version 1.11, 2003/07/27 13:18:46 |
version 1.13, 2003/07/28 01:36:36 |
|
|
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.10 2003/05/20 23:25:28 takayama Exp $ */ |
/*$OpenXM: OpenXM/src/asir-contrib/packages/doc/sm1.oxweave,v 1.12 2003/07/28 01:17:39 takayama Exp $ */ |
|
|
/*&C-texi |
/*&C-texi |
@c DO NOT EDIT THIS FILE oxphc.texi |
@c DO NOT EDIT THIS FILE oxphc.texi |
Line 109 See the appendix. |
|
Line 109 See the appendix. |
|
* sm1.rank:: |
* sm1.rank:: |
* sm1.auto_reduce:: |
* sm1.auto_reduce:: |
* sm1.slope:: |
* sm1.slope:: |
* sm1.gb_d:: |
|
* sm1.syz_d:: |
|
* sm1.ahg:: |
* sm1.ahg:: |
* sm1.bfunction:: |
* sm1.bfunction:: |
* sm1.generalized_bfunction:: |
* sm1.generalized_bfunction:: |
|
|
/*&eg-texi |
/*&eg-texi |
@c sort-sm1.gb |
@c sort-sm1.gb |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb_d,,, SM1 Functions |
|
@subsection @code{sm1.gb} |
@subsection @code{sm1.gb} |
@findex sm1.gb |
@findex sm1.gb |
@findex sm1.gb_d |
@findex sm1.gb_d |
|
|
/*&jp-texi |
/*&jp-texi |
@c sort-sm1.gb |
@c sort-sm1.gb |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb,,, SM1 Functions |
@node sm1.gb_d,,, SM1 Functions |
|
@subsection @code{sm1.gb} |
@subsection @code{sm1.gb} |
@findex sm1.gb |
@findex sm1.gb |
@findex sm1.gb_d |
@findex sm1.gb_d |
Line 1327 basic_plus(basic_times(basic_power(x,4),1),basic_times |
|
Line 1323 basic_plus(basic_times(basic_power(x,4),1),basic_times |
|
/*&eg-texi |
/*&eg-texi |
@c sort-sm1.syz |
@c sort-sm1.syz |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz_d,,, SM1 Functions |
|
@subsection @code{sm1.syz} |
@subsection @code{sm1.syz} |
@findex sm1.syz |
@findex sm1.syz |
@findex sm1.syz_d |
@findex sm1.syz_d |
Line 1354 Here @var{s} is the syzygy of @var{f} in the ring of d |
|
Line 1349 Here @var{s} is the syzygy of @var{f} in the ring of d |
|
operators with the variable @var{v}. |
operators with the variable @var{v}. |
@var{g} is a Groebner basis of @var{f} with the weight vector @var{w}, |
@var{g} is a Groebner basis of @var{f} with the weight vector @var{w}, |
and @var{m} is a matrix that translates the input matrix @var{f} to the Gr\"obner |
and @var{m} is a matrix that translates the input matrix @var{f} to the Gr\"obner |
basis @var {g}. |
basis @var{g}. |
@var{t} is the syzygy of the Gr\"obner basis @var{g}. |
@var{t} is the syzygy of the Gr\"obner basis @var{g}. |
In summary, @var{g} = @var{m} @var{f} and |
In summary, @var{g} = @var{m} @var{f} and |
@var{s} @var{f} = 0 hold as matrices. |
@var{s} @var{f} = 0 hold as matrices. |
Line 1371 In summary, @var{g} = @var{m} @var{f} and |
|
Line 1366 In summary, @var{g} = @var{m} @var{f} and |
|
/*&jp-texi |
/*&jp-texi |
@c sort-sm1.syz |
@c sort-sm1.syz |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz,,, SM1 Functions |
@node sm1.syz_d,,, SM1 Functions |
|
@subsection @code{sm1.syz} |
@subsection @code{sm1.syz} |
@findex sm1.syz |
@findex sm1.syz |
@findex sm1.syz_d |
@findex sm1.syz_d |