| version 1.2, 2000/01/16 07:55:42 |
version 1.7, 2003/06/26 13:00:11 |
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|
| %% $OpenXM$ |
%% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.6 2003/06/26 08:14:47 takayama Exp $ |
| %% usage.sm1 |
%% usage.sm1 |
| %% [(key word) |
%% [(key word) |
| %% [( ) |
%% [( ) |
|
|
| (The user cannot use the variable names h, e, H and E.) |
(The user cannot use the variable names h, e, H and E.) |
| (cf. show_ring, system_variable --- CurrentRing) |
(cf. show_ring, system_variable --- CurrentRing) |
| ( print_switch_status, switch_function) |
( print_switch_status, switch_function) |
| |
(Example: [(x,y) ring_of_differential_operators [[(Dx) 1 (Dy) 1]]) |
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( weight_vector 0] define_ring) |
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( Define the ring of differential operators Q<x,y,Dx,Dy> with the order) |
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( obtained by refining the partial order defined by the weight vector) |
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( [x,y,Dx,Dy] = [0,0,1,1] ) |
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(Example: [(x,y) ring_of_differential_operators 0 [(weightedHomogenization) 1]]) |
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( define_ring ) |
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(Example: [(x,y) ring_of_differential_operators [[(x) -1 (Dx) 1]] weight_vector) |
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( 0 [(degreeShift) [[1 0 1]]] ]) |
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( define_ring ) |
| (Example: [(x,y,z) ring_of_differential_operators (Dx,Dy) elimination_order 0] define_ring) |
(Example: [(x,y,z) ring_of_differential_operators (Dx,Dy) elimination_order 0] define_ring) |
| ( Dx,Dy, and Dz are corresponding differential operators to the ) |
( Dx,Dy, and Dz are corresponding differential operators to the ) |
| ( space variables x, y and z.) |
( space variables x, y and z.) |
|
|
| |
|
| [(ring_of_difference_operators) |
[(ring_of_difference_operators) |
| [ (string ring_of_difference_operators) |
[ (string ring_of_difference_operators) |
| |
(!!! OBSOLETE !!!) |
| ( ) |
( ) |
| (This command has not been maintained since 1996. So, there may be) |
(This command has not been maintained since 1996. So, there may be) |
| (troubles if it is used with new features of kan/sm1.) |
(troubles if it is used with new features of kan/sm1.) |
|
|
| ] |
] |
| ] putUsages |
] putUsages |
| |
|
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[(ring_of_differential_difference_operators) |
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[ ([string1 string2] ring_of_differential_difference operators) |
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(This command is used to define a ring of differential-difference operators ) |
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(with the macros define_ring, weight_vector and elimination_order.) |
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(string1 is a set of variables for differential operators.) |
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(string2 is a set of variables for difference operators.) |
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(The user cannot use the variable names h, e, H and E.) |
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(cf. show_ring, system_variable --- CurrentRing) |
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( print_switch_status, switch_function) |
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(Example: [[(x,y) (s)] ring_of_differential_difference_operators ) |
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( [[(Es) 1] [(s) 1]] weight_vector 0] define_ring) |
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( Dx and Dy are corresponding differential operators to the ) |
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( space variables x and y. Try show_ring to see the commutation) |
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( relations.) |
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] |
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] putUsages |
| |
|
| [(define_ring) |
[(define_ring) |
| [( [varlist ring_of_??? order characteristic options] define_ring) |
[( [varlist ring_of_??? order characteristic options] define_ring) |
|
|
| [(obj toVectors vec) |
[(obj toVectors vec) |
| (Convert the internal expression of vector into the array <<vec>>.) |
(Convert the internal expression of vector into the array <<vec>>.) |
| (obj can be [n [g1 ... gm]] where n is the length of the vector.) |
(obj can be [n [g1 ... gm]] where n is the length of the vector.) |
| |
$cf. [(toe_) array_of_poly] gbext $ |
| $Example 1: [(x) ring_of_polynomials 0] define_ring $ |
$Example 1: [(x) ring_of_polynomials 0] define_ring $ |
| $ (e_ + 2). toVectors :: $ |
$ (e_ + 2). toVectors :: $ |
| ( ---> [2 , 1] ) |
( ---> [2 , 1] ) |
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