OpenXM/src/k097/Doc/complex.texi - diff

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Diff for /OpenXM/src/k097/Doc/complex.texi between version 1.1 and 1.3

version 1.1, 2001/01/04 12:29:32

version 1.3, 2001/01/08 05:26:50

Line 1

%% $OpenXM$

%% $OpenXM: OpenXM/src/k097/Doc/complex.texi,v 1.2 2001/01/05 11:14:26 takayama Exp $

/*&C

\input texinfo

@iftex

Line 92

@findex Res_solv

@table @t

@item Res_solv(@var{m},@var{d})

:: $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{d} $B$N2r$r$b$H$a$k(B.

@item Res_solv(@var{m},@var{d},@var{r})

:: $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{d} $B$N2r$r$b$H$a$k(B. @var{r} $B$O(B ring.

@end table

Line 218 In(5)= Res_solv([[1,2],[3,4]],[5,0],r):

@table @t

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 240 In(5)= Res_solv([[1,2],[3,4]],[5,0],r):

Line 244 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})

:: $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{v} mod @var{j} $B$N2r$r$b$H$a$k(B.

@item Res_solv2(@var{m},@var{v},@var{j},@var{r})

:: $B0l<!ITDjJ}Dx<0(B u @var{m} =@var{v} mod @var{j} $B$N2r$r$b$H$a$k(B.

@var{r} $B$O(B ring.

Line 258 In(5)= Res_solv([[1,2],[3,4]],[5,0],r):

Line 262 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}.

@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}.

Line 363 The output implies that

Line 367 The output implies that

@table @t

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 502 In(5)= k=Kernel([[1,2],[2,4]],r); k[0]:

Line 510 In(5)= k=Kernel([[1,2],[2,4]],r); k[0]:

@table @t

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 614 In(43)=Kernel2([[0,0,0],[0,0,0]],[],r):

Line 626 In(43)=Kernel2([[0,0,0],[0,0,0]],[],r):

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 743 In(13)= Gb(m,r):

Line 759 In(13)= Gb(m,r):

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 865 In(19)=Pmat(Substitute(k2[0],t,1));

Line 885 In(19)=Pmat(Substitute(k2[0],t,1));

@table @t

@item $B;2>H(B

@code{Gb}, (m,(u,v))-$B%0%l%V%J4pDl(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 894 In(19)=Pmat(Substitute(k2[0],t,1));

Line 918 In(19)=Pmat(Substitute(k2[0],t,1));

/*&C

@menu

* changeRing::

* ChangeRing::

* GetRing::

* SetRing::

* Intersection::

* Getxvars::

* Firstn::

Line 904 In(19)=Pmat(Substitute(k2[0],t,1));

Line 926 In(19)=Pmat(Substitute(k2[0],t,1));

/*&ja

@c %%%%%%%%%%%%%%%%%%%% start changeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@c %%%%%%%%%%%%%%%%%%%% start ChangeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@node changeRing,,, $B4pK\(B $BH!?t(B

@node ChangeRing,,, $B4pK\(B $BH!?t(B

@subsection @code{changeRing}

@subsection @code{ChangeRing}

@findex changeRing

@findex ChangeRing

@table @t

@item changeRing(@var{f})

@item ChangeRing(@var{f})

:: changeRing $B$O(B @var{f} $B$NMWAG$,B0$9$k4D$r(B current ring $B$K$9$k(B.

:: ChangeRing $B$O(B @var{f} $B$NMWAG$,B0$9$k4D$r(B current ring $B$K$9$k(B.

@end table

@table @var

Line 923 true $B$+(B false

Line 945 true $B$+(B false

RingD("x,y");

f=[x+y,0];

RingD("p,q,r");

changeRing(f);

ChangeRing(f);

@end example

@c %%%%%%%%%%%%%%%%%%%% end of changeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

/*&ja

@c %%%%%%%%%%%%%%%%%%%% start of GetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@menu

* GetRing::

@end menu

@node GetRing,,, $B4pK\(B $BH!?t(B

@subsection @code{GetRing}

@findex GetRing

@table @t

@item GetRing(@var{f})

@item Files

:: @var{f} $B$NMWAG$NB0$9$k4D$rLa$9(B.

@code{lib/restriction/complex.k}

@end table

@c %%%%%%%%%%%%%%%%%%%% end of ChangeRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@table @var

@item return

$B4D(B

@item f

$B%*%V%8%'%/%H(B

@end table

@itemize @bullet

@item @var{f} $B$NMWAG$^$?$O(B @var{f} $B<+?H$NB0$9$k4D$rLa$9(B.

$B4D$,$J$$$H$-$O(B null $B$rLa$9(B.

@end itemize

@example

In(16)= RingD("x,y");

In(17)= r = GetRing([x^2,0,1]);

@end example

@table @t

@item $B;2>H(B

@code{SetRing}, @code{ChangeRing}.

@end table

@c %%%%%%%%%%%%%%%%%%%% end of GetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

/*&ja

@c %%%%%%%%%%%%%%%%%%%% start of SetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@menu

* SetRing::

@end menu

@node SetRing,,, $B4pK\(B $BH!?t(B

@subsection @code{SetRing}

@findex SetRing

@table @t

@item SetRing(@var{r})

:: Current ring $B$r(B @var{r} $B$KJQ99$9$k(B.

@end table

@table @var

@item return

$B$J$7(B

@item r

$B4D(B

@end table

@itemize @bullet

@item Current ring $B$r(B @var{r} $B$KJQ99$9$k(B.

@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 $B;2>H(B

@code{GetRing}, @code{ChangeRing}, @code{DC}.

@end table

@c %%%%%%%%%%%%%%%%%%%% end of SetRing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

/*&ja

@c %%%%%%%%%%%%%%%%%%%% start of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@menu

Line 1043 In(33)=Intersection(mm,nn):

Line 995 In(33)=Intersection(mm,nn):

@table @t

@item $B;2>H(B

@item Files

@code{lib/restriction/complex.k}

@end table

@c %%%%%%%%%%%%%%%%%%%% end of Intersection %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 1108 In(5)=Getxvars():

Line 1061 In(5)=Getxvars():

@table @t

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Line 1197 In(17)= Firstn(mm,2):

Line 1152 In(17)= Firstn(mm,2):

@table @t

@item $B;2>H(B

@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 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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