=================================================================== RCS file: /home/cvs/OpenXM/src/kan96xx/Kan/usage.sm1,v retrieving revision 1.1.1.1 retrieving revision 1.8 diff -u -p -r1.1.1.1 -r1.8 --- OpenXM/src/kan96xx/Kan/usage.sm1 1999/10/08 02:12:02 1.1.1.1 +++ OpenXM/src/kan96xx/Kan/usage.sm1 2004/09/10 22:21:27 1.8 @@ -1,3 +1,4 @@ +%% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.7 2003/06/26 13:00:11 takayama Exp $ %% usage.sm1 %% [(key word) %% [( ) @@ -102,6 +103,16 @@ (The user cannot use the variable names h, e, H and E.) (cf. show_ring, system_variable --- CurrentRing) ( print_switch_status, switch_function) + (Example: [(x,y) ring_of_differential_operators [[(Dx) 1 (Dy) 1]]) + ( weight_vector 0] define_ring) + ( Define the ring of differential operators Q with the order) + ( obtained by refining the partial order defined by the weight vector) + ( [x,y,Dx,Dy] = [0,0,1,1] ) + (Example: [(x,y) ring_of_differential_operators 0 [(weightedHomogenization) 1]]) + ( define_ring ) + (Example: [(x,y) ring_of_differential_operators [[(x) -1 (Dx) 1]] weight_vector) + ( 0 [(degreeShift) [[1 0 1]]] ]) + ( 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 ) ( space variables x, y and z.) @@ -110,6 +121,7 @@ [(ring_of_difference_operators) [ (string ring_of_difference_operators) + (!!! OBSOLETE !!!) ( ) (This command has not been maintained since 1996. So, there may be) (troubles if it is used with new features of kan/sm1.) @@ -145,6 +157,22 @@ ] ] putUsages +[(ring_of_differential_difference_operators) + [ ([string1 string2] ring_of_differential_difference operators) + (This command is used to define a ring of differential-difference operators ) + (with the macros define_ring, weight_vector and elimination_order.) + (string1 is a set of variables for differential operators.) + (string2 is a set of variables for difference operators.) + (The user cannot use the variable names h, e, H and E.) + (cf. show_ring, system_variable --- CurrentRing) + ( print_switch_status, switch_function) + (Example: [[(x,y) (s)] ring_of_differential_difference_operators ) + ( [[(Es) 1] [(s) 1]] weight_vector 0] define_ring) + ( Dx and Dy are corresponding differential operators to the ) + ( space variables x and y. Try show_ring to see the commutation) + ( relations.) + ] +] putUsages [(define_ring) [( [varlist ring_of_??? order characteristic options] define_ring) @@ -157,7 +185,7 @@ ( <> ring_of_polynomials, ring_of_differential_operators, ) ( ring_of_difference_operators) ( <> elimination_order, weight_vector) - ( ring_def,ring , << ,, >>) + ( ring_def,ring , << __ >>) ] ] putUsages @@ -277,6 +305,7 @@ def [(obj toVectors vec) (Convert the internal expression of vector into the array <>.) (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 $ $ (e_ + 2). toVectors :: $ ( ---> [2 , 1] )