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1;;; -*- Mode: Lisp -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22(defpackage "MONOM"
23 (:use :cl :copy)
24 (:export "MONOM"
25 "TERM"
26 "EXPONENT"
27 "MONOM-DIMENSION"
28 "MONOM-EXPONENTS"
29 "UNIVERSAL-EQUALP"
30 "MONOM-ELT"
31 "TOTAL-DEGREE"
32 "SUGAR"
33 "MULTIPLY-BY"
34 "DIVIDE-BY"
35 "DIVIDE"
36 "MULTIPLY-2"
37 "MULTIPLY"
38 "DIVIDES-P"
39 "DIVIDES-LCM-P"
40 "LCM-DIVIDES-LCM-P"
41 "LCM-EQUAL-LCM-P"
42 "DIVISIBLE-BY-P"
43 "REL-PRIME-P"
44 "UNIVERSAL-LCM"
45 "UNIVERSAL-GCD"
46 "DEPENDS-P"
47 "LEFT-TENSOR-PRODUCT-BY"
48 "RIGHT-TENSOR-PRODUCT-BY"
49 "LEFT-CONTRACT"
50 "MAKE-MONOM-VARIABLE"
51 "MAKE-MONOM-CONSTANT"
52 "MAKE-TERM-CONSTANT"
53 "->LIST"
54 "->INFIX"
55 "LEX>"
56 "GRLEX>"
57 "REVLEX>"
58 "GREVLEX>"
59 "INVLEX>"
60 "REVERSE-MONOMIAL-ORDER"
61 "MAKE-ELIMINATION-ORDER-FACTORY"
62 "TERM-COEFF"
63 "UNARY-MINUS"
64 "UNIVERSAL-ZEROP")
65 (:documentation
66 "This package implements basic operations on monomials, including
67various monomial orders.
68
69DATA STRUCTURES: Conceptually, monomials can be represented as lists:
70
71 monom: (n1 n2 ... nk) where ni are non-negative integers
72
73However, lists may be implemented as other sequence types, so the
74flexibility to change the representation should be maintained in the
75code to use general operations on sequences whenever possible. The
76optimization for the actual representation should be left to
77declarations and the compiler.
78
79EXAMPLES: Suppose that variables are x and y. Then
80
81 Monom x*y^2 ---> (1 2) "))
82
83(in-package :monom)
84
85(proclaim '(optimize (speed 0) (space 0) (safety 3) (debug 0)))
86
87(deftype exponent ()
88 "Type of exponent in a monomial."
89 'fixnum)
90
91(defclass monom ()
92 ((exponents :initarg :exponents :accessor monom-exponents
93 :documentation "The powers of the variables."))
94 ;; default-initargs are not needed, they are handled by SHARED-INITIALIZE
95 ;;(:default-initargs :dimension 'foo :exponents 'bar :exponent 'baz)
96 (:documentation
97 "Implements a monomial, i.e. a product of powers
98of variables, like X*Y^2."))
99
100(defmethod print-object ((self monom) stream)
101 (print-unreadable-object (self stream :type t :identity t)
102 (with-accessors ((exponents monom-exponents))
103 self
104 (format stream "EXPONENTS=~A"
105 exponents))))
106
107(defmethod initialize-instance :after ((self monom)
108 &key
109 (dimension 0 dimension-supplied-p)
110 (exponents nil exponents-supplied-p)
111 (exponent 0)
112 &allow-other-keys
113 )
114 "The following INITIALIZE-INSTANCE method allows instance initialization
115of a MONOM in a style similar to MAKE-ARRAY, e.g.:
116
117 (MAKE-INSTANCE 'MONOM :EXPONENTS '(1 2 3)) --> #<MONOM EXPONENTS=#(1 2 3)>
118 (MAKE-INSTANCE 'MONOM :DIMENSION 3) --> #<MONOM EXPONENTS=#(0 0 0)>
119 (MAKE-INSTANCE 'MONOM :DIMENSION 3 :EXPONENT 7) --> #<MONOM EXPONENTS=#(7 7 7)>
120
121If both DIMENSION and EXPONENTS are supplied, they must be compatible,
122i.e. the length of EXPONENTS must be equal DIMENSION. If EXPONENTS
123is not supplied, a monom with repeated value EXPONENT is created.
124By default EXPONENT is 0, which results in a constant monomial.
125"
126 (cond
127 (exponents-supplied-p
128 (when (and dimension-supplied-p
129 (/= dimension (length exponents)))
130 (error "EXPONENTS (~A) must have supplied length DIMENSION (~A)"
131 exponents dimension))
132 (let ((dim (length exponents)))
133 (setf (slot-value self 'exponents) (make-array dim :initial-contents exponents))))
134 (dimension-supplied-p
135 ;; when all exponents are to be identical
136 (setf (slot-value self 'exponents) (make-array (list dimension)
137 :initial-element exponent
138 :element-type 'exponent)))
139 (t
140 (error "Initarg DIMENSION or EXPONENTS must be supplied."))))
141
142(defgeneric monom-dimension (self)
143 (:method ((self monom))
144 (length (monom-exponents self))))
145
146(defgeneric universal-equalp (object1 object2)
147 (:documentation "Returns T iff OBJECT1 and OBJECT2 are equal.")
148 (:method ((object1 cons) (object2 cons)) (every #'universal-equalp object1 object2))
149 (:method ((object1 number) (object2 number)) (= object1 object2))
150 (:method ((m1 monom) (m2 monom))
151 "Returns T iff monomials M1 and M2 have identical EXPONENTS."
152 (equalp (monom-exponents m1) (monom-exponents m2))))
153
154(defgeneric monom-elt (m index)
155 (:documentation "Return the power in the monomial M of variable number INDEX.")
156 (:method ((m monom) index)
157 "Return the power in the monomial M of variable number INDEX."
158 (with-slots (exponents)
159 m
160 (elt exponents index))))
161
162(defgeneric (setf monom-elt) (new-value m index)
163 (:documentation "Set the power in the monomial M of variable number INDEX.")
164 (:method (new-value (m monom) index)
165 (with-slots (exponents)
166 m
167 (setf (elt exponents index) new-value))))
168
169(defgeneric total-degree (m &optional start end)
170 (:documentation "Return the total degree of a monomoal M. Optinally, a range
171of variables may be specified with arguments START and END.")
172 (:method ((m monom) &optional (start 0) (end (monom-dimension m)))
173 (declare (type fixnum start end))
174 (with-slots (exponents)
175 m
176 (reduce #'+ exponents :start start :end end))))
177
178(defgeneric sugar (m &optional start end)
179 (:documentation "Return the sugar of a monomial M. Optinally, a range
180of variables may be specified with arguments START and END.")
181 (:method ((m monom) &optional (start 0) (end (monom-dimension m)))
182 (declare (type fixnum start end))
183 (total-degree m start end)))
184
185(defgeneric multiply-by (self other)
186 (:documentation "Multiply SELF by OTHER, return SELF.")
187 (:method ((self number) (other number)) (* self other))
188 (:method ((self monom) (other monom))
189 (with-slots ((exponents1 exponents))
190 self
191 (with-slots ((exponents2 exponents))
192 other
193 (unless (= (length exponents1) (length exponents2))
194 (error "Incompatible dimensions"))
195 (map-into exponents1 #'+ exponents1 exponents2)))
196 self)
197 (:method ((self number) (other term))
198 (reinitialize-instance other :coeff (multiply self (term-coeff other))))
199 (:method ((self term) (other number))
200 (reinitialize-instance self :coeff (multiply (term-coeff self) other))))
201
202(defgeneric divide-by (self other)
203 (:documentation "Divide SELF by OTHER, return SELF.")
204 (:method ((self number) (other number)) (/ self other))
205 (:method ((self monom) (other monom))
206 (with-slots ((exponents1 exponents))
207 self
208 (with-slots ((exponents2 exponents))
209 other
210 (unless (= (length exponents1) (length exponents2))
211 (error "divide-by: Incompatible dimensions."))
212 (unless (every #'>= exponents1 exponents2)
213 (error "divide-by: Negative power would result."))
214 (map-into exponents1 #'- exponents1 exponents2)))
215 self)
216 (:method ((self term) (other number))
217 (reinitialize-instance self :coeff (divide (term-coeff self) other))))
218
219(defmethod copy-instance :around ((object monom) &rest initargs &key &allow-other-keys)
220 "An :AROUND method of COPY-INSTANCE. It replaces
221exponents with a fresh copy of the sequence."
222 (declare (ignore object initargs))
223 (let ((copy (call-next-method)))
224 (setf (monom-exponents copy) (copy-seq (monom-exponents copy)))
225 copy))
226
227(defun multiply-2 (object1 object2)
228 "Multiply OBJECT1 by OBJECT2"
229 (multiply-by (copy-instance object1) (copy-instance object2)))
230
231(defun multiply (&rest factors)
232 "Non-destructively multiply list FACTORS."
233 (cond ((endp factors) 1)
234 ((endp (rest factors)) (first factors))
235 (t (reduce #'multiply-2 factors :initial-value 1))))
236
237(defun divide (numerator &rest denominators)
238 "Non-destructively divide object NUMERATOR by product of DENOMINATORS."
239 (cond ((endp denominators)
240 (divide-by 1 numerator))
241 (t (divide-by (copy-instance numerator) (apply #'multiply denominators)))))
242
243(defgeneric divides-p (object1 object2)
244 (:documentation "Returns T if OBJECT1 divides OBJECT2.")
245 (:method ((m1 monom) (m2 monom))
246 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
247 (with-slots ((exponents1 exponents))
248 m1
249 (with-slots ((exponents2 exponents))
250 m2
251 (every #'<= exponents1 exponents2)))))
252
253(defgeneric divides-lcm-p (object1 object2 object3)
254 (:documentation "Returns T if OBJECT1 divides LCM(OBJECT2,OBJECT3), NIL otherwise.")
255 (:method ((m1 monom) (m2 monom) (m3 monom))
256 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
257 (with-slots ((exponents1 exponents))
258 m1
259 (with-slots ((exponents2 exponents))
260 m2
261 (with-slots ((exponents3 exponents))
262 m3
263 (every #'(lambda (x y z) (<= x (max y z)))
264 exponents1 exponents2 exponents3))))))
265
266(defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
267 (:method ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
268 "Returns T if monomial LCM(M1,M2) divides LCM(M3,M4), NIL otherwise."
269 (with-slots ((exponents1 exponents))
270 m1
271 (with-slots ((exponents2 exponents))
272 m2
273 (with-slots ((exponents3 exponents))
274 m3
275 (with-slots ((exponents4 exponents))
276 m4
277 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
278 exponents1 exponents2 exponents3 exponents4)))))))
279
280(defgeneric monom-lcm-equal-lcm-p (object1 object2 object3 object4)
281 (:method ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
282 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
283 (with-slots ((exponents1 exponents))
284 m1
285 (with-slots ((exponents2 exponents))
286 m2
287 (with-slots ((exponents3 exponents))
288 m3
289 (with-slots ((exponents4 exponents))
290 m4
291 (every
292 #'(lambda (x y z w) (= (max x y) (max z w)))
293 exponents1 exponents2 exponents3 exponents4)))))))
294
295(defgeneric divisible-by-p (object1 object2)
296 (:documentation "Return T if OBJECT1 is divisible by OBJECT2.")
297 (:method ((m1 monom) (m2 monom))
298 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
299 (with-slots ((exponents1 exponents))
300 m1
301 (with-slots ((exponents2 exponents))
302 m2
303 (every #'>= exponents1 exponents2)))))
304
305(defgeneric rel-prime-p (object1 object2)
306 (:documentation "Returns T if objects OBJECT1 and OBJECT2 are relatively prime.")
307 (:method ((m1 monom) (m2 monom))
308 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
309 (with-slots ((exponents1 exponents))
310 m1
311 (with-slots ((exponents2 exponents))
312 m2
313 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2)))))
314
315(defgeneric universal-lcm (object1 object2)
316 (:documentation "Returns the multiple of objects OBJECT1 and OBJECT2.")
317 (:method ((m1 monom) (m2 monom))
318 "Returns least common multiple of monomials M1 and M2."
319 (with-slots ((exponents1 exponents))
320 m1
321 (with-slots ((exponents2 exponents))
322 m2
323 (let* ((exponents (copy-seq exponents1)))
324 (map-into exponents #'max exponents1 exponents2)
325 (make-instance 'monom :exponents exponents))))))
326
327
328(defgeneric universal-gcd (object1 object2)
329 (:documentation "Returns GCD of objects OBJECT1 and OBJECT2")
330 (:method ((object1 number) (object2 number)) (gcd object1 object2))
331 (:method ((m1 monom) (m2 monom))
332 "Returns greatest common divisor of monomials M1 and M2."
333 (with-slots ((exponents1 exponents))
334 m1
335 (with-slots ((exponents2 exponents))
336 m2
337 (let* ((exponents (copy-seq exponents1)))
338 (map-into exponents #'min exponents1 exponents2)
339 (make-instance 'monom :exponents exponents))))))
340
341(defgeneric depends-p (object k)
342 (:documentation "Returns T iff object OBJECT depends on variable K.")
343 (:method ((m monom) k)
344 "Return T if the monomial M depends on variable number K."
345 (declare (type fixnum k))
346 (with-slots (exponents)
347 m
348 (plusp (elt exponents k)))))
349
350(defgeneric left-tensor-product-by (self other)
351 (:documentation "Returns a tensor product SELF by OTHER, stored into
352 SELF. Return SELF.")
353 (:method ((self monom) (other monom))
354 (with-slots ((exponents1 exponents))
355 self
356 (with-slots ((exponents2 exponents))
357 other
358 (setf exponents1 (concatenate 'vector exponents2 exponents1))))
359 self))
360
361(defgeneric right-tensor-product-by (self other)
362 (:documentation "Returns a tensor product of OTHER by SELF, stored
363 into SELF. Returns SELF.")
364 (:method ((self monom) (other monom))
365 (with-slots ((exponents1 exponents))
366 self
367 (with-slots ((exponents2 exponents))
368 other
369 (setf exponents1 (concatenate 'vector exponents1 exponents2))))
370 self))
371
372(defgeneric left-contract (self k)
373 (:documentation "Drop the first K variables in object SELF.")
374 (:method ((self monom) k)
375 "Drop the first K variables in monomial M."
376 (declare (fixnum k))
377 (with-slots (exponents)
378 self
379 (setf exponents (subseq exponents k)))
380 self))
381
382(defun make-monom-variable (nvars pos &optional (power 1)
383 &aux (m (make-instance 'monom :dimension nvars)))
384 "Construct a monomial in the polynomial ring
385RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
386which represents a single variable. It assumes number of variables
387NVARS and the variable is at position POS. Optionally, the variable
388may appear raised to power POWER. "
389 (declare (type fixnum nvars pos power) (type monom m))
390 (with-slots (exponents)
391 m
392 (setf (elt exponents pos) power)
393 m))
394
395(defun make-monom-constant (dimension)
396 (make-instance 'monom :dimension dimension))
397
398;; pure lexicographic
399(defgeneric lex> (p q &optional start end)
400 (:documentation "Return T if P>Q with respect to lexicographic
401order, otherwise NIL. The second returned value is T if P=Q,
402otherwise it is NIL.")
403 (:method ((p monom) (q monom) &optional (start 0) (end (monom-dimension p)))
404 (declare (type fixnum start end))
405 (do ((i start (1+ i)))
406 ((>= i end) (values nil t))
407 (cond
408 ((> (monom-elt p i) (monom-elt q i))
409 (return-from lex> (values t nil)))
410 ((< (monom-elt p i) (monom-elt q i))
411 (return-from lex> (values nil nil)))))))
412
413;; total degree order, ties broken by lexicographic
414(defgeneric grlex> (p q &optional start end)
415 (:documentation "Return T if P>Q with respect to graded
416lexicographic order, otherwise NIL. The second returned value is T if
417P=Q, otherwise it is NIL.")
418 (:method ((p monom) (q monom) &optional (start 0) (end (monom-dimension p)))
419 (declare (type monom p q) (type fixnum start end))
420 (let ((d1 (total-degree p start end))
421 (d2 (total-degree q start end)))
422 (declare (type fixnum d1 d2))
423 (cond
424 ((> d1 d2) (values t nil))
425 ((< d1 d2) (values nil nil))
426 (t
427 (lex> p q start end))))))
428
429;; reverse lexicographic
430(defgeneric revlex> (p q &optional start end)
431 (:documentation "Return T if P>Q with respect to reverse
432lexicographic order, NIL otherwise. The second returned value is T if
433P=Q, otherwise it is NIL. This is not and admissible monomial order
434because some sets do not have a minimal element. This order is useful
435in constructing other orders.")
436 (:method ((p monom) (q monom) &optional (start 0) (end (monom-dimension p)))
437 (declare (type fixnum start end))
438 (do ((i (1- end) (1- i)))
439 ((< i start) (values nil t))
440 (declare (type fixnum i))
441 (cond
442 ((< (monom-elt p i) (monom-elt q i))
443 (return-from revlex> (values t nil)))
444 ((> (monom-elt p i) (monom-elt q i))
445 (return-from revlex> (values nil nil)))))))
446
447
448;; total degree, ties broken by reverse lexicographic
449(defgeneric grevlex> (p q &optional start end)
450 (:documentation "Return T if P>Q with respect to graded reverse
451lexicographic order, NIL otherwise. The second returned value is T if
452P=Q, otherwise it is NIL.")
453 (:method ((p monom) (q monom) &optional (start 0) (end (monom-dimension p)))
454 (declare (type fixnum start end))
455 (let ((d1 (total-degree p start end))
456 (d2 (total-degree q start end)))
457 (declare (type fixnum d1 d2))
458 (cond
459 ((> d1 d2) (values t nil))
460 ((< d1 d2) (values nil nil))
461 (t
462 (revlex> p q start end))))))
463
464(defgeneric invlex> (p q &optional start end)
465 (:documentation "Return T if P>Q with respect to inverse
466lexicographic order, NIL otherwise The second returned value is T if
467P=Q, otherwise it is NIL.")
468 (:method ((p monom) (q monom) &optional (start 0) (end (monom-dimension p)))
469 (declare (type fixnum start end))
470 (do ((i (1- end) (1- i)))
471 ((< i start) (values nil t))
472 (declare (type fixnum i))
473 (cond
474 ((> (monom-elt p i) (monom-elt q i))
475 (return-from invlex> (values t nil)))
476 ((< (monom-elt p i) (monom-elt q i))
477 (return-from invlex> (values nil nil)))))))
478
479(defun reverse-monomial-order (order)
480 "Create the inverse monomial order to the given monomial order ORDER."
481 #'(lambda (p q &optional (start 0) (end (monom-dimension q)))
482 (declare (type monom p q) (type fixnum start end))
483 (funcall order q p start end)))
484
485;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
486;;
487;; Order making functions
488;;
489;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
490
491;; This returns a closure with the same signature
492;; as all orders such as #'LEX>.
493(defun make-elimination-order-factory-1 (&optional (secondary-elimination-order #'lex>))
494 "It constructs an elimination order used for the 1-st elimination ideal,
495i.e. for eliminating the first variable. Thus, the order compares the degrees of the
496first variable in P and Q first, with ties broken by SECONDARY-ELIMINATION-ORDER."
497 #'(lambda (p q &optional (start 0) (end (monom-dimension p)))
498 (declare (type monom p q) (type fixnum start end))
499 (cond
500 ((> (monom-elt p start) (monom-elt q start))
501 (values t nil))
502 ((< (monom-elt p start) (monom-elt q start))
503 (values nil nil))
504 (t
505 (funcall secondary-elimination-order p q (1+ start) end)))))
506
507;; This returns a closure which is called with an integer argument.
508;; The result is *another closure* with the same signature as all
509;; orders such as #'LEX>.
510(defun make-elimination-order-factory (&optional
511 (primary-elimination-order #'lex>)
512 (secondary-elimination-order #'lex>))
513 "Return a function with a single integer argument K. This should be
514the number of initial K variables X[0],X[1],...,X[K-1], which precede
515remaining variables. The call to the closure creates a predicate
516which compares monomials according to the K-th elimination order. The
517monomial orders PRIMARY-ELIMINATION-ORDER and
518SECONDARY-ELIMINATION-ORDER are used to compare the first K and the
519remaining variables, respectively, with ties broken by lexicographical
520order. That is, if PRIMARY-ELIMINATION-ORDER yields (VALUES NIL T),
521which indicates that the first K variables appear with identical
522powers, then the result is that of a call to
523SECONDARY-ELIMINATION-ORDER applied to the remaining variables
524X[K],X[K+1],..."
525 #'(lambda (k)
526 (cond
527 ((<= k 0)
528 (error "K must be at least 1"))
529 ((= k 1)
530 (make-elimination-order-factory-1 secondary-elimination-order))
531 (t
532 #'(lambda (p q &optional (start 0) (end (monom-dimension p)))
533 (declare (type monom p q) (type fixnum start end))
534 (multiple-value-bind (primary equal)
535 (funcall primary-elimination-order p q start k)
536 (if equal
537 (funcall secondary-elimination-order p q k end)
538 (values primary nil))))))))
539
540(defclass term (monom)
541 ((coeff :initarg :coeff :accessor term-coeff))
542 (:default-initargs :coeff nil)
543 (:documentation "Implements a term, i.e. a product of a scalar
544and powers of some variables, such as 5*X^2*Y^3."))
545
546(defmethod update-instance-for-different-class ((old monom) (new term) &key (coeff 1))
547 "Converts OLD of class MONOM to a NEW of class TERM, initializing coefficient to COEFF."
548 (reinitialize-instance new :coeff coeff))
549
550(defmethod print-object ((self term) stream)
551 (print-unreadable-object (self stream :type t :identity t)
552 (with-accessors ((exponents monom-exponents)
553 (coeff term-coeff))
554 self
555 (format stream "EXPONENTS=~A COEFF=~A"
556 exponents coeff))))
557
558(defun make-term-constant (dimension &optional (coeff 1))
559 (make-instance 'term :dimension dimension :coeff coeff))
560
561(defmethod universal-equalp ((term1 term) (term2 term))
562 "Returns T if TERM1 and TERM2 are equal as MONOM, and coefficients
563are UNIVERSAL-EQUALP."
564 (and (call-next-method)
565 (universal-equalp (term-coeff term1) (term-coeff term2))))
566
567(defmethod update-instance-for-different-class :after ((old monom) (new term) &key)
568 (setf (term-coeff new) 1))
569
570(defmethod multiply-by :before ((self term) (other term))
571 "Destructively multiply terms SELF and OTHER and store the result into SELF.
572It returns SELF."
573 (setf (term-coeff self) (multiply-by (term-coeff self) (term-coeff other))))
574
575(defmethod left-tensor-product-by :before ((self term) (other term))
576 (setf (term-coeff self) (multiply-by (term-coeff self) (term-coeff other))))
577
578(defmethod right-tensor-product-by :before ((self term) (other term))
579 (setf (term-coeff self) (multiply-by (term-coeff self) (term-coeff other))))
580
581(defmethod divide-by :before ((self term) (other term))
582 (setf (term-coeff self) (divide-by (term-coeff self) (term-coeff other))))
583
584(defgeneric unary-minus (self)
585 (:documentation "Negate object SELF and return it.")
586 (:method ((self number)) (- self))
587 (:method ((self term))
588 (setf (term-coeff self) (unary-minus (term-coeff self)))
589 self))
590
591(defgeneric universal-zerop (self)
592 (:documentation "Return T iff SELF is zero.")
593 (:method ((self number)) (zerop self))
594 (:method ((self term))
595 (universal-zerop (term-coeff self))))
596
597(defgeneric ->list (self)
598 (:method ((self monom))
599 "A human-readable representation of a monomial SELF as a list of exponents."
600 (coerce (monom-exponents self) 'list))
601 (:method ((self term))
602 "A human-readable representation of a term SELF as a cons of the list of exponents and the coefficient."
603 (cons (coerce (monom-exponents self) 'list) (term-coeff self))))
604
605(defgeneric ->infix (self &optional vars)
606 (:method ((self monom) &optional vars)
607 (with-slots (exponents dimension)
608 (makelist-1 (exp (elt i vars) ( elt i exponents)) i 0 dimension))))
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