kenzo/archive/Kenzo-2/Kenzo-2-Acl5/loop-spaces.cl
2017-02-20 07:38:35 -06:00

611 lines
21 KiB
Common Lisp

;;; LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES
;;; LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES
;;; LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES LOOP-SPACES
(IN-PACKAGE "CAT")
(PROVIDE "loop-spaces")
(DEFCONSTANT +NULL-LOOP+ (make-loop :list +empty-list+))
;;; NILOOP = non-normalized iloop; a common dgop is possible.
(DEFUN NORMALIZE-LOOP (dmns niloop)
(declare (list niloop))
(the absm
(progn
(unless niloop
(return-from normalize-loop
(absm (mask dmns) +null-loop+)))
(let ((dgop (apply #'logand (mapcar #'car niloop))))
(declare (fixnum dgop))
(if (zerop dgop)
(absm 0 (make-loop :list niloop))
(absm dgop
(make-loop
:list (mapcar #'(lambda (apowr)
(cons
(dgop/dgop (apdgop apowr) dgop)
(cdr apowr)))
niloop))))))))
#|
(normalize-loop 4 +empty-list+)
(normalize-loop 4 '((1 a . 1)))
(normalize-loop 4 '((1 a . 1) (3 b . 1) (5 b . 1)))
|#
(DEFUN UNNORMALIZE-LOOP (absm)
(declare (type absm absm))
(the iloop
(with-absm (dgop loop) absm
(mapcar #'(lambda (apowr)
(declare (type apowr apowr))
(cons (dgop*dgop dgop (car apowr))
(cdr apowr)))
(loop-list loop)))))
#|
(unnormalize-loop (absm 1 (loop3 2 'a 3)))
|#
(DEFUN LOOP3 (&rest list)
(when (and (= 1 (length list))
(listp (first list)))
(setf list (first list)))
(unless (zerop (mod (length list) 3))
(error "In LOOP3, 3 should divide the list length."))
(flet ((fixnumpp (object)
(unless (typep object 'fixnum)
(error "In LOOP3, ~A should be a fixnum." object))
object))
(do ((rslt +empty-list+ (cons (apowr
(fixnumpp (car mark))
(cadr mark)
(fixnumpp (caddr mark)))
rslt))
(mark list (cdddr mark)))
((endp mark) (make-loop :list (nreverse rslt)))
(declare (list rslt mark)))))
#|
(loop3 nil)
(loop3 '(1 a 2 3 b -2))
(loop3 '(1 a 2 3 b b))
(loop3 '(1 a 2 3 b))
(loop3 1 'a 2 3 'b 4)
(loop3 1 'a 2 3 'b)
|#
(DEFMETHOD PRINT-KEYCONS ((car (eql :loop)) cdr stream)
(declare
(list cdr)
(stream stream))
(the loop
(progn
(format stream "<<Loop")
(dolist (apowr cdr)
(declare (type apowr apowr))
(with-apowr (dgop gmsm expn) apowr
(format stream "[")
(unless (zerop dgop)
(format stream "~A " (hyphenize-list (dgop-int-ext dgop))))
(format stream "~A" gmsm)
(unless (= 1 expn)
(format stream "\\~D" expn))
(format stream "]")))
(format stream ">>")
(cons car cdr))))
#|
(loop3 nil)
(loop3 '(0 a 2))
(loop3 '(1 a 2))
(loop3 '(3 a 2 5 b -1 6 c 4))
(loop3 '(7 a 1 11 b 1 13 c 1 14 d 1))
(loop3 '(7 a 1 11 b 1 13 c 1 7 d 1))
(loop3 '(0 a 1 0 b 2 0 c -1 1 d 1))
|#
(DEFUN APOWR-NILOOP (cmpr apowr niloop)
(declare
(type cmprf cmpr)
(type apowr apowr)
(type iloop niloop))
(the iloop
(progn
(unless niloop
(return-from apowr-niloop
(list apowr)))
(let ((apowr2 (first niloop)))
(declare (type apowr apowr2))
(with-apowr (dgop2 gmsm2 expn2) apowr2
(unless (and (= (apdgop apowr) dgop2)
(eq :equal (funcall cmpr (apgmsm apowr) gmsm2)))
(return-from apowr-niloop
(cons apowr niloop)))
(incf expn2 (apexpn apowr))
(if (zerop expn2)
(rest niloop)
(cons (apowr dgop2 gmsm2 expn2) (rest niloop))))))))
#|
(apowr-niloop #'s-cmpr '(0 a . 1) +empty-list+)
(apowr-niloop #'s-cmpr '(0 a . 1) '((1 a . 1)))
(apowr-niloop #'s-cmpr '(0 a . 1) '((0 b . 1)))
(apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . 1) (0 b . 1)))
(apowr-niloop #'s-cmpr '(0 a . 1) '((0 a . -1) (0 b . 1)))
|#
(DEFUN LOOP-SPACE-CMPR (cmpr)
(declare (type cmprf cmpr))
(flet ((2apowr-cmpr (apowr1 apowr2)
(declare (type apowr apowr1 apowr2))
(lexico
(f-cmpr (apdgop apowr1) (apdgop apowr2))
(funcall cmpr (apgmsm apowr1) (apgmsm apowr2))
(f-cmpr (apexpn apowr1) (apexpn apowr2)))))
(flet ((rslt (loop1 loop2)
(declare (type loop loop1 loop2))
(maplexico #'2apowr-cmpr (loop-list loop1) (loop-list loop2))))
(the cmprf #'rslt))))
#|
(setf cmpr (loop-space-cmpr #'s-cmpr))
(funcall cmpr (loop3 '(1 a 2)) (loop3 '(1 a -1)))
(funcall cmpr (loop3 '(3 b 4 1 a 2)) (loop3 '(3 b 4 1 a -1)))
|#
(DEFUN APOWR-FACE4 (face indx dmns apowr)
;; dmns = dimension in the loop-space
(declare
(type face face)
(type apowr apowr))
(with-apowr (dgop gmsm expn) apowr
(let ((face (a-face4 face indx (1+ dmns) (absm dgop gmsm))))
(declare (type absm face))
(with-absm (dgop gmsm) face
(if (logbitp (1- dmns) dgop)
nil
(apowr dgop gmsm expn))))))
#|
(setf face (face (delta-infinity)))
(apowr-face4 face 3 4 (apowr 1 31 5))
(setf face (face (sphere 5)))
(apowr-face4 face 2 5 (apowr 1 's5 4))
(apowr-face4 face 2 5 (apowr 2 's5 4))
|#
(DEFUN APOWR-LASTFACE4 (cmpr face dmns apowr)
;; indx =dmns
(declare
(type cmprf cmpr)
(type face face)
(fixnum dmns)
(type apowr apowr))
(the list
(with-apowr (dgop gmsm expn) apowr
(let ((absm (absm dgop gmsm)))
(declare (type absm absm))
(let ((face-n (a-face4 face dmns (1+ dmns) absm))
(face-n+1 (a-face4 face (1+ dmns) (1+ dmns) absm)))
(declare (type absm face-n face-n+1))
(with-absm (dgop1 gmsm1) face-n
(with-absm (dgop2 gmsm2) face-n+1
(if (logbitp (1- dmns) dgop1)
(if (logbitp (1- dmns) dgop2)
(return-from apowr-lastface4 +empty-list+)
(return-from apowr-lastface4
(list (apowr dgop2 gmsm2 (- expn)))))
(when (logbitp (1- dmns) dgop2)
(return-from apowr-lastface4
(list (apowr dgop1 gmsm1 expn)))))
(when (and (= dgop1 dgop2)
(eq :equal (funcall cmpr gmsm1 gmsm2)))
(return-from apowr-lastface4 +empty-list+))
(case expn
(+1 (list (apowr dgop2 gmsm2 -1) (apowr dgop1 gmsm1 +1)))
(-1 (list (apowr dgop1 gmsm1 -1) (apowr dgop2 gmsm2 +1)))
(otherwise
(if (plusp expn)
(do ((rslt +empty-list+ (cons apowr2 (cons apowr1 rslt)))
(apowr1 (apowr dgop1 gmsm1 +1))
(apowr2 (apowr dgop2 gmsm2 -1))
(nark expn (1- nark)))
((zerop nark) rslt)
(declare
(list rslt)
(type apowr apowr1 apowr2)))
(do ((rslt +empty-list+ (cons apowr1 (cons apowr2 rslt)))
(apowr1 (apowr dgop1 gmsm1 -1))
(apowr2 (apowr dgop2 gmsm2 +1))
(nark expn (1+ nark)))
((zerop nark) rslt)
(declare
(list rslt)
(type apowr apowr1 apowr2)))))))))))))
#|
(setf cmpr #'f-cmpr face (face (delta-infinity)))
(apowr-lastface4 cmpr face 4 (apowr 0 63 1))
(apowr-lastface4 cmpr face 4 (apowr 0 63 -1))
(apowr-lastface4 cmpr face 4 (apowr 0 63 3))
(apowr-lastface4 cmpr face 4 (apowr 0 63 -3))
(apowr-lastface4 cmpr face 4 (apowr 8 31 1))
(setf face #'(lambda (indx dmns gmsm) ; dmns = 5
(case indx
(5 (absm 8 'a))
(4 (absm 8 'a)))))
(setf cmpr #'s-cmpr)
(apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
(setf face #'(lambda (indx dmns gmsm) ; dmns = 5
(case indx
(5 (absm 1 'a))
(4 (absm 8 'a)))))
(apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
(setf face #'(lambda (indx dmns gmsm) ; dmns = 5
(case indx
(5 (absm 1 'a))
(4 (absm 1 'a)))))
(apowr-lastface4 cmpr face 4 (apowr 0 'a 2))
|#
(DEFUN LOOP-SPACE-FACE (cmpr face)
(declare
(type cmprf cmpr)
(type face face))
(flet ((rslt (indx dmns loop)
(declare
(fixnum indx dmns)
(type loop loop))
(the absm
(let ((rslt +empty-list+))
(declare (type iloop rslt))
(if (< indx dmns)
(dolist (apowr (loop-list loop))
(declare (type apowr apowr))
(let ((lface (apowr-face4 face indx dmns apowr)))
(declare (type (or null apowr) lface))
(when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
(dolist (apowr (loop-list loop))
(declare (type apowr apowr))
(let ((lface (apowr-lastface4 cmpr face dmns apowr)))
(declare (list lface))
(dolist (apowr lface)
(declare (type apowr apowr))
(setf rslt (apowr-niloop cmpr apowr rslt))))))
(normalize-loop (1- dmns) (nreverse rslt))))))
(the face #'rslt)))
#|
(setf cmpr #'f-cmpr
face (face (delta-infinity)))
(setf rslt (loop-space-face cmpr face))
(funcall rslt 2 4 (loop3 '(0 63 3 1 31 -3)))
(funcall rslt 2 4 (loop3 '(0 63 3 0 63 -3)))
(funcall rslt 4 4 (loop3 '(0 63 3 0 63 -3)))
(funcall rslt 4 4 (loop3 '(0 63 3)))
|#
(DEFUN LOOP-SPACE-FACE* (cmpr face)
(declare
(type cmprf cmpr)
(type face face))
(flet ((rslt (indx dmns loop)
(declare
(fixnum indx dmns)
(type loop loop))
(the (or loop (eql :degenerate))
(let ((rslt +empty-list+))
(declare (type iloop rslt))
(if (< indx dmns)
(dolist (apowr (loop-list loop))
(declare (type apowr apowr))
(let ((lface (apowr-face4 face indx dmns apowr)))
(declare (type (or null apowr) lface))
(when lface (setf rslt (apowr-niloop cmpr lface rslt)))))
(dolist (apowr (loop-list loop))
(declare (type apowr apowr))
(let ((lface (apowr-lastface4 cmpr face dmns apowr)))
(declare (list lface))
(dolist (apowr lface)
(declare (type apowr apowr))
(setf rslt (apowr-niloop cmpr apowr rslt))))))
(if (zerop (apply #'logand (mapcar #'car rslt)))
(make-loop :list (nreverse rslt))
:degenerate)))))
(the face* #'rslt)))
(DEFUN LOOP-SPACE-GRIN-SINTR (dmns loop)
(declare
(ignore dmns)
(type loop loop))
(the absm
(absm 0 (make-loop
:list (mapcar #'(lambda (apowr)
(declare (type apowr apowr))
(with-apowr (dgop gmsm expn) apowr
(apowr dgop gmsm (- expn))))
(reverse (loop-list loop)))))))
#|
(loop-space-grin-sintr 5 (loop3 0 'a 2 3 'b -3))
|#
(DEFUN LOOP-SPACE-GRML-SINTR (cmpr)
(declare (type cmprf cmpr))
(flet ((rslt (dmns crpr)
(declare
(fixnum dmns)
(type crpr crpr))
(the absm
(with-crpr (absm1 absm2) crpr
(let ((niloop1 (nreverse (unnormalize-loop absm1)))
(niloop2 (unnormalize-loop absm2)))
(declare (type iloop niloop1 niloop2))
(loop
(unless niloop1 (return))
(unless niloop2 (return))
(let ((apowr1 (first niloop1))
(apowr2 (first niloop2)))
(declare (type apowr apowr1 apowr2))
(with-apowr (dgop1 gmsm1 expn1) apowr1
(with-apowr (dgop2 gmsm2 expn2) apowr2
(unless (and (= dgop1 dgop2)
(eq :equal (funcall cmpr gmsm1 gmsm2)))
(return))
(incf expn1 expn2)
(cond ((zerop expn1)
(pop niloop1)
(pop niloop2))
(t
(pop niloop1)
(setf niloop2
(cons (apowr dgop2 gmsm2 expn1)
(rest niloop2)))
(return)))))))
(normalize-loop dmns
(nreconc niloop1 niloop2)))))))
(the sintr #'rslt)))
#|
(setf cmpr #'s-cmpr)
(setf ml (loop-space-grml-sintr cmpr))
(funcall ml 2 (crpr 3 (loop3) 0 (loop3 0 'a 2)))
(funcall ml 2 (crpr 0 (loop3 0 'a 2) 3 (loop3)))
(funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -2)))
(funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'a -3)))
(funcall ml 2 (crpr 0 (loop3 0 'a 2) 0 (loop3 0 'b -3)))
(funcall ml 2 (crpr 0 (loop3 0 'a 2 0 'b -3)
0 (loop3 0 'b +3 0 'a -2)))
|#
(DEFUN LOOP-SPACE (smst &optional (n 1))
(declare
(type simplicial-set smst)
(fixnum n))
(the simplicial-group
(if (= n 1)
(with-slots (cmpr face) smst
(declare
(type cmprf cmpr)
(type face face))
(simplicial-group
:cmpr (loop-space-cmpr cmpr)
:basis :locally-effective
:bsgn +null-loop+
:face (loop-space-face cmpr face)
:face* (loop-space-face* cmpr face)
:grml-sintr (loop-space-grml-sintr cmpr)
:grin-sintr #'loop-space-grin-sintr
:dfnt `(loop-space ,smst)))
(loop-space (loop-space smst) (1- n)))))
(DEFUN GDELTAB ()
(loop-space (deltab)))
#|
(cat-init)
(setf g (gdeltab))
(cmpr g (loop3 0 3 2) (loop3 0 3 2))
(cmpr g (loop3 0 3 2) (loop3 0 3 3))
(cmpr g (loop3 0 3 2) (loop3 0 5 2))
(cmpr g (loop3 0 5 2) (loop3 0 3 2))
(face g 3 3 (loop3 12 7 3))
(face g 3 3 (loop3 5 7 3))
(face g 3 3 (loop3 6 7 3 5 7 3 3 7 3))
(face g 4 4 (absm 4 (loop3 6 7 3 5 7 3 3 7 3)))
(check-faces (cmpr g) (face g) 3 (loop3 6 7 -3 5 7 -3 3 7 -3))
(setf dd (cmps g g))
(? dd 3 (loop3 6 7 3 5 7 3 3 7 3))
(grml g 2 (crpr 0 (loop3 0 15 3) 0 (loop3 0 15 4)))
(grin g 2 (loop3 0 15 -2))
(setf rslt (loop3 0 31 1))
(setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
(<a-b> 0 3)))
(dotimes (i 4)
(print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
(check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
(setf g (loop-space (sphere 2)))
(setf rslt (loop3 3 's2 2 5 's2 -2 6 's2 2))
(setf hat (mapcar #'(lambda (i) (face g i 3 rslt))
(<a-b> 0 3)))
(dotimes (i 4)
(print (kfll g i 3 (remove (nth i hat) hat :test #'equal)))
(check-kan g i 3 (remove (nth i hat) hat :test #'equal)))
(setf g (loop-space (sphere 3) 2))
(setf x (first (basis (echcm g) 4)))
(setf efhm (efhm g))
(setf x (lf efhm (rg efhm 4 x)))
(setf rslt (gnrt (first (cmbn-list x))))
(setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
(<a-b> 0 4)))
(dotimes (i 5)
(print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
(check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
(setf rslt (gnrt (third (cmbn-list x))))
(setf hat (mapcar #'(lambda (i) (face g i 4 rslt))
(<a-b> 0 4)))
(dotimes (i 5)
(print (kfll g i 4 (remove (nth i hat) hat :test #'equal)))
(check-kan g i 4 (remove (nth i hat) hat :test #'equal)))
(setf g (loop-space (sphere 3) 2))
(setf efhm (efhm g))
(setf echcm (rbcc efhm))
(setf basis (basis echcm 4))
(setf cmbn (cmbn 4 1 (first basis) 10 (second basis)
100 (third basis)))
(setf cmbn2 (lf efhm (rg efhm cmbn)))
(setf loop-list (mapcar #'cdr (cmbn-list cmbn2)))
(dolist (loop loop-list)
(setf hat (mapcar #'(lambda (i) (face g i 4 loop))
(<a-b> 0 4)))
(dotimes (i 5)
(print (kfll g i 4 (remove (nth i hat) hat)))
(check-kan g i 4 (remove (nth i hat) hat))))
|#
#|
(cat-init)
(setf p (r-proj-space 3))
(setf op (loop-space p))
(defun random-apowr (dmns max-expn)
(loop
(let* ((dgop (random (2-exp (1- dmns))))
(gmsm (- dmns (logcount dgop))))
(unless (< 0 gmsm 3)
(return-from random-apowr
(apowr dgop gmsm (srandom max-expn)))))))
(dotimes (i 15) (print (random-apowr 8 3)))
(defun random-niloop (dmns max-expn length)
(mapcar #'(lambda (dummy)
(random-apowr (1+ dmns) max-expn))
(make-list length)))
(dotimes (i 20)
(print (normalize-loop 7 (random-niloop 7 3 3))))
(defun random-loop-cmbn (cmpr degr max-cffc max-expn loop-length cmbn-length)
(do ((rslt +empty-list+ (cons term rslt))
(i cmbn-length (1- i))
(term))
((zerop i)
(apply #'nterm-add cmpr degr rslt))
(setf term
(term (srandom max-cffc)
(make-loop :list (random-niloop degr max-expn loop-length))))))
(setf cmpr (cmpr op))
(setf +too-much-time+ -1)
(setf c (random-loop-cmbn cmpr 8 10 4 4 100))
(time (? op (? op c)))
(time (? op (? op c)))
|#
#| ;; in EAT.
(DEFUN PR-INFINITY-EQS (gsm1 gsm2)
(declare (fixnum gsm1 gsm2))
t)
(DEFUN PR-INFINITY-BASIS (k)
(declare (fixnum k))
(flet ((rslt (dmns)
(declare (fixnum dmns))
(if (< 0 dmns k)
empty-list
(list dmns))))
(the basis #'rslt)))
(DEFUN PR-INFINITY-GDL (k)
(declare (fixnum k))
(flet ((rslt (indx dmns gsm)
(declare (fixnum indx dmns gsm))
(if (<= dmns k)
(asm (nreverse (<a-b< 0 (1- dmns))) 0)
(if (or (zerop indx)
(= indx dmns))
(asm nil (1- dmns))
(if (= dmns (1+ k))
(asm (nreverse (<a-b< 0 (1- dmns))) 0)
(asm (list (1- indx)) (- dmns 2)))))))
(the function #'rslt)))
(DEFUN PR-INFINITY (&optional (k 1))
(declare (fixnum k))
(build-ss
:eqs #'pr-infinity-eqs
:sbs (pr-infinity-basis k)
:bsp 0
:gdl (pr-infinity-gdl k)
:org `(pr-infinity ,k)))
(setf p (pr-infinity))
(sbs p 4)
(dotimes (i 5)
(print (gdl p i 4 4)))
(setf cc (ss-cc p))
(dotimes (i 5)
(print (d-? cc i i)))
(setf dd (cmp-mrp (cc-d cc) (cc-d cc)))
(dotimes (i 6)
(print (? dd i i)))
(setf p (pr-infinity 3))
(dotimes (i 7)
(print (sbs p i)))
(dotimes (i 5)
(print (gdl p i 4 4)))
(setf d (cc-d (ss-cc p)))
(dotimes (i 7)
(print (? d i i)))
(setf dd (cmp-mrp d d))
(dotimes (i 7)
(print (? dd i i)))
(setf p (pr-infinity 3))
(setf op (loop-space p))
(defun srandom (max)
(let ((rslt (- (random (+ max max)) max)))
(if (zerop rslt)
max
rslt)))
(dotimes (i 20) (print (srandom 3)))
(DEFUN DGOP-INT-EXT (dop)
(declare (fixnum dop))
(the list
(do ((dop dop (ash dop -1))
(rslt empty-list)
(bmark 0 (1+ bmark)))
((zerop dop) rslt)
(declare
(fixnum dop bmark)
(list rslt))
(when (oddp dop)
(push bmark rslt)))))
(defun random-apowr (dmns max-expn)
(let ((dgop (dgop-int-ext (* 2 (random (2-exp (1- dmns)))))))
(pwr (asm dgop (- 8 (length dgop))) (srandom max-expn))))
(dotimes (i 5) (print (random-apowr 8 3)))
(defun random-niloop (dmns max-expn length)
(mapcar #'(lambda (dummy)
(random-apowr (1+ dmns) max-expn))
(make-list length)))
(dotimes (i 20)
(print (normalize-loop 7 (make-strloop :lst (random-niloop 7 3 3)))))
(defun random-loop-cmbn (degr max-cffc max-expn loop-length cmbn-length)
(do ((rslt empty-list (cons mnm rslt))
(i cmbn-length (1- i))
(term))
((zerop i)
(make-cmb :dgr degr :lst rslt))
(setf mnm
(mnm (srandom max-cffc)
(make-strloop :lst (random-niloop degr max-expn loop-length))))))
(setf d (cc-d (ss-cc op)))
(setf c (random-loop-cmbn 8 10 4 4 100))
(time (??? d (??? d c)))
(time (??? d (??? d c)))
|#