| version 1.1.1.1, 1999/10/08 02:12:02 |
version 1.13, 2013/08/30 01:00:15 |
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%% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.12 2005/06/15 02:22:51 takayama Exp $ |
| %% usage.sm1 |
%% usage.sm1 |
| %% [(key word) |
%% [(key word) |
| %% [( ) |
%% [( ) |
|
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| (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) |
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(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.) |
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| [(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.) |
|
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| ] |
] |
| ] 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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(Example: contiguity of 1F1. Eb b = (b-1) Eb) |
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( [ [(x) (a,b)] ring_of_differential_difference_operators ) |
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( [[(Dx) 1]] weight_vector 0] define_ring ) |
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( [ ( x Dx (x Dx+b-1) -x (x Dx+a) ). ) |
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( ( (x Dx +b-1) - (b-1) Eb ). ] /ff set ) |
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( ff {dehomogenize homogenize} map /ff2 set ) |
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( [ff2] groebner /gg set ) |
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( gg dehomogenize 0 get /gg set ) |
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( gg [(Dx)] eliminatev /gg2 set ) |
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( gg2 pmat ) |
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] |
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] putUsages |
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| [(define_ring) |
[(define_ring) |
| [( [varlist ring_of_??? order characteristic options] define_ring) |
[( [varlist ring_of_??? order characteristic options] define_ring) |
| ( Pointer to the ring.) |
( Pointer to the ring.) |
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| ( <<ring_of_???>> ring_of_polynomials, ring_of_differential_operators, ) |
( <<ring_of_???>> ring_of_polynomials, ring_of_differential_operators, ) |
| ( ring_of_difference_operators) |
( ring_of_difference_operators) |
| ( <<order>> elimination_order, weight_vector) |
( <<order>> elimination_order, weight_vector) |
| ( ring_def,ring , << ,, >>) |
( ring_def,ring , << __ >>) |
| ] |
] |
| ] putUsages |
] putUsages |
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| [(join) |
[(join) |
| [(list1 list2 join list3) |
[(list1 list2 join list3) |
| (Ex. [1 2] [3 [4 (ab)]] join [1 2 3 [4 (ab)]]) |
(Ex. [1 2] [3 [4 (ab)]] join [1 2 3 [4 (ab)]]) |
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(Note: Join should use for arrays. It works for list too,) |
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( but it does not copy cells. cf. cons) |
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( So, it might generate looped lists or destroy other lists.) |
| ] |
] |
| ] putUsages |
] putUsages |
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| [(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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| ]] putUsages |
]] putUsages |
| [(toVectors2) |
[(toVectors2) |
| [(Remained for the compatibility. cf. toVectors) |
[(Remained for the compatibility. cf. toVectors) |
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]] putUsages |
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|
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[(extension-examples) |
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[ |
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$putAttributeList$ |
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$ [(putAttributeList) [[(x+y-1) (x-y-2)] (x,y)] $ |
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$ [(needSyz) 1 (sugar) 1]] extension /myarg set $ |
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$ [(getAttributeList) myarg] extension :: $ |
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$ [(getAttribute) myarg (sugar)] extension :: $ |
| ]] putUsages |
]] putUsages |
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|
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