0 , -4 , 3 , 3 , 7 ] ] ] + + +@end example + +@table @t +@item 参照 +@item Files + @code{lib/restriction/demo2.k} +@end table +@c %%%%%%%%%%%%%%%%%%%% end of Slope %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ /*&ja