272 lines
9.2 KiB
Common Lisp
272 lines
9.2 KiB
Common Lisp
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(in-package :kenzo-test)
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(def-suite :kenzo)
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(defparameter *n* -1)
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(defun ff (degr i)
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(declare (special *n*))
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(do ((2*n* (ash *n* 1))
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(rslt cat:+empty-list+
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(cons (cons (let ((cffc (- (random 2*n*) *n*)))
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(if (minusp cffc) cffc (1+ cffc)))
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(decf gnrt (1+ (random *n*))))
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rslt))
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(gnrt i)
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(k 0 (1+ k)))
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((= k *n*)
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(cat:make-cmbn :degr degr :list rslt))))
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(defun cdelta (dmns)
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(the cat:chain-complex
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(cat:build-chcm
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:cmpr #'cat:l-cmpr
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:basis :locally-effective
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:bsgn '(0)
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:intr-dffr #'(lambda (degr gmsm)
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(cat:make-cmbn
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:degr (1- degr)
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:list (do ((rslt cat:+empty-list+
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(cons (cons sign
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(append
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(subseq gmsm 0 nark)
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(subseq gmsm (1+ nark))))
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rslt))
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(sign 1 (- sign))
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(nark 0 (1+ nark)))
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((> nark degr) rslt))))
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:strt :gnrt
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:orgn `(locally effective version of C_* delta ,dmns))))
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(defun make-f (tdmns bdmns)
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(cat:build-mrph
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:sorc (cdelta tdmns) :trgt (cdelta bdmns) :degr 0
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:intr #'(lambda (degr gmsm)
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(let ((pos (position-if #'(lambda (vertex)
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(>= vertex bdmns)) gmsm)))
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(if pos
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(if (< pos degr)
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(cat:zero-cmbn degr)
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(cat:cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
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(cat:cmbn degr 1 gmsm))))
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:strt :gnrt
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:orgn `(projection delta ,tdmns => delta ,bdmns)))
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(defun make-g (tdmns bdmns)
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(cat:build-mrph
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:sorc (cdelta bdmns) :trgt (cdelta tdmns) :degr 0
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:intr #'identity
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:strt :cmbn
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:orgn `(injection delta ,bdmns => delta ,tdmns)))
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(defun make-h (tdmns bdmns)
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(cat:build-mrph
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:sorc (cdelta tdmns) :trgt (cdelta tdmns) :degr +1
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:intr #'(lambda (degr gmsm)
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(let ((pos (position-if #'(lambda (vertex)
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(>= vertex bdmns)) gmsm)))
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(if pos
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(if (member bdmns gmsm)
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(cat:zero-cmbn (1+ degr))
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(cat:cmbn (1+ degr) (cat:-1-expt-n pos)
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(append (subseq gmsm 0 pos) (list bdmns)
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(subseq gmsm pos))))
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(cat:zero-cmbn (1+ degr)))))
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:strt :gnrt
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:orgn `(homotopy for delta ,tdmns => ,bdmns)))
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(defun make-rdct (tdmns bdmns)
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(let ((rdct (cat:build-rdct
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:f (make-f tdmns bdmns)
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:g (make-g tdmns bdmns)
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:h (make-h tdmns bdmns)
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:orgn `(reduction delta ,tdmns ,bdmns))))
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rdct))
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(defun cdelta1 (dmns)
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(cat:build-chcm
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:cmpr #'cat:l-cmpr
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:basis #'(lambda (n)
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(mapcar #'cat:dlop-int-ext (funcall (cat:delta-n-basis dmns) n)))
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:bsgn '(0)
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:intr-dffr #'(lambda (degr gmsm)
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(cat:make-cmbn
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:degr (1- degr)
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:list (do ((rslt cat:+empty-list+
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(cons (cons sign (append
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(subseq gmsm 0 nark)
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(subseq gmsm (1+ nark))))
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rslt))
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(sign 1 (- sign))
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(nark 0 (1+ nark)))
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((> nark degr) rslt))))
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:strt :gnrt
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:orgn `(locally effective version of C_* delta ,dmns)))
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(defun make-f1 (tdmns bdmns)
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(cat:build-mrph
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:sorc (cdelta1 tdmns) :trgt (cdelta1 bdmns) :degr 0
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:intr #'(lambda (degr gmsm)
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(let ((pos (position-if #'(lambda (vertex)
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(>= vertex bdmns)) gmsm)))
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(if pos
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(if (< pos degr)
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(cat:zero-cmbn degr)
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(cat:cmbn degr 1 (nconc (butlast gmsm) (list bdmns))))
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(cat:cmbn degr 1 gmsm))))
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:strt :gnrt
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:orgn `(projection delta ,tdmns => delta ,bdmns)))
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(defun make-g1 (tdmns bdmns)
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(cat:build-mrph
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:sorc (cdelta1 bdmns) :trgt (cdelta1 tdmns) :degr 0
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:intr #'identity
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:strt :cmbn
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:orgn `(injection delta ,bdmns => delta ,tdmns)))
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(defun make-h1 (tdmns bdmns)
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(cat:build-mrph
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:sorc (cdelta1 tdmns) :trgt (cdelta1 tdmns) :degr +1
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:intr #'(lambda (degr gmsm)
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(let ((pos (position-if #'(lambda (vertex)
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(>= vertex bdmns)) gmsm)))
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(if pos
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(if (member bdmns gmsm)
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(cat:zero-cmbn (1+ degr))
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(cat:cmbn (1+ degr) (cat:-1-expt-n pos)
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(append (subseq gmsm 0 pos) (list bdmns)
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(subseq gmsm pos))))
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(cat:zero-cmbn (1+ degr)))))
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:strt :gnrt
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:orgn `(homotopy for delta ,tdmns => ,bdmns)))
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(defun make-rdct1 (tdmns bdmns)
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(let ((rdct (cat:build-rdct
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:f (make-f1 tdmns bdmns)
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:g (make-g1 tdmns bdmns)
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:h (make-h1 tdmns bdmns)
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:orgn `(reduction delta ,tdmns ,bdmns))))
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rdct))
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(defun check-rdct ()
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(dolist (phi '(cat:*tdd* cat:*bdd* cat:*df-fd* cat:*dg-gd* cat:*id-fg*
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cat:*id-gf-dh-hd* cat:*hh* cat:*fh* cat:*hg*))
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(declare (type symbol phi))
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(is (cat:cmbn-zero-p
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(cat:cmbn-? (eval phi)
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(if (member phi '(cat:*bdd* cat:*dg-gd* cat:*id-fg*
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cat:*dg-gd* cat:*hg*))
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cat:*bc*
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cat:*tc*))))))
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(defun aleat-tc ()
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(do ((tdegr 0 (+ tdegr degr))
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(degr (+ 2 (random 3)) (+ 2 (random 3)))
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(gnrt (intern (coerce (vector (code-char (+ 65 (random 4)))) 'string))
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(intern (coerce (vector (code-char (+ 65 (random 4)))) 'string)))
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(rslt nil (cons (cat:brgn degr gnrt) rslt)))
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((> tdegr 8) (setf cat:*tc* (cat:cmbn tdegr 1 (cat:make-abar
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:list rslt))))))
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(defun aleat-bc ()
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(do ((tdegr 0 (+ tdegr degr))
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(degr (1+ (random 4)) (1+ (random 4)))
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(gnrt (intern (coerce (vector (code-char (+ 67 (random 2)))) 'string))
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(intern (coerce (vector (code-char (+ 67 (random 2)))) 'string)))
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(rslt nil (cons (cat:brgn degr gnrt) rslt)))
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((> tdegr 8) (setf cat:*bc* (cat:cmbn tdegr 1 (cat:make-abar
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:list rslt))))))
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(defun c ()
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(aleat-tc)
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(aleat-bc)
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(check-rdct))
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(defun random-abar (tot-degr~ max-degr)
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(do ((rslt nil)
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(cum-degr 0 (+ cum-degr degr 1))
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(degr))
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((>= cum-degr tot-degr~) (cat:make-abar :list rslt))
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(setf degr (1+ (random max-degr)))
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(push (cat:brgn (1+ degr)
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(let ((list (make-list degr)))
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(mapl
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#'(lambda (sublist)
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(setf (car sublist) (- (random 21) 10)))
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list)
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list))
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rslt)))
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(defun random-allp (length)
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(let ((rslt nil))
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(dotimes (i length)
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(let* ((gmsm (random (cat:mask 9)))
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(dmns (1- (logcount gmsm))))
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(when (plusp dmns)
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(push (cat:cbgn (1- dmns) gmsm) rslt))))
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(cat:make-allp :list rslt)))
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(defun random-apowr (dmns max-expn)
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(loop
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(let* ((dgop (random (cat:2-exp (1- dmns))))
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(gmsm (- dmns (logcount dgop))))
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(unless (< 0 gmsm 3)
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(return-from random-apowr
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(cat:apowr dgop gmsm (cat:srandom max-expn)))))))
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(defun random-cmbn (cmpr degr max-cffc max-expn loop-length cmbn-length)
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(apply #'cat:nterm-add cmpr degr
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(mapcar #'(lambda (dummy)
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(declare (ignore dummy))
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(cat:term (cat:srandom max-cffc)
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(random-crpr degr max-expn loop-length)))
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(make-list cmbn-length))))
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(defun random-crpr (dmns max-expn length)
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(loop
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(let ((loop (cat:normalize-loop dmns
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(random-niloop dmns max-expn length)))
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(dgop (random (cat:2-exp dmns))))
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(let ((absm (cat:2absm-acrpr (cat:absm dgop (- dmns (logcount dgop)))
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loop)))
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(when (and (zerop (cat:dgop absm))
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(not (< (cat:gmsm1 (cat:gmsm absm)) 3)))
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(return (cat:gmsm absm)))))))
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(defun random-loop-cmbn (cmpr degr max-cffc max-expn loop-length cmbn-length)
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(do ((rslt cat:+empty-list+ (cons term rslt))
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(i cmbn-length (1- i))
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(term))
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((zerop i)
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(apply #'cat:nterm-add cmpr degr rslt))
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(setf term
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(cat:term (cat:srandom max-cffc)
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(cat:make-loop :list (random-niloop degr max-expn
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loop-length))))))
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(defun random-niloop (dmns max-expn length)
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(mapcar #'(lambda (dummy)
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(declare (ignore dummy))
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(random-apowr (1+ dmns) max-expn))
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(make-list length)))
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