version 1.5, 2003/08/04 11:42:42 |
version 1.6, 2003/08/13 03:52:25 |
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% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.4 2003/07/30 09:00:51 takayama Exp $ |
% $OpenXM: OpenXM/src/kan96xx/Doc/ecart.sm1,v 1.5 2003/08/04 11:42:42 takayama Exp $ |
%[(parse) (hol.sm1) pushfile] extension |
%[(parse) (hol.sm1) pushfile] extension |
%[(parse) (appell.sm1) pushfile] extension |
%[(parse) (appell.sm1) pushfile] extension |
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} { } ifelse |
} { } ifelse |
wv isInteger { |
wv isInteger { |
[v ring_of_differential_operators |
[v ring_of_differential_operators |
[ v ecart.wv1 v ecart.wv2 ] weight_vector |
% [ v ecart.wv1 v ecart.wv2 ] weight_vector |
gb.characteristic |
gb.characteristic |
opt |
opt |
] define_ring |
] define_ring |
}{ |
}{ |
degreeShift isInteger { |
degreeShift isInteger { |
[v ring_of_differential_operators |
[v ring_of_differential_operators |
[v ecart.wv1 v ecart.wv2] wv join weight_vector |
% [v ecart.wv1 v ecart.wv2] wv join weight_vector |
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wv weight_vector |
gb.characteristic |
gb.characteristic |
opt |
opt |
] define_ring |
] define_ring |
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}{ |
}{ |
[v ring_of_differential_operators |
[v ring_of_differential_operators |
[v ecart.wv1 v ecart.wv2] wv join weight_vector |
% [v ecart.wv1 v ecart.wv2] wv join weight_vector |
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wv weight_vector |
gb.characteristic |
gb.characteristic |
[(degreeShift) degreeShift] opt join |
[(degreeShift) degreeShift] opt join |
] define_ring |
] define_ring |
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%%% Enf of the preprocess |
%%% Enf of the preprocess |
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ecart.gb.verbose { |
ecart.gb.verbose { |
(The first and the second weight vectors are automatically set as follows) |
(The first and the second weight vectors for automatic homogenization: ) |
message |
message |
v ecart.wv1 message |
v ecart.wv1 message |
v ecart.wv2 message |
v ecart.wv2 message |
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( not to dehomogenize and homogenize) |
( not to dehomogenize and homogenize) |
( ) |
( ) |
$Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) $ |
$Example 1: [ [( (x Dx)^2 + (y Dy)^2 -1) ( x y Dx Dy -1)] (x,y) $ |
$ [ [ (Dx) 1 ] ] ] ecart.gb pmat ; $ |
$ [ [ (Dx) 1 ] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecart.gb pmat ; $ |
(Example 2: ) |
(Example 2: ) |
(To put H and h=1, type in, e.g., ) |
(To put H and h=1, type in, e.g., ) |
$ [ [(2 x Dx + 3 y Dy+6) (2 y Dx + 3 x^2 Dy)] (x,y) $ |
$ [ [(2 x Dx + 3 y Dy+6) (2 y Dx + 3 x^2 Dy)] (x,y) $ |
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$ [ [ (Dx) 1 (Dy) 1] ] ] ecart.gb pmat ; $ |
$ [ [ (Dx) 1 (Dy) 1] ] ] ecart.gb pmat ; $ |
( ) |
( ) |
$Example 4: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $ |
$Example 4: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $ |
$ [ [ (x) -1 (y) -1] ] ] ecart.gb pmat ; $ |
$ [ [ (x) -1 (y) -1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1]] ] ecart.gb pmat ; $ |
( ) |
( ) |
$Example 5: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $ |
$Example 5: [[ [(x^2) (y+x)] [(x+y) (y^3)] [(2 x^2+x y) (y+x+x y^3)]] (x,y) $ |
$ [ [ (x) -1 (y) -1] ] [[0 1] [-3 1] ] ] ecart.gb pmat ; $ |
$ [ [(Dx) 1 (Dy) 1] [(x) -1 (y) -1 (Dx) 1 (Dy) 1] ] [[0 1] [-3 1] ] ] ecart.gb pmat ; (buggy infinite loop)$ |
( ) |
( ) |
(cf. gb, groebner, ecart.syz, ecart.begin, ecart.end, ecart.homogenize01, ) |
(cf. gb, groebner, ecart.syz, ecart.begin, ecart.end, ecart.homogenize01, ) |
( ecart.dehomogenize, ecart.dehomogenizeH) |
( ecart.dehomogenize, ecart.dehomogenizeH) |
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/i set |
/i set |
vv i get . /tt set |
vv i get . /tt set |
tt (1). add init (1). eq { } |
tt (1). add init (1). eq { } |
{ [vv i get ( is larger than 1) vv i get] cat error} ifelse |
{ [vv i get ( is larger than 1 ) ] cat error} ifelse |
} for |
} for |
/arg1 1 def |
/arg1 1 def |
] pop |
] pop |