CoCalc -- code.lsp

build open-axiom
open-axiom-build / src / algebra / ACF-.NRLIB / code.lsp
⁵⁴⁵⁵⁰ views
1

2
(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;zeroOf;Sup$;1|)) 
3

4
(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;rootOf;Sup$;2|)) 
5

6
(DECLAIM
7
 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;zerosOf;SupL;3|)) 
8

9
(DECLAIM
10
 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;rootsOf;SupL;4|)) 
11

12
(DECLAIM
13
 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) (|%List| *))
14
  |ACF-;rootsOf;SupSL;5|)) 
15

16
(DECLAIM
17
 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) (|%List| *))
18
  |ACF-;zerosOf;SupSL;6|)) 
19

20
(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |ACF-;assign|)) 
21

22
(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;zeroOf;P$;8|)) 
23

24
(DECLAIM (FTYPE (FUNCTION (|%Thing| |%Shell|) |%Thing|) |ACF-;rootOf;P$;9|)) 
25

26
(DECLAIM
27
 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;zerosOf;PL;10|)) 
28

29
(DECLAIM
30
 (FTYPE (FUNCTION (|%Thing| |%Shell|) (|%List| *)) |ACF-;rootsOf;PL;11|)) 
31

32
(DECLAIM
33
 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|)
34
  |ACF-;zeroOf;SupS$;12|)) 
35

36
(DECLAIM
37
 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|) (|%List| *))
38
  |ACF-;binomialRoots|)) 
39

40
(DECLAIM
41
 (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|) (|%List| *))
42
  |ACF-;allroots|)) 
43

44
(DEFUN |ACF-;zeroOf;Sup$;1| (|p| $)
45
  (PROG (|x|)
46
    (RETURN
47
     (|ACF-;assign|
48
      (LETT |x| (SPADCALL (|shellEntry| $ 8)) |ACF-;zeroOf;Sup$;1|)
49
      (SPADCALL |p| |x| (|shellEntry| $ 10)) $)))) 
50

51
(DEFUN |ACF-;rootOf;Sup$;2| (|p| $)
52
  (PROG (|x|)
53
    (RETURN
54
     (|ACF-;assign|
55
      (LETT |x| (SPADCALL (|shellEntry| $ 8)) |ACF-;rootOf;Sup$;2|)
56
      (SPADCALL |p| |x| (|shellEntry| $ 12)) $)))) 
57

58
(DEFUN |ACF-;zerosOf;SupL;3| (|p| $)
59
  (SPADCALL |p| (SPADCALL (|shellEntry| $ 8)) (|shellEntry| $ 15))) 
60

61
(DEFUN |ACF-;rootsOf;SupL;4| (|p| $)
62
  (SPADCALL |p| (SPADCALL (|shellEntry| $ 8)) (|shellEntry| $ 17))) 
63

64
(DEFUN |ACF-;rootsOf;SupSL;5| (|p| |y| $)
65
  (|ACF-;allroots| |p| |y| (|shellEntry| $ 12) $)) 
66

67
(DEFUN |ACF-;zerosOf;SupSL;6| (|p| |y| $)
68
  (|ACF-;allroots| |p| |y| (|shellEntry| $ 10) $)) 
69

70
(DEFUN |ACF-;assign| (|x| |f| $)
71
  (PROGN (|assignSymbol| |x| |f| (|shellEntry| $ 6)) |f|)) 
72

73
(DEFUN |ACF-;zeroOf;P$;8| (|p| $)
74
  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
75
    (COND ((NULL |l|) (|error| "zeroOf: constant polynomial"))
76
          (T
77
           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
78
                     (|shellEntry| $ 10)))))) 
79

80
(DEFUN |ACF-;rootOf;P$;9| (|p| $)
81
  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
82
    (COND ((NULL |l|) (|error| "rootOf: constant polynomial"))
83
          (T
84
           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
85
                     (|shellEntry| $ 12)))))) 
86

87
(DEFUN |ACF-;zerosOf;PL;10| (|p| $)
88
  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
89
    (COND ((NULL |l|) (|error| "zerosOf: constant polynomial"))
90
          (T
91
           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
92
                     (|shellEntry| $ 15)))))) 
93

94
(DEFUN |ACF-;rootsOf;PL;11| (|p| $)
95
  (LET ((|l| (SPADCALL |p| (|shellEntry| $ 23))))
96
    (COND ((NULL |l|) (|error| "rootsOf: constant polynomial"))
97
          (T
98
           (SPADCALL (SPADCALL |p| (|shellEntry| $ 27)) (|SPADfirst| |l|)
99
                     (|shellEntry| $ 17)))))) 
100

101
(DEFUN |ACF-;zeroOf;SupS$;12| (|p| |y| $)
102
  (PROG (|r| |b| |a|)
103
    (RETURN
104
     (LET ((|d| (SPADCALL |p| (|shellEntry| $ 35))))
105
       (COND ((ZEROP |d|) (|error| "zeroOf: constant polynomial"))
106
             ((SPADCALL (SPADCALL |p| 0 (|shellEntry| $ 40))
107
                        (|shellEntry| $ 41))
108
              (|spadConstant| $ 37))
109
             (T
110
              (SEQ
111
               (LETT |a| (SPADCALL |p| (|shellEntry| $ 42))
112
                     . #1=(|ACF-;zeroOf;SupS$;12|))
113
               (EXIT
114
                (COND
115
                 ((EQL |d| 2)
116
                  (PROGN
117
                   (LETT |b| (SPADCALL |p| 1 (|shellEntry| $ 40)) . #1#)
118
                   (SPADCALL
119
                    (SPADCALL
120
                     (SPADCALL
121
                      (SPADCALL (SPADCALL |b| 2 (|shellEntry| $ 48))
122
                                (SPADCALL (SPADCALL 4 |a| (|shellEntry| $ 49))
123
                                          (SPADCALL |p| 0 (|shellEntry| $ 40))
124
                                          (|shellEntry| $ 50))
125
                                (|shellEntry| $ 51))
126
                      (|shellEntry| $ 52))
127
                     |b| (|shellEntry| $ 51))
128
                    (SPADCALL 2 |a| (|shellEntry| $ 49)) (|shellEntry| $ 53))))
129
                 (T
130
                  (PROGN
131
                   (LETT |r|
132
                         (SPADCALL (SPADCALL |p| (|shellEntry| $ 54))
133
                                   (|shellEntry| $ 56))
134
                         . #1#)
135
                   (COND
136
                    ((EQL (CAR |r|) 1) (SPADCALL |p| |y| (|shellEntry| $ 12)))
137
                    (T
138
                     (SPADCALL
139
                      (SPADCALL (SPADCALL (CDR |r|) |a| (|shellEntry| $ 53))
140
                                (|shellEntry| $ 57))
141
                      |d| (|shellEntry| $ 59))))))))))))))) 
142

143
(DEFUN |ACF-;binomialRoots| (|p| |y| |fn| $)
144
  (PROG (|beta| |cyclo|)
145
    (RETURN
146
     (LET* ((|x| (SPADCALL |y| (|shellEntry| $ 61)))
147
            (|alpha|
148
             (|ACF-;assign| |x| (FUNCALL (CAR |fn|) |p| |x| (CDR |fn|)) $))
149
            (|n| (SPADCALL |p| (|shellEntry| $ 35))))
150
       (COND ((EQL |n| 1) (LIST |alpha|))
151
             (T
152
              (PROGN
153
               (LETT |cyclo|
154
                     (SPADCALL |n|
155
                               (SPADCALL (|spadConstant| $ 44) 1
156
                                         (|shellEntry| $ 64))
157
                               (|shellEntry| $ 66))
158
                     . #1=(|ACF-;binomialRoots|))
159
               (SETQ |x| (SPADCALL |y| (|shellEntry| $ 61)))
160
               (LETT |beta|
161
                     (|ACF-;assign| |x|
162
                      (FUNCALL (CAR |fn|) |cyclo| |x| (CDR |fn|)) $)
163
                     . #1#)
164
               (LET ((|i| 0)
165
                     (#2=#:G615
166
                      (LET ((#3=#:G589 (- |n| 1)))
167
                        (COND ((NOT (MINUSP #3#)) #3#)
168
                              (T
169
                               (|moanRetract| #3# '(|NonNegativeInteger|))))))
170
                     (#4=#:G583 NIL))
171
                 (LOOP
172
                  (COND ((< #2# |i|) (RETURN (|reverse!| #4#)))
173
                        (T
174
                         (SETQ #4#
175
                                 (CONS
176
                                  (SPADCALL |alpha|
177
                                            (SPADCALL |beta| |i|
178
                                                      (|shellEntry| $ 68))
179
                                            (|shellEntry| $ 50))
180
                                  #4#))))
181
                  (SETQ |i| (+ |i| 1))))))))))) 
182

183
(DEFUN |ACF-;allroots| (|p| |y| |fn| $)
184
  (PROG (|q| |alpha| |x| |ans| |groots| |g| |h| |decompList|)
185
    (RETURN
186
     (COND
187
      ((SPADCALL |p| (|shellEntry| $ 69))
188
       (|error| "allroots: polynomial must be nonzero"))
189
      ((SPADCALL (SPADCALL |p| 0 (|shellEntry| $ 40)) (|shellEntry| $ 41))
190
       (CONS (|spadConstant| $ 37)
191
             (|ACF-;allroots|
192
              (SPADCALL |p|
193
                        (SPADCALL (|spadConstant| $ 44) 1 (|shellEntry| $ 64))
194
                        (|shellEntry| $ 70))
195
              |y| |fn| $)))
196
      (T
197
       (LET ((|p1| (SPADCALL |p| (|shellEntry| $ 54))))
198
         (COND ((SPADCALL |p1| (|shellEntry| $ 69)) NIL)
199
               ((SPADCALL (SPADCALL |p1| (|shellEntry| $ 54))
200
                          (|shellEntry| $ 69))
201
                (|ACF-;binomialRoots| |p| |y| |fn| $))
202
               (T
203
                (SEQ
204
                 (LETT |decompList| (SPADCALL |p| (|shellEntry| $ 76))
205
                       . #1=(|ACF-;allroots|))
206
                 (EXIT
207
                  (COND
208
                   ((< 1 (LIST-LENGTH |decompList|))
209
                    (PROGN
210
                     (LETT |h| (SPADCALL |decompList| (|shellEntry| $ 79))
211
                           . #1#)
212
                     (LETT |g|
213
                           (LET ((#2=#:G613
214
                                  (SPADCALL |p| |h| (|shellEntry| $ 81))))
215
                             (COND ((ZEROP (CAR #2#)) (CDR #2#))
216
                                   (T
217
                                    (|moanRetract| #2#
218
                                                   (LIST
219
                                                    '|SparseUnivariatePolynomial|
220
                                                    (|shellEntry| $ 6))))))
221
                           . #1#)
222
                     (LETT |groots| (|ACF-;allroots| |g| |y| |fn| $) . #1#)
223
                     (LET ((#3=#:G593 NIL) (#4=#:G594 T) (#5=#:G616 |groots|))
224
                       (LOOP
225
                        (COND
226
                         ((NOT (CONSP #5#)) (RETURN (COND (#4# NIL) (T #3#))))
227
                         (T
228
                          (LET ((#6=#:G592
229
                                 (|ACF-;allroots|
230
                                  (SPADCALL |h|
231
                                            (SPADCALL (CAR #5#)
232
                                                      (|shellEntry| $ 82))
233
                                            (|shellEntry| $ 83))
234
                                  |y| |fn| $)))
235
                            (PROGN
236
                             (COND (#4# (SETQ #3# #6#))
237
                                   (T (SETQ #3# (APPEND #3# #6#))))
238
                             (SETQ #4# NIL)))))
239
                        (SETQ #5# (CDR #5#))))))
240
                   (T
241
                    (SEQ (LETT |ans| NIL . #1#)
242
                         (LOOP
243
                          (COND
244
                           ((SPADCALL |p| (|shellEntry| $ 86)) (RETURN NIL))
245
                           (T
246
                            (SEQ
247
                             (LETT |x| (SPADCALL |y| (|shellEntry| $ 61))
248
                                   . #1#)
249
                             (LETT |alpha|
250
                                   (|ACF-;assign| |x|
251
                                    (FUNCALL (CAR |fn|) |p| |x| (CDR |fn|)) $)
252
                                   . #1#)
253
                             (LETT |q|
254
                                   (SPADCALL
255
                                    (SPADCALL (|spadConstant| $ 44) 1
256
                                              (|shellEntry| $ 64))
257
                                    (SPADCALL |alpha| (|shellEntry| $ 82))
258
                                    (|shellEntry| $ 83))
259
                                   . #1#)
260
                             (EXIT
261
                              (COND
262
                               ((SPADCALL
263
                                 (SPADCALL |p| |alpha| (|shellEntry| $ 88))
264
                                 (|shellEntry| $ 41))
265
                                (LOOP
266
                                 (COND
267
                                  ((NOT
268
                                    (SPADCALL
269
                                     (SPADCALL |p| |alpha| (|shellEntry| $ 88))
270
                                     (|shellEntry| $ 41)))
271
                                   (RETURN NIL))
272
                                  (T
273
                                   (PROGN
274
                                    (SETQ |p|
275
                                            (LET ((#7=#:G614
276
                                                   (SPADCALL |p| |q|
277
                                                             (|shellEntry| $
278
                                                                           90))))
279
                                              (COND
280
                                               ((ZEROP (CAR #7#)) (CDR #7#))
281
                                               (T
282
                                                (|moanRetract| #7#
283
                                                               (LIST
284
                                                                '|SparseUnivariatePolynomial|
285
                                                                (|shellEntry| $
286
                                                                              6)))))))
287
                                    (SETQ |ans| (CONS |alpha| |ans|)))))))
288
                               (T
289
                                (PROGN
290
                                 (SETQ |p|
291
                                         (SPADCALL |p| |q|
292
                                                   (|shellEntry| $ 70)))
293
                                 (SETQ |ans| (CONS |alpha| |ans|))))))))))
294
                         (EXIT (|reverse!| |ans|))))))))))))))) 
295

296
(DEFUN |AlgebraicallyClosedField&| (|#1|)
297
  (LET* ((|dv$1| (|devaluate| |#1|))
298
         (|dv$| (LIST '|AlgebraicallyClosedField&| |dv$1|))
299
         ($ (|newShell| 92))
300
         (|pv$| (|buildPredVector| 0 0 NIL)))
301
    (PROGN
302
     (SETF (|shellEntry| $ 0) |dv$|)
303
     (SETF (|shellEntry| $ 3) |pv$|)
304
     (|stuffDomainSlots| $)
305
     (SETF (|shellEntry| $ 6) |#1|)
306
     $))) 
307

308
(MAKEPROP '|AlgebraicallyClosedField&| '|infovec|
309
          (LIST
310
           '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Symbol|) (0 . |new|)
311
              (|SparseUnivariatePolynomial| $) (4 . |zeroOf|)
312
              |ACF-;zeroOf;Sup$;1| (10 . |rootOf|) |ACF-;rootOf;Sup$;2|
313
              (|List| $) (16 . |zerosOf|) |ACF-;zerosOf;SupL;3|
314
              (22 . |rootsOf|) |ACF-;rootsOf;SupL;4| |ACF-;rootsOf;SupSL;5|
315
              |ACF-;zerosOf;SupSL;6| (|Polynomial| 6) (|List| 7)
316
              (28 . |variables|) (|Boolean|) (33 . |empty?|)
317
              (|SparseUnivariatePolynomial| 6) (38 . |univariate|)
318
              (43 . |first|) (|Polynomial| $) |ACF-;zeroOf;P$;8|
319
              |ACF-;rootOf;P$;9| |ACF-;zerosOf;PL;10| |ACF-;rootsOf;PL;11|
320
              (|NonNegativeInteger|) (48 . |degree|) (53 . |zero?|)
321
              (58 . |Zero|) (62 . |Zero|) (66 . |Zero|) (70 . |coefficient|)
322
              (76 . |zero?|) (81 . |leadingCoefficient|) (86 . =) (92 . |One|)
323
              (96 . |One|) (|PositiveInteger|) (100 . |One|) (104 . **)
324
              (110 . *) (116 . *) (122 . -) (128 . |sqrt|) (133 . /)
325
              (139 . |reductum|) (|Union| 6 '#1="failed")
326
              (144 . |retractIfCan|) (149 . -) (|Integer|) (154 . |nthRoot|)
327
              |ACF-;zeroOf;SupS$;12| (160 . |new|) (165 . |one?|) (170 . |One|)
328
              (174 . |monomial|) (|NumberTheoreticPolynomialFunctions| 26)
329
              (180 . |cyclotomic|) (186 . -) (192 . **) (198 . |zero?|)
330
              (203 . |quo|) (|List| 6) (209 . |concat|) (215 . |empty|)
331
              (|PolynomialDecomposition| 26 6) (|List| 26) (219 . |decompose|)
332
              (224 . |#|) (229 . >) (235 . |last|) (|Union| 26 '"failed")
333
              (240 . |leftFactor|) (246 . |coerce|) (251 . -) (257 . |append|)
334
              (263 . |nil|) (267 . |ground?|) (272 . |not|) (277 . |elt|)
335
              (|Union| $ '#1#) (283 . |exquo|) (289 . |reverse!|))
336
           '#(|zerosOf| 294 |zeroOf| 310 |rootsOf| 326 |rootOf| 342) 'NIL
337
           (CONS (|makeByteWordVec2| 1 'NIL)
338
                 (CONS '#()
339
                       (CONS '#()
340
                             (|makeByteWordVec2| 91
341
                                                 '(0 7 0 8 2 6 0 9 7 10 2 6 0 9
342
                                                   7 12 2 6 14 9 7 15 2 6 14 9
343
                                                   7 17 1 21 22 0 23 1 22 24 0
344
                                                   25 1 21 26 0 27 1 22 7 0 28
345
                                                   1 26 34 0 35 1 34 24 0 36 0
346
                                                   6 0 37 0 26 0 38 0 34 0 39 2
347
                                                   26 6 0 34 40 1 6 24 0 41 1
348
                                                   26 6 0 42 2 34 24 0 0 43 0 6
349
                                                   0 44 0 26 0 45 0 46 0 47 2 6
350
                                                   0 0 46 48 2 6 0 46 0 49 2 6
351
                                                   0 0 0 50 2 6 0 0 0 51 1 6 0
352
                                                   0 52 2 6 0 0 0 53 1 26 0 0
353
                                                   54 1 26 55 0 56 1 6 0 0 57 2
354
                                                   6 0 0 58 59 1 7 0 0 61 1 34
355
                                                   24 0 62 0 34 0 63 2 26 0 6
356
                                                   34 64 2 65 26 34 26 66 2 58
357
                                                   0 0 0 67 2 6 0 0 34 68 1 26
358
                                                   24 0 69 2 26 0 0 0 70 2 71 0
359
                                                   6 0 72 0 71 0 73 1 74 75 26
360
                                                   76 1 75 34 0 77 2 34 24 0 0
361
                                                   78 1 75 26 0 79 2 74 80 26
362
                                                   26 81 1 26 0 6 82 2 26 0 0 0
363
                                                   83 2 71 0 0 0 84 0 71 0 85 1
364
                                                   26 24 0 86 1 24 0 0 87 2 26
365
                                                   6 0 6 88 2 26 89 0 0 90 1 71
366
                                                   0 0 91 2 0 14 9 7 20 1 0 14
367
                                                   29 32 1 0 14 9 16 2 0 0 9 7
368
                                                   60 1 0 0 29 30 1 0 0 9 11 2
369
                                                   0 14 9 7 19 1 0 14 29 33 1 0
370
                                                   14 9 18 1 0 0 29 31 1 0 0 9
371
                                                   13)))))
372
           '|lookupComplete|)) 
373

374
(SETF (|dbTemplate| (|constructorDB| '|AlgebraicallyClosedField&|))
375
        #(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Symbol|) (0 . |new|)
376
          (|SparseUnivariatePolynomial| $) (4 . |zeroOf|) |ACF-;zeroOf;Sup$;1|
377
          (10 . |rootOf|) |ACF-;rootOf;Sup$;2| (|List| $) (16 . |zerosOf|)
378
          |ACF-;zerosOf;SupL;3| (22 . |rootsOf|) |ACF-;rootsOf;SupL;4|
379
          |ACF-;rootsOf;SupSL;5| |ACF-;zerosOf;SupSL;6| (|Polynomial| 6)
380
          (|List| 7) (28 . |variables|) (|Boolean|) (33 . |empty?|)
381
          (|SparseUnivariatePolynomial| 6) (38 . |univariate|) (43 . |first|)
382
          (|Polynomial| $) |ACF-;zeroOf;P$;8| |ACF-;rootOf;P$;9|
383
          |ACF-;zerosOf;PL;10| |ACF-;rootsOf;PL;11| (|NonNegativeInteger|)
384
          (48 . |degree|) (53 . |zero?|) (58 . |Zero|) (62 . |Zero|)
385
          (66 . |Zero|) (70 . |coefficient|) (76 . |zero?|)
386
          (81 . |leadingCoefficient|) (86 . =) (92 . |One|) (96 . |One|)
387
          (|PositiveInteger|) (100 . |One|) (104 . **) (110 . *) (116 . *)
388
          (122 . -) (128 . |sqrt|) (133 . /) (139 . |reductum|)
389
          (|Union| 6 '#1="failed") (144 . |retractIfCan|) (149 . -) (|Integer|)
390
          (154 . |nthRoot|) |ACF-;zeroOf;SupS$;12| (160 . |new|) (165 . |one?|)
391
          (170 . |One|) (174 . |monomial|)
392
          (|NumberTheoreticPolynomialFunctions| 26) (180 . |cyclotomic|)
393
          (186 . -) (192 . **) (198 . |zero?|) (203 . |quo|) (|List| 6)
394
          (209 . |concat|) (215 . |empty|) (|PolynomialDecomposition| 26 6)
395
          (|List| 26) (219 . |decompose|) (224 . |#|) (229 . >) (235 . |last|)
396
          (|Union| 26 '"failed") (240 . |leftFactor|) (246 . |coerce|)
397
          (251 . -) (257 . |append|) (263 . |nil|) (267 . |ground?|)
398
          (272 . |not|) (277 . |elt|) (|Union| $ '#1#) (283 . |exquo|)
399
          (289 . |reverse!|))) 
400

401
(SETF (|dbLookupFunction| (|constructorDB| '|AlgebraicallyClosedField&|))
402
        '|lookupComplete|) 
403

404
(SETF (|dbConstructorForm| (|constructorDB| '|AlgebraicallyClosedField&|))
405
        '(|AlgebraicallyClosedField&| S)) 
406

407
(SETF (|dbConstructorKind| (|constructorDB| '|AlgebraicallyClosedField&|))
408
        '|package|) 
409

410
(SETF (|dbConstructorModemap| (|constructorDB| '|AlgebraicallyClosedField&|))
411
        '(((|AlgebraicallyClosedField&| |#1|)
412
           (CATEGORY |package|
413
            (SIGNATURE |zerosOf|
414
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
415
            (SIGNATURE |zerosOf|
416
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|)))
417
            (SIGNATURE |zerosOf| ((|List| |#1|) (|Polynomial| |#1|)))
418
            (SIGNATURE |zeroOf|
419
             (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
420
            (SIGNATURE |zeroOf| (|#1| (|SparseUnivariatePolynomial| |#1|)))
421
            (SIGNATURE |zeroOf| (|#1| (|Polynomial| |#1|)))
422
            (SIGNATURE |rootsOf|
423
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
424
            (SIGNATURE |rootsOf|
425
             ((|List| |#1|) (|SparseUnivariatePolynomial| |#1|)))
426
            (SIGNATURE |rootsOf| ((|List| |#1|) (|Polynomial| |#1|)))
427
            (SIGNATURE |rootOf|
428
             (|#1| (|SparseUnivariatePolynomial| |#1|) (|Symbol|)))
429
            (SIGNATURE |rootOf| (|#1| (|SparseUnivariatePolynomial| |#1|)))
430
            (SIGNATURE |rootOf| (|#1| (|Polynomial| |#1|))))
431
           (|AlgebraicallyClosedField|))
432
          (T |AlgebraicallyClosedField&|))) 
433

434
(SETF (|dbDualSignature| (|constructorDB| '|AlgebraicallyClosedField&|))
435
        '(NIL T)) 
436

437
(SETF (|dbSourceFile| (|constructorDB| '|AlgebraicallyClosedField&|))
438
        '"algfunc.spad") 
439

440
(SETF (|dbOperations| (|constructorDB| '|AlgebraicallyClosedField&|))
441
        '((|zerosOf| (((|List| $) (|Polynomial| $)) 32 T ELT)
442
           (((|List| $) (|SparseUnivariatePolynomial| $)) 16 T ELT)
443
           (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 20 T ELT))
444
          (|zeroOf| (($ (|Polynomial| $)) 30 T ELT)
445
           (($ (|SparseUnivariatePolynomial| $)) 11 T ELT)
446
           (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) 60 T ELT))
447
          (|rootsOf| (((|List| $) (|Polynomial| $)) 33 T ELT)
448
           (((|List| $) (|SparseUnivariatePolynomial| $)) 18 T ELT)
449
           (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) 19 T ELT))
450
          (|rootOf| (($ (|Polynomial| $)) 31 T ELT)
451
           (($ (|SparseUnivariatePolynomial| $)) 13 T ELT)
452
           (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) NIL T ELT)))) 
453

454
(SETF (|dbOperationTable| (|constructorDB| '|AlgebraicallyClosedField&|))
455
        #(|zerosOf| 294 |zeroOf| 310 |rootsOf| 326 |rootOf| 342)) 
456

457
(SETF (|dbCapsuleDefinitions| (|constructorDB| '|AlgebraicallyClosedField&|))
458
        '((|ACF-;zeroOf;SupS$;12|
459
           ($ (|SparseUnivariatePolynomial| $) (|Symbol|)))
460
          (|ACF-;rootsOf;PL;11| ((|List| $) (|Polynomial| $)))
461
          (|ACF-;zerosOf;PL;10| ((|List| $) (|Polynomial| $)))
462
          (|ACF-;rootOf;P$;9| ($ (|Polynomial| $)))
463
          (|ACF-;zeroOf;P$;8| ($ (|Polynomial| $)))
464
          (|ACF-;zerosOf;SupSL;6|
465
           ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)))
466
          (|ACF-;rootsOf;SupSL;5|
467
           ((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)))
468
          (|ACF-;rootsOf;SupL;4| ((|List| $) (|SparseUnivariatePolynomial| $)))
469
          (|ACF-;zerosOf;SupL;3| ((|List| $) (|SparseUnivariatePolynomial| $)))
470
          (|ACF-;rootOf;Sup$;2| ($ (|SparseUnivariatePolynomial| $)))
471
          (|ACF-;zeroOf;Sup$;1| ($ (|SparseUnivariatePolynomial| $))))) 
472

473
(SETF (|dbAbbreviation| (|constructorDB| '|AlgebraicallyClosedField&|)) 'ACF-) 
474

475
Product

Resources

Company
