Annotation of OpenXM/src/kan96xx/Kan/usage.sm1, Revision 1.5
1.5 ! takayama 1: %% $OpenXM: OpenXM/src/kan96xx/Kan/usage.sm1,v 1.4 2002/02/09 06:21:02 takayama Exp $
1.1 maekawa 2: %% usage.sm1
3: %% [(key word)
4: %% [( )
5: %% ( )
6: %% ]
7: %% ] putUsages
8: [(putUsages)
9: [$[(key word) [(explanation line 1) (explanation line 2) ... ]] putUsages$ ]
10: ] putUsages
11:
12: [(;)
13: [(Output the prompt sm1>)]
14: ] putUsages
15:
16: [(::)
17: [(Pop the top of the stack and print it.)]
18: ] putUsages
19:
20: [(Libraries)
21: [
22: (Doc/appell.sm1 : It generates Appell differential equations.)
23: (Doc/bfunction.sm1: Computing the b-function of a given polynomial)
24: ( by using Groebner basis. Written by T.Oaku.)
25: (Doc/factor-a.sm1: A sample interface to factor polynomials by risa/asir.)
26: (Doc/gkz.sm1 : It generates GKZ systems for given A and b.)
27: (Doc/hol.sm1 : Basic package for holonomic systems. Holonomic rank,)
28: ( characteristic ideal, singular locus.)
29: (Doc/resol0.sm1 : Constructing Schreyer resolutions. tower.sm1, tower-sugar.sm1)
30: (Doc/rest0.sm1 : Computing the restriction (inverse image) as a complex.)
31: ( This package is under developement by T.Oaku.)
32: ( cf. restall_s.sm1, resol0.sm1)
33: ]
34: ] putUsages
35: /Loadall {
36: [(parse) (bfunction.sm1) pushfile] extension
37: [(parse) (hol.sm1) pushfile] extension
38: [(parse) (gkz.sm1) pushfile] extension
39: [(parse) (appell.sm1)pushfile] extension
40: [(parse) (resol0.sm1)pushfile] extension
41: } def
42: [(Loadall)
43: [(Loadall loads the packages bfunction.sm1, hol.sm1, gkz.sm1, appell.sm1,)
44: (resol0.sm1)
45: ]] putUsages
46:
47: [(Version)
48: [(Packages must be loaded in a proper version of kan/sm1.)
49: (It can be checked as follows.)
50: (Example: )
51: ( /factor-a.version (2.981101) def)
52: ( factor-a.version [(Version)] system_variable gt )
53: $ { (This package requires the latest version of kan/sm1) message$
54: $ (Please get it from http://www.math.kobe-u.ac.jp/KAN) message$
55: $ error$
56: $ } { } ifelse$
57: ]]putUsages
58:
59:
60: [(bugs)
61: [(All known bugs are fixed.)
62: ]
63: ] putUsages
64:
65: [(factor)
66: [(Load Doc/factor-a.sm1, then factorization can be computed by invoking )
67: (asir, of which ftp cite is at http://www.math.kobe-u.ac.jp)
68: ]
69: ] putUsages
70:
71:
72: [(message)
73: [ (string message)
74: (Output the string to the screen with the newline.)
75: (cf. messagen.)
76: $Example: (Hello world) message$
77: ]
78: ] putUsages
79:
80: [(messagen)
81: [ (string messagen)
82: (Output the string to the screen without the newline.)
83: (cf. message.)
84: $Example: (Hello world) messagen$
85: ]
86: ] putUsages
87:
88: [(ring_of_polynomials)
89: [ (string ring_of_polynomials)
90: (This command is used to define a ring of polynomials with the macros)
91: (define_ring, weight_vector and elimination_order.)
92: (The user cannot use the variable names h, e, H and E.)
93: (cf. show_ring, system_variable --- CurrentRing)
94: ( print_switch_status, switch_function)
95: (Example: [(x,y,z) ring_of_polynomials (x,y) elimination_order 0] define_ring)
96: ]
97: ] putUsages
98:
99: [(ring_of_differential_operators)
100: [ (string ring_of_differential_operators)
101: (This command is used to define a ring of differential operators )
102: (with the macros define_ring, weight_vector and elimination_order.)
103: (The user cannot use the variable names h, e, H and E.)
104: (cf. show_ring, system_variable --- CurrentRing)
105: ( print_switch_status, switch_function)
1.5 ! takayama 106: (Example: [(x,y) ring_of_differential_operators [[(Dx) 1 (Dy) 1]])
! 107: ( weight_vector 0] define_ring)
! 108: ( Define the ring of differential operators Q<x,y,Dx,Dy> with the order)
! 109: ( obtained by refining the partial order defined by the weight vector)
! 110: ( [x,y,Dx,Dy] = [0,0,1,1] )
! 111: (Example: [(x,y) ring_of_differential_operators 0 [(weightedHomogenization) 1]])
! 112: ( define_ring )
1.1 maekawa 113: (Example: [(x,y,z) ring_of_differential_operators (Dx,Dy) elimination_order 0] define_ring)
114: ( Dx,Dy, and Dz are corresponding differential operators to the )
115: ( space variables x, y and z.)
116: ]
117: ] putUsages
118:
119: [(ring_of_difference_operators)
120: [ (string ring_of_difference_operators)
1.4 takayama 121: (!!! OBSOLETE !!!)
1.1 maekawa 122: ( )
123: (This command has not been maintained since 1996. So, there may be)
124: (troubles if it is used with new features of kan/sm1.)
125: ( )
126: (This command is used to define a ring of difference operators )
127: (with the macros define_ring, weight_vector and elimination_order.)
128: (The user cannot use the variable names h, e, H and E.)
129: (cf. show_ring, system_variable --- CurrentRing)
130: ( print_switch_status, switch_function)
131: (Example: [(x,y,z) ring_of_difference_operators (Ex,Ey) elimination_order 0] define_ring)
132: ( Ex,Ey, and Ez are corresponding difference operators to the )
133: ( space variables x, y and z ( Ex x = (x+1) Ex).)
134: ]
135: ] putUsages
136:
137:
138: [(ring_of_q_difference_operators)
139: [ (string ring_of_q_difference_operators)
140: ( )
141: (This command has not been maintained since 1996. So, there may be)
142: (troubles if it is used with new features of kan/sm1.)
143: ( )
144: (This command is used to define a ring of q-difference operators )
145: (with the macros define_qring, weight_vector and elimination_order.)
146: (Note that you should use this macro with define_qring instead of)
147: (define_ring.)
148: (The user cannot use the variable names h, e, q and E.)
149: (cf. show_ring, system_variable --- CurrentRing)
150: ( print_switch_status, switch_function)
151: (Example: [(x,y,z) ring_of_q_difference_operators (Qx,Qy) elimination_order 0] define_qring)
152: ( Qx,Qy, and Qz are corresponding q-difference operators to the )
153: ( space variables x, y and z ( Qx x = (q) x Q).)
154: ]
155: ] putUsages
156:
1.4 takayama 157: [(ring_of_differential_difference_operators)
158: [ ([string1 string2] ring_of_differential_difference operators)
159: (This command is used to define a ring of differential-difference operators )
160: (with the macros define_ring, weight_vector and elimination_order.)
161: (string1 is a set of variables for differential operators.)
162: (string2 is a set of variables for difference operators.)
163: (The user cannot use the variable names h, e, H and E.)
164: (cf. show_ring, system_variable --- CurrentRing)
165: ( print_switch_status, switch_function)
166: (Example: [[(x,y) (s)] ring_of_differential_difference_operators )
167: ( [[(Es) 1] [(s) 1]] weight_vector 0] define_ring)
168: ( Dx and Dy are corresponding differential operators to the )
169: ( space variables x and y. Try show_ring to see the commutation)
170: ( relations.)
171: ]
172: ] putUsages
1.1 maekawa 173:
174: [(define_ring)
175: [( [varlist ring_of_??? order characteristic options] define_ring)
176: ( Pointer to the ring.)
177: (Example: [(x,y,z) ring_of_polynomials [[(x) 100 (y) 10 (z) 1]] weight_vector)
178: ( 11] define_qring )
179: (Example: [(x,y) ring_of_polynomials [[(x) 1]] weight_vector 0 ] define_ring)
180: ( /R set)
181: (cf. define_qring, set_up_ring@ <coefficient ring>)
182: ( <<ring_of_???>> ring_of_polynomials, ring_of_differential_operators, )
183: ( ring_of_difference_operators)
184: ( <<order>> elimination_order, weight_vector)
185: ( ring_def,ring , << ,, >>)
186: ]
187: ] putUsages
188:
189:
190: [(.)
191: [(string . polynomial)
192: (Parse the string as a polynomial in the current ring and put it on the stack)
193: (Example ( (x+2)^3 ) .)
194: ]
195: ] putUsages
196:
197: [(evenQ)
198: [ (number evenQ bool)
199: ]
200: ] putUsages
201:
202: [(reverse)
203: [ (array reverse reversed_array)
204: ]
205: ] putUsages
206:
207: [(memberQ)
208: [(element array(list) memberQ bool)
209: ]
210: ] putUsages
211:
212: [(transpose)
213: [( matrix transpose transposed_matrix)
214: ]
215: ] putUsages
216:
217: [(timer)
218: [( { codes } timer )
219: (It outputs the execution time to execute << codes >>.)
220: (If you type in ctrl-C while you are executing this macro,)
221: (you need to type in set_timer after you type in ctrl-C to reset)
222: (the timer.)
223: ]] putUsages
224:
225: [(complement)
226: [( set universal_set complement complement_set)
227: (Example: [1 2] [3 4 1 2 5] complement ::)
228: ]
229: ] putUsages
230:
231: [(pushVariables)
232: [ (varlist pushVariables pushed-variables)
233: (The macro is used to define local variables in a macro.)
234: (Example : /foo { )
235: ( /arg1 set )
236: ( [/abc /cd] pushVariables )
237: ( [ /abc arg1 def )
238: ( /cd abc 1 add def )
239: ( /arg1 cd def )
240: ( ] pop )
241: ( popVariables)
242: ( arg1 )
243: ( } def )
244: ( 10 foo :: returns 11 )
245: ( In the example, abc and cd are local variables.)
246: ]
247: ] putUsages
248:
249:
250:
251: /@@@.global.usage1
252: [(@@@. is the prefix for the global control variables and global functions.)
253: (@@@.quiet : 1 ---> quiet mode, 0 ---> not. cf. sm1 -q)
254: (@@@.esymbol : (e_) is the standard value. It is used to express)
255: ( vectors internally. cf. fromVectors, toVectors)
256: (@@@.Dsymbol : (D) is the standard value for differential operator.)
257: ( cf. ring_of_differential_operators)
258: (@@@.diffEsymbol : (E) is the standard value for difference operator.)
259: ( cf. ring_of_difference_operators)
260: (@@@.Qsymbol : (Q) is the standard value for q-difference operator.)
261: ( cf. ring_of_qdifference_operators)
262: ]
263: def
264: [(@@@.quiet) @@@.global.usage1] putUsages
265: [(@@@.Dsymbol) @@@.global.usage1] putUsages
266: [(@@@.diffEsymbol) @@@.global.usage1] putUsages
267: [(@@@.Qsymbol) @@@.global.usage1] putUsages
268: [(@@@.esymbol) @@@.global.usage1] putUsages
269:
270: [(join)
271: [(list1 list2 join list3)
272: (Ex. [1 2] [3 [4 (ab)]] join [1 2 3 [4 (ab)]])
273: ]
274: ] putUsages
275:
276: [(not)
277: [(int not int)
278: (1 not 0)
279: (0 not 1)
280: ]
281: ] putUsages
282:
283: [(append)
284: [(list1 obj2 append list3)
285: (Ex. [1 2] 3 append [1 2 3])
286: ]
287: ] putUsages
288:
289: [(null)
290: [(<<null>> returns null object)]
291: ] putUsages
292:
293: [(oxasir)
294: [(ox_asir is an asir server which is complient to open xxx protocol.)
295: (This module is necessary for efficient execution factorization )
296: (of b-functions in annfs, deRham. cf. lib/oxasir.sm1)
297: (ox_asir has not yet been put on the ftp cite. 12/17, 1998.)
298: ]
299: ] putUsages
300:
301: [(toVectors)
302: [(obj toVectors vec)
303: (Convert the internal expression of vector into the array <<vec>>.)
304: (obj can be [n [g1 ... gm]] where n is the length of the vector.)
1.3 takayama 305: $cf. [(toe_) array_of_poly] gbext $
1.1 maekawa 306: $Example 1: [(x) ring_of_polynomials 0] define_ring $
307: $ (e_ + 2). toVectors :: $
308: ( ---> [2 , 1] )
309: (Example 2: [3 (e_ +2).] toVectors ::)
310: ( ---> [2 , 1 , 0 ])
311: (Example 3: [(e_+2). (e_^2+1).] toVectors ::)
312: ( ---> [[2 , 1] [1 , 0 , 1]] )
313: (Example 4: [2 [(e x + 1). (x+1).]] toVectors )
314: ( ===> [ [1 , x] [x+1 , 0] ] )
315: ]] putUsages
316: [(toVectors2)
317: [(Remained for the compatibility. cf. toVectors)
318: ]] putUsages
319:
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