384 lines
11 KiB
Common Lisp
384 lines
11 KiB
Common Lisp
;;; CLASSIFYING-SPACES CLASSIFYING-SPACES CLASSIFYING-SPACES
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;;; CLASSIFYING-SPACES CLASSIFYING-SPACES CLASSIFYING-SPACES
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;;; CLASSIFYING-SPACES CLASSIFYING-SPACES CLASSIFYING-SPACES
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(IN-PACKAGE "CAT")
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(provide "classifying-spaces")
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(DEFCONSTANT +NULL-GBAR+ (make-gbar :dmns 0 :list +empty-list+))
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;;; NIGBAR = non-normalized igbar (with dimension)
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(DEFUN NORMALIZE-GBAR (nigbar)
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(declare (list nigbar))
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(the absm
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(let ((dmns (first nigbar))
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(igbar (rest nigbar)))
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(declare
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(fixnum dmns)
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(list igbar))
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(when (zerop dmns)
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(return-from normalize-gbar (absm 0 +null-gbar+)))
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(do ((mark igbar (cdr mark))
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(indx (1- dmns) (1- indx))
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(2-indx (2-exp (1- dmns)) (ash 2-indx -1))
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(mask (mask (1- dmns)) (ash mask -1))
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(and-dgops -1 (logand and-dgops (dgop (car mark))))
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;; r = result
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(r-dgop 0)
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(r-absm-list +empty-list+))
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((endp mark)
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(absm r-dgop
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(make-gbar
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:dmns (- dmns (logcount r-dgop))
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:list (nreverse r-absm-list))))
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(declare
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(list mark r-absm-list)
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(fixnum indx 2-indx mask and-dgops rdgop))
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(when (zerop and-dgops)
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(return-from normalize-gbar
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(absm r-dgop
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(make-gbar
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:dmns (- dmns (logcount r-dgop))
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:list (nreconc r-absm-list mark)))))
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(let ((absm (car mark)))
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(with-absm (dgop gmsm) absm
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(declare (ignore gmsm))
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(if (and (= dgop mask)
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(logbitp indx and-dgops))
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(progn
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(incf r-dgop 2-indx)
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(mapl
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#'(lambda (sublist)
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(declare (list sublist))
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(setf (car sublist)
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(let ((absm (car sublist)))
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(declare (type absm absm))
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(with-absm (dgop gmsm) absm
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(absm (multiple-value-bind (q r)
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(floor dgop 2-indx)
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(declare (fixnum q r))
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(+ (ash (1- q) (1- indx)) r))
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gmsm)))))
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r-absm-list))
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(push absm r-absm-list))))))))
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#|
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(normalize-gbar (list 0))
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(normalize-gbar (list 1 (absm 0 'i)))
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(normalize-gbar (list 2 (absm 1 'i) (absm 0 'i)))
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(normalize-gbar (list 2 (absm 0 'a) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 0 'a) (absm 0 'b) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 7 'i) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 0 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 2 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 4 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 3 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 5 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 6 'a) (absm 3 'i) (absm 0 'c) (absm 0 'i)))
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(normalize-gbar (list 4 (absm 1 'a) (absm 3 'i) (absm 1 'i) (absm 0 'i)))
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|#
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(DEFMETHOD PRINT-KEYCONS ((car (eql :gbar)) cdr stream)
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(declare
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(list cdr)
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(stream stream))
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(the (eql t)
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(progn
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(princ "<<GBar" stream)
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(dolist (absm (rest cdr))
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(declare (type absm absm))
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(with-absm (dgop gmsm) absm
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(format stream "<~A ~A>"
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(hyphenize-list (dgop-int-ext dgop))
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gmsm)))
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(princ ">>" stream)
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t)))
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(DEFUN UNNORMALIZE-GBAR (absm idnt)
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(declare
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(type absm absm)
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(type gmsm idnt))
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(the igbar
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(with-absm (dgop gbar) absm
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(with-gbar (dmns list) gbar
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(setf list (reverse list))
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(do ((dgop2 dgop (ash dgop2 -1))
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(indx 0 (1+ indx))
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(2-indx 1 (ash 2-indx 1))
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(dgop3 0)
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(rslt +empty-list+))
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((zerop dgop2)
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(cons (+ dmns (logcount dgop))
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(nreconc
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(mapcar
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#'(lambda (absm)
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(declare (type absm absm))
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(ndgnr dgop3 absm))
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list)
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rslt)))
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(declare
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(list rslt)
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(fixnum dgop2 2-indx dgop3))
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(if (oddp dgop2)
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(progn
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(push (absm (mask indx) idnt) rslt)
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(incf dgop3 2-indx))
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(push (ndgnr dgop3 (pop list)) rslt)))))))
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#|
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(unnormalize-gbar (absm 1 +null-gbar+) 'i)
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(unnormalize-gbar (absm 15 +null-gbar+) 'i)
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(normalize-gbar (unnormalize-gbar (absm 15 +null-gbar+) 'i))
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(unnormalize-gbar
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(absm 0 (make-gbar :dmns 4
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:list (list (absm 0 'a) (absm 0 'b)
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(absm 0 'c) (absm 0 'i)))) 'i)
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(normalize-gbar
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(unnormalize-gbar
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(absm 0 (make-gbar :dmns 4
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:list (list (absm 0 'a) (absm 0 'b)
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(absm 0 'c) (absm 0 'i)))) 'i))
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(unnormalize-gbar
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(absm 5 (make-gbar :dmns 4
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:list (list (absm 0 'a) (absm 0 'b)
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(absm 0 'c) (absm 0 'i)))) 'i)
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(normalize-gbar
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(unnormalize-gbar
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(absm 5 (make-gbar :dmns 4
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:list (list (absm 0 'a) (absm 0 'b)
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(absm 0 'c) (absm 0 'i)))) 'i))
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(unnormalize-gbar
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(absm 9 (make-gbar :dmns 4
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:list (list (absm 0 'a) (absm 0 'b)
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(absm 0 'c) (absm 0 'i)))) 'i)
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(normalize-gbar
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(unnormalize-gbar
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(absm 9 (make-gbar :dmns 4
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:list (list (absm 0 'a) (absm 0 'b)
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(absm 0 'c) (absm 0 'i)))) 'i))
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|#
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(DEFUN GBAR (dmns &rest rest)
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(the gbar
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(progn
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(unless (= (+ dmns dmns) (length rest))
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(error "In GBAR, the argument list has a wrong length."))
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(make-gbar :dmns dmns
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:list (do ((mark rest (cddr mark))
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(rslt +empty-list+
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(cons (absm (car mark) (cadr mark))
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rslt)))
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((endp mark) (nreverse rslt))
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(declare (list mark rslt)))))))
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#|
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(gbar 0)
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(gbar 1)
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(gbar 2 1 'a 2 'b)
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|#
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(DEFUN CLASSIFYING-SPACE-CMPR (cmpr)
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(declare (type cmprf cmpr))
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(flet ((rslt (gbar1 gbar2)
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(declare (type gbar gbar1 gbar2))
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(maplexico
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#'(lambda (absm1 absm2)
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(declare (type absm absm1 absm2))
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(a-cmpr3 cmpr absm1 absm2))
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(gbar-list gbar1) (gbar-list gbar2))))
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(the cmprf #'rslt)))
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#|
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(setf cmpr (classifying-space-cmpr 's-cmpr))
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(funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 1 'a 0 'a))
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(funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'b 0 'a))
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(funcall cmpr (gbar 2 0 'a 0 'a) (gbar 2 0 'a 0 'a))
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|#
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(DEFUN CLASSIFYING-SPACE-BASIS (basis)
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(declare (type basis basis))
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(when (eq basis :locally-effective)
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(return-from classifying-space-basis :locally-effective))
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(let ((crts-basis :locally-effective) ;; to be redefined
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(idnt (first (funcall basis 0))))
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(declare
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(type basis crts-basis)
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(type gmsm idnt))
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(labels ((rslt (dmns)
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(declare (fixnum dmns))
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(when (minusp dmns)
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(return-from rslt +empty-list+))
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(when (zerop dmns)
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(return-from rslt (list +null-gbar+)))
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(let ((basis-1 (funcall crts-basis (1- dmns))))
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(declare (list basis-1))
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(nreverse
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(mapcar
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#'(lambda (crpr)
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(declare (type crpr crpr))
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(with-crpr (absm1 absm2) crpr
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(make-gbar
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:dmns dmns
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:list (cons absm1
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(rest (unnormalize-gbar absm2 idnt))))))
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(member-if
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#'(lambda (dgop)
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(declare (fixnum dgop))
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(< dgop (mask (1- dmns))))
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(reverse basis-1)
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:key #'caadr))))))
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(setf crts-basis (crts-prdc-basis basis #'rslt))
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(the basis #'rslt))))
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#|
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(cat-init)
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(setf k (k-z2-1))
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(setf b (classifying-space-basis (basis k)))
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(dotimes (i 5) (print (funcall b i)))
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|#
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(DEFUN CLASSIFYING-SPACE-FACE (face grml-sintr)
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(declare
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(type face face)
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(type sintr grml-sintr))
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(flet ((rslt (indx dmns gbar)
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(declare
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(fixnum indx dmns)
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(type gbar gbar))
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(when (= indx dmns)
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(return-from rslt
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(normalize-gbar (cons (1- dmns) (rest (gbar-list gbar))))))
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(do ((mark (gbar-list gbar) (cdr mark))
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(dmns2 (1- dmns) (1- dmns2))
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(rslt +empty-list+
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(cons (a-face4 face indx dmns2 (car mark))
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rslt)))
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((= dmns2 indx)
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(if (zerop indx)
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(normalize-gbar (cons (1- dmns) (nreverse rslt)))
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(normalize-gbar
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(cons (1- dmns)
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(nreconc
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rslt
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(cons (a-grml4 grml-sintr (1- indx)
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(second mark)
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(a-face4 face indx indx (first mark)))
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(nthcdr 2 mark))))))))))
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(the face #'rslt)))
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#|
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(setf om (loop-space (moore 2 2)))
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(setf face (classifying-space-face (face om) (sintr (grml om))))
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(setf gbar (gbar 4 0 (loop3 3 'm2 1 4 'n3 1)
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0 (loop3 0 'n3 1)
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0 (loop3 0 'm2 1)
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0 +null-loop+))
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(dotimes (i 5)
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(print (funcall face i 4 gbar)))
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|#
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(DEFMETHOD CLASSIFYING-SPACE ((smgr simplicial-group))
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(the simplicial-set
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(simplicial-set :cmpr (classifying-space-cmpr (cmpr smgr))
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:basis (classifying-space-basis (basis smgr))
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:bsgn +null-gbar+
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:face (classifying-space-face (face smgr) (sintr (grml smgr)))
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:dfnt `(classifying-space ,smgr))))
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#|
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(cat-init)
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(setf c (classifying-space (k-z2-1)))
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(dfnt c)
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(first (basis c 4))
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(? c 4 (first (basis c 4)))
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(? c *)
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(cprd c 4 ***)
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(dotimes (i 5)
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(print (face c i 4 (first (basis c 4)))))
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|#
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(DEFUN CLASSIFYING-SPACE-GRML-SINTR (idnt grml-sintr)
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(declare
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(type gmsm idnt)
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(type sintr grml-sintr))
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(flet ((rslt (dmns crpr)
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(declare
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(fixnum dmns)
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(type crpr crpr))
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(with-crpr (absm1 absm2) crpr
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(let ((absm-list-1 (rest (unnormalize-gbar absm1 idnt)))
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(absm-list-2 (rest (unnormalize-gbar absm2 idnt))))
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(declare (list absm-list-1 absm-list-2))
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(normalize-gbar
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(cons dmns
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(mapcar
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#'(lambda (absm1 absm2)
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(declare (type absm absm1 absm2))
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(decf dmns) ;; !!
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(a-grml4 grml-sintr dmns absm1 absm2))
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absm-list-1 absm-list-2)))))))
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(the sintr #'rslt)))
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#|
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(setf grml (classifying-space-grml-sintr '() (sintr (grml (k-z-1)))))
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(funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
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0 (gbar 3 0 '(-1 -2) 0 '(-3) 0 '())))
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(funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
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4 (gbar 2 0 '(-3) 0 '())))
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(funcall grml 3 (crpr 0 (gbar 3 0 '(1 2) 0 '(3) 0 '())
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1 (gbar 2 0 '(-3) 0 '())))
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|#
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(DEFUN CLASSIFYING-SPACE-GRIN-SINTR (grin-sintr)
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(declare (type sintr grin-sintr))
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(flet ((rslt (dmns gbar)
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(declare
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(fixnum dmns)
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(type gbar gbar))
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(absm 0
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(make-gbar
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:dmns dmns
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:list (mapcar
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#'(lambda (absm)
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(declare (type absm absm))
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(a-grin4 grin-sintr dmns absm))
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(gbar-list gbar))))))
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(the sintr #'rslt)))
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#|
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(setf grin (classifying-space-grin-sintr (sintr (grin (k-z-1)))))
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(funcall grin 3 (gbar 3 0 '(1 2) 1 '() 0 '()))
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|#
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(DEFMETHOD CLASSIFYING-SPACE ((smgr ab-simplicial-group))
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(the ab-simplicial-group
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(change-class
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(simplicial-group :cmpr (classifying-space-cmpr (cmpr smgr))
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:basis (classifying-space-basis (basis smgr))
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:bsgn +null-gbar+
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:face (classifying-space-face (face smgr) (sintr (grml smgr)))
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:grml-sintr (classifying-space-grml-sintr
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(bsgn smgr)
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(sintr (grml smgr)))
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:grin-sintr (classifying-space-grin-sintr
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(sintr (grin smgr)))
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:dfnt `(classifying-space ,smgr))
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'ab-simplicial-group)))
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#|
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(setf k-z-1 (k-z-1))
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(setf k-z-2 (classifying-space k-z-1))
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(setf k-z-3 (classifying-space k-z-2))
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(homology k-z-3 0 10)
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(setf k-z2-1 (k-z2-1))
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(setf k-z2-2 (classifying-space k-z2-1))
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(setf k-z2-3 (classifying-space k-z2-2))
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(setf k-z2-4 (classifying-space k-z2-3))
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(setf k-z2-5 (classifying-space k-z2-4))
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(homology k-z2-5 0 7)
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|#
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