share/simplification/scifac.lisp

   1 ;;; -*- Mode: Lisp; Package: Macsyma -*-                                 ;;;
   2 ;;;    (c) Copyright 1984 the Regents of the University of California.   ;;;
   3 ;;;        All Rights Reserved.                                          ;;;
   4 ;;;        This work was produced under the sponsorship of the           ;;;
   5 ;;;        U.S. Department of Energy.  The Government retains            ;;;
   6 ;;;        certain rights therein.                                       ;;;
   7 ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
   8
   9 (macsyma-module scifac)
  10
  11 (declaim (special $negdistrib))
  12
  13 (defmacro make-expt (base exponent) ``((mexpt simp) ,,base ,,exponent))
  14
  15 (defmacro acceptable-power (x)
  16    `(and (alike1 (cadr ,x) var)
  17          (setq minpow (cond (nstate (and (integerp expon) (min minpow expon)))
  18                             (number (and ($numberp expon)
  19                                          (integerp (sub minpow expon))
  20                                          (mfuncall '$min minpow expon)))
  21                             (t
  22                              (let ((powdif (sub minpow expon)))
  23                                (cond ((integerp powdif)
  24                                       (cond ((> powdif 0) expon)
  25                                             (t minpow)))
  26                                      (t
  27                                       (let ((g ($gcd minpow expon)))
  28                                         (let ((d1 ($ratsimp (div minpow g)))
  29                                               (d2 ($ratsimp (div expon g))))
  30                                           (and (integerp d1)
  31                                                (integerp d2)
  32                                                (cond ((> d1 d2) expon)
  33                                                      (t minpow)))))))))))
  34          (or (eq expon-sign
  35                  (cond (number (mnegp expon))
  36                        ((mtimesp expon)
  37                         (equal -1 (cadr expon)))))
  38              (return nil))))
  39
  40 (defun factorout-monomial (exp)
  41   (let ((monomials)
  42         (lead-term (cadr exp))
  43         (alone t)
  44         (minuslogic (and (> (length exp) 3)
  45                          (let ((minusobj (car (last exp))))
  46                            (cond ((integerp minusobj) (minusp minusobj))
  47                                  ((mtimesp minusobj)
  48                                   (and (integerp (cadr minusobj))
  49                                        (minusp (cadr minusobj)))))))))
  50     (do ((rem-prod (cond ((or ($mapatom lead-term)
  51                               (eq (caar lead-term) 'mexpt))
  52                           (ncons lead-term))
  53                          ((eq (caar lead-term) 'mtimes)
  54                           (setq alone nil)
  55                           (cdr lead-term))
  56                          (t nil))
  57                    (cdr rem-prod))
  58          (follow lead-term rem-prod)
  59          (j 1 (1+ j)))
  60         ((null rem-prod)
  61          (cond ((null monomials) exp)
  62                (t
  63                 (let (($negdistrib))
  64                   (muln `(,.monomials ,(addn (cdr exp) nil)) nil)))))
  65       (let ((potentl-mon (car rem-prod)) (truth) (leadfix))
  66         (cond ((or (setq leadfix (integerp potentl-mon)) minuslogic)
  67                (let ((intgcd (cond (leadfix potentl-mon)
  68                                    (t (prog1 1
  69                                         (cond (alone
  70                                                (rplaca (cdr exp) `((mtimes simp) 1 ,potentl-mon))
  71                                                (setq rem-prod (cdadr exp)
  72                                                      alone nil))
  73                                               (t (rplacd follow (append (ncons 1) rem-prod))
  74                                                  (setq rem-prod (cdr follow))))))))
  75                      (single (list (and leadfix alone))))
  76                  (do ((ge (cddr exp) (cdr ge))
  77                       (all-minus (minusp intgcd)))
  78                      ((null ge)
  79                       (and (or minuslogic all-minus)
  80                            (or (minusp intgcd)
  81                                (setq intgcd (- intgcd)))
  82                            (setq minuslogic nil))
  83                       (or (equal intgcd 1)
  84                           (progn
  85                             (setq monomials `(,@monomials ,intgcd))
  86                             (do ((redu-const (cdr exp) (cdr redu-const))
  87                                  (in-follow exp redu-const)
  88                                  (logic single (cdr logic)))
  89                                 ((null redu-const))
  90                               (let ((term1 (car redu-const)))
  91                                 (cond ((car logic) (rplaca redu-const (quotient term1 intgcd)))
  92                                       (t (cond ((equal 1 (car (rplaca (cdr term1) (quotient (cadr term1) intgcd))))
  93                                                 (and (eq logic single)
  94                                                      (setq j (1- j)
  95                                                            rem-prod follow))
  96                                                 (rplacd term1 (cddr term1))
  97                                                 (or (cddr term1)
  98                                                     (let ((pluscontac (cadr term1)))
  99                                                       (cond ((mplusp pluscontac)
 100                                                              (rplacd in-follow (append (cdr pluscontac) (cdr redu-const)))
 101                                                              (setq redu-const (nthcdr (1- (length pluscontac)) in-follow))
 102                                                              (and (eq logic single)
 103                                                                   (let ((new-lead (cadr exp)))
 104                                                                     (cond ((mtimesp new-lead)
 105                                                                            (setq rem-prod new-lead))
 106                                                                           (t (setq alone t
 107                                                                                    rem-prod `(nil ,new-lead)))))))
 108                                                             (t (rplaca redu-const pluscontac)
 109                                                                (and (eq logic single)
 110                                                                     (setq alone t)))))))))))))))
 111                    (let ((leadnum (car ge)))
 112                      (cond ((integerp leadnum)
 113                             (setq single `(,@single t)
 114                                   intgcd (gcd intgcd leadnum)
 115                                   all-minus (and all-minus (minusp leadnum))))
 116                            ((mtimesp leadnum)
 117                             (let ((numb (cadr leadnum)))
 118                               (cond ((integerp numb)
 119                                      (setq single `(,@single nil)
 120                                            intgcd (gcd intgcd numb)
 121                                            all-minus (and all-minus (minusp numb))))
 122                                     (minuslogic
 123                                      (setq single `(,@single nil)
 124                                            intgcd 1)
 125                                      (rplacd leadnum (append (ncons 1) (cdr leadnum))))
 126                                     (t (return nil)))))
 127                            (minuslogic
 128                             (setq single `(,@single nil)
 129                                   intgcd 1)
 130                             (rplaca ge `((mtimes simp) 1 ,leadnum)))
 131                            (t (return nil)))))))
 132               (t (or ($mapatom potentl-mon)
 133                      (setq truth (eq (caar potentl-mon) 'mexpt)))
 134                  (let ((power (list (cond (truth (caddr potentl-mon))
 135                                           (t 1))))
 136                        (place (list (cond (alone -1)
 137                                           (t j))))
 138                        (var (cond (truth (cadr potentl-mon))
 139                                   (t potentl-mon))))
 140                    (let* ((minpow (car power)) (number ($numberp minpow)))
 141                      (do ((ge (cddr exp) (cdr ge))
 142                           (expon-sign (and truth
 143                                            (cond (number (mnegp minpow))
 144                                                  ((mtimesp minpow)
 145                                                   (equal -1 (cadr minpow))))))
 146                           (nstate (integerp minpow)))
 147                          ((null ge)
 148                           (or number (and expon-sign
 149                                           (setq minpow (mul -1 minpow))))
 150                           (setq monomials
 151                                 `(,.monomials ,(cond ((equal minpow 1) var)
 152                                                      (t (make-expt (cadr potentl-mon) minpow)))))
 153                           (do ((deflate (cdr exp) (cdr deflate))
 154                                (d-follow exp deflate)
 155                                (pl place (cdr pl))
 156                                (pow power (cdr pow)))
 157                               ((null deflate))
 158                             (let ((pownum (car pow)) (plnum (car pl)))
 159                               (cond ((minusp plnum)
 160                                      (cond ((cond (nstate (equal pownum minpow))
 161                                                   (t (alike1 pownum minpow)))
 162                                             (rplaca deflate 1))
 163                                            (t (cond ((cond (nstate (equal pownum (1+ minpow)))
 164                                                            (t (alike1 pownum (add 1 minpow))))
 165                                                      (rplaca deflate (cadar deflate)))
 166                                                     (t (rplaca (cddar deflate) (cond (nstate (- pownum minpow))
 167                                                                                      (t (sub pownum minpow)))))))))
 168                                     (t (let* ((term (car deflate)) (point (nthcdr plnum term)))
 169                                          (cond ((cond (nstate (equal pownum minpow))
 170                                                       (t (alike1 pownum minpow)))
 171                                                 (rplacd (nthcdr (1- plnum) term) (cdr point))
 172                                                 (and (eq pl place)
 173                                                      (setq j (1- j)
 174                                                            rem-prod follow))
 175                                                 (or (cddr term)
 176                                                     (let ((pluscontac (cadr term)))
 177                                                       (cond ((mplusp pluscontac)
 178                                                              (rplacd d-follow (append (cdr pluscontac) (cdr deflate)))
 179                                                              (setq deflate (nthcdr (1- (length pluscontac)) d-follow))
 180                                                              (and (eq pl place)
 181                                                                   (let ((new-lead (cadr exp)))
 182                                                                     (cond ((mtimesp new-lead)
 183                                                                            (setq rem-prod new-lead))
 184                                                                           (t (setq alone t
 185                                                                                    rem-prod `(nil ,new-lead)))))))
 186                                                             (t (rplaca deflate pluscontac)
 187                                                                (and (eq pl place)
 188                                                                     (setq alone t)))))))
 189                                                (t (cond ((cond (nstate (equal pownum (1+ minpow)))
 190                                                                (t (alike1 pownum (add 1 minpow))))
 191                                                          (rplaca point (cadar point)))
 192                                                         (t (rplaca (cddar point) (cond (nstate (- pownum minpow))
 193                                                                                        (t (sub pownum minpow))))))))))))))
 194                        (let ((exam-term (car ge)))
 195                          (cond (($mapatom exam-term)
 196                                 (cond ((and nstate (alike1 exam-term var))
 197                                        (setq place `(,@place -1)
 198                                              minpow 1
 199                                              power `(,@power 1)))
 200                                       (t (return nil))))
 201                                ((eq (caar exam-term) 'mexpt)
 202                                 (let ((expon (caddr exam-term)))
 203                                   (cond ((acceptable-power exam-term)
 204                                          (setq place `(,@place -2)
 205                                                power `(,@power ,expon)))
 206                                         (t (return nil)))))
 207                                ((eq (caar exam-term) 'mtimes)
 208                                 (cond ((do ((pick (cdr exam-term) (cdr pick))
 209                                             (k 1 (1+ k)))
 210                                            ((null pick))
 211                                          (let ((morcel (car pick)))
 212                                            (cond (($mapatom morcel)
 213                                                   (cond ((and nstate
 214                                                               (alike1 morcel var))
 215                                                          (setq place `(,@place ,k)
 216                                                                minpow 1
 217                                                                power `(,@power 1))
 218                                                          (return t))))
 219                                                  ((eq (caar morcel) 'mexpt)
 220                                                   (let ((expon (caddr morcel)))
 221                                                     (cond ((acceptable-power morcel)
 222                                                            (setq place `(,@place ,k)
 223                                                                  power `(,@power ,expon))
 224                                                            (return t)))))
 225                                                  (t (cond ((and nstate
 226                                                                 (alike1 morcel var)
 227                                                                 (or (not expon-sign)
 228                                                                     (return nil)))
 229                                                            (setq place `(,@place ,k)
 230                                                                  minpow 1
 231                                                                  power `(,@power 1))
 232                                                            (return t))))))))
 233                                       (t (return nil))))
 234                                ((and nstate (alike1 exam-term var) (not expon-sign))
 235                                 (setq place `(,@place -1)
 236                                       minpow 1
 237                                       power `(,@power 1)))
 238                                (t (return nil)))))))))))))
 239
 240
 241 (defun pair-factor (gel flag)
 242   (cond ((and flag (or ($mapatom gel) (null (cdddr gel)))) gel)
 243         (t (do ((lcl (cdr gel) (cdr lcl))
 244                 (backpnt gel lcl))
 245                ((null (cdr lcl)) gel)
 246              (let* ((pntr (add (car lcl) (cadr lcl)))
 247                     (g (factorout-monomial pntr)))
 248                 (or (eq pntr g)
 249                     (progn (let ((again (more-subfactors-q g)))
 250                              (or (eq again g) (setq g again)))
 251                            (rplaca lcl g)
 252                            (let ((exp (cddr lcl)))
 253                              (rplacd lcl exp)
 254                              (and exp
 255                                   (pair-factor backpnt nil))
 256                              (return (cond ((null (cddr gel)) (cadr gel))
 257                                            (t gel)))))))))))
 258
 259
 260 (defun more-subfactors-q (gg)
 261        (cond ((eq (caar gg) 'mtimes)
 262               (do ((lom (cdr gg) (cdr lom))
 263                    (modified)
 264                    (back gg lom))
 265                   ((null lom) (cond (modified (muln (cdr gg) t))
 266                                     (t gg)))
 267                 (let ((obj (car lom)))
 268                   (and (mplusp obj)
 269                        (let ((pntr (pair-factor obj t)))
 270                          (or (eq pntr obj)
 271                              (let ((fit (cdr pntr)))
 272                                (rplacd back (append fit (cdr lom)))
 273                                (setq lom (nthcdr (length fit) back)
 274                                      modified t))))))))
 275              (t (pair-factor gg t))))
 276
 277
 278 (defun gcfac-prodscan (x)
 279     (do ((inlev (cdr x) (cdr inlev))
 280          (modified)
 281          (backpnt x inlev))
 282         ((null inlev) (cond (modified (muln (cdr x) t))
 283                             (t x)))
 284       (let* ((possibl-sum (car inlev))
 285              (pntr (monomial-factor possibl-sum)))
 286         (or (eq pntr possibl-sum)
 287             (let ((fit (cdr pntr)))
 288               (rplacd backpnt (append fit (cdr inlev)))
 289               (setq inlev (nthcdr (length fit) backpnt)
 290                     modified t))))))
 291
 292
 293 (defun monomial-factor (exp)
 294   (cond (($mapatom exp) exp)
 295         ((eq (caar exp) 'mtimes)
 296          (gcfac-prodscan exp))
 297         ((eq (caar exp) 'mplus)
 298          (do ((mlm (cdr exp) (cdr mlm)))
 299              ((null mlm))
 300            (let ((potenl-prod (car mlm)))
 301              (cond ((mtimesp potenl-prod)
 302                     (let ((w (gcfac-prodscan potenl-prod)))
 303                       (or (eq w potenl-prod) (rplaca mlm w))))
 304                    (t (monomial-factor potenl-prod)))))
 305          (more-subfactors-q (factorout-monomial exp)))
 306         (t (do ((mlm (cdr exp) (cdr mlm)))
 307                ((null mlm) exp)
 308              (let* ((obj (car mlm)) (res (monomial-factor obj)))
 309                (or (eq obj res) (rplaca mlm res)))))))
 310
 311 (defun $gcfac (x)
 312   (cond (($mapatom x) x)
 313         (t (monomial-factor (copy-tree ($totaldisrep x))))))
 314