528 lines
21 KiB
Common Lisp
528 lines
21 KiB
Common Lisp
;;;; -*- Mode: Lisp; indent-tabs-mode: nil -*-
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;;;
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;;; BAR BAR BAR BAR BAR BAR BAR BAR BAR
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;;; BAR BAR BAR BAR BAR BAR BAR BAR BAR
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;;; BAR BAR BAR BAR BAR BAR BAR BAR BAR
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;;;
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;;; MAC-LANE signs (p. 306)
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;;;
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(IN-PACKAGE #:cat)
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(PROVIDE "bar")
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(DEFUN ABAR (&rest list)
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(when (= 1 (length list))
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(setf list (first list)))
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(unless (evenp (length list))
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(error "In ABAR, the length list should be even."))
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(the abar
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(let ((rslt +empty-list+))
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(declare (list rslt))
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(do ((mark list (cddr mark)))
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((endp mark))
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(declare (list mark))
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(push (brgn (car mark) (cadr mark)) rslt))
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(make-abar :list (nreverse rslt)))))
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#-sbcl (DEFINE-CONSTANT +NULL-ABAR+ (make-abar :list +empty-list+))
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#+sbcl (DEFPARAMETER +NULL-ABAR+ (make-abar :list +empty-list+))
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;;; -[CLISP
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#|
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(DEFMETHOD PRINT-KEYCONS ((car (eql :abar)) cdr stream)
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(declare
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(list cdr)
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(stream stream))
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(the abar
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(progn
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(format stream "<<Abar")
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(dolist (brgn cdr)
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(declare (type brgn brgn))
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(with-brgn (degr gnrt) brgn
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(format stream "[~D ~A]" degr gnrt)))
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(format stream ">>")
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(cons car cdr))))
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|#
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;;; CLISP]-
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;;; +[CLISP
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(DEFUN ABAR-PRINT (abar stream depth)
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(declare
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(type abar abar) (stream stream)
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(ignore depth))
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(the abar
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(progn
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(format stream "<<Abar")
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(dolist (brgn (abar-list abar))
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(declare (type brgn brgn))
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(with-brgn (degr gnrt) brgn
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(format stream "[~D ~A]" degr gnrt)))
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(format stream ">>")
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abar)))
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;;; CLISP]+
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(DEFUN BAR-CMPR (cmpr)
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(declare (type cmprf cmpr))
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(flet ((rslt (abar1 abar2)
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(declare (type abar abar1 abar2))
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(the cmpr
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(let ((list1 (abar-list abar1))
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(list2 (abar-list abar2)))
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(declare (list list1 list2))
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(lexico
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(f-cmpr (length list1) (length list2))
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(maplexico
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#'(lambda (brgn1 brgn2)
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(lexico
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(f-cmpr (bdegr brgn1) (bdegr brgn2))
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(funcall cmpr (bgnrt brgn1) (bgnrt brgn2))))
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list1 list2))))))
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(the cmprf #'rslt)))
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(DEFUN BAR-BASIS-LENGTH (basis degr length)
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(declare
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(type basis basis)
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(fixnum degr length))
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(the list
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(progn
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(when (= 1 length)
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(return-from bar-basis-length
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(mapcar
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#'(lambda (item)
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(declare (type gnrt item))
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(list (brgn degr item)))
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(funcall basis (1- degr)))))
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(when (< degr 4)
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(return-from bar-basis-length +empty-list+))
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(mapcan
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#'(lambda (degr1)
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(declare (fixnum degr1))
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(let ((list1 (funcall basis (1- degr1)))
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(list2 (bar-basis-length
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basis (- degr degr1) (1- length))))
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(declare (list list1 list2))
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(mapcan
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#'(lambda (item1)
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(declare (type gnrt item1))
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(mapcar
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#'(lambda (item2)
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(declare (type iabar item2))
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(cons (brgn degr1 item1) item2))
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list2))
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list1)))
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(>a-b< 1 (1- degr))))))
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(DEFUN BAR-BASIS (basis)
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(declare (type basis basis))
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(the basis
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(progn
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(when (eq :locally-effective basis)
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(return-from bar-basis :locally-effective))
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(flet
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((rslt (degr)
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(declare (fixnum degr))
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(cond ((zerop degr) (list +null-abar+))
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((< degr 2) +empty-list+)
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(t
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(mapcan
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#'(lambda (length)
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(declare (fixnum length))
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(mapcar
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#'(lambda (iabar)
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(declare (type iabar iabar))
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(make-abar :list iabar))
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(bar-basis-length basis degr length)))
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(>a-b> 0 (floor degr 2)))))))
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#'rslt))))
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(DEFUN BAR-INTR-VRTC-DFFR (dffr)
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(declare (type morphism dffr))
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(labels ((rslt (degr iabar)
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;; the argument iabar is an internal algebraic bar,
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;; without the keyword :abar
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;; rslt returns an internal combination
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;; without the keyword :cmbn, without degree
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(declare
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(fixnum degr)
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(type iabar iabar))
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(progn
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(unless iabar
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(return-from rslt +empty-list+))
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(let ((brgn1 (first iabar))
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(rest2 (rest iabar)))
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(declare
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(type brgn brgn1)
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(type iabar rest2))
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(with-brgn (degr1 gnrt1) brgn1
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(let ((d-gnrt1 (cmbn-list (gnrt-? dffr (1- degr1)
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gnrt1)))
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(d-rest2 (rslt (- degr degr1) rest2))
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(degr1-1 (1- degr1))
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(rest-sign (-1-expt-n degr1)))
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(declare
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(type icmbn d-gnrt1 d-rest2)
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(fixnum degr1-1 rest-sign))
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(nconc
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(mapcar
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#'(lambda (term)
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(declare (type term term))
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(with-term (cffc gnrt) term
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(term (- cffc)
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(cons (brgn degr1-1 gnrt)
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rest2))))
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d-gnrt1)
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(mapcar
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#'(lambda (term)
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(with-term (cffc gnrt) term
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(term (* rest-sign cffc)
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(cons brgn1 gnrt))))
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d-rest2))))))))
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(the intr-mrph
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#'(lambda (degr abar)
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(declare
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(fixnum degr)
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(type abar abar))
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(make-cmbn
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:degr (1- degr)
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:list (mapcar
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#'(lambda (term)
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(with-term (cffc iabar) term
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(term cffc (make-abar :list iabar))))
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(rslt degr (abar-list abar))))))))
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(DEFGENERIC VRTC-BAR (chcm-hmeq-mrph))
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(DEFMETHOD VRTC-BAR ((chcm chain-complex))
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(the chain-complex
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(with-slots (cmpr basis dffr) chcm
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(declare
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(type cmprf cmpr)
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(type basis basis)
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(type morphism dffr))
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(build-chcm
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:cmpr (bar-cmpr cmpr)
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:basis (bar-basis basis)
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:bsgn +null-abar+
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:intr-dffr (bar-intr-vrtc-dffr dffr)
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:strt :gnrt
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:orgn `(vrtc-bar ,chcm)))))
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(DEFUN BAR-INTR-HRZN-DFFR (aprd)
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(declare (type morphism aprd))
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(labels ((rslt (degr iabar)
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(declare
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(fixnum degr)
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(type iabar iabar))
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(the icmbn
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(progn
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(unless (cdr iabar)
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(return-from rslt +empty-list+))
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(let ((brgn1 (first iabar))
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(brgn2 (second iabar))
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(rest1 (rest iabar))
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(rest2 (cddr iabar)))
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(declare
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(type brgn brgn1 brgn2)
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(type iabar rest1 rest2))
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(with-brgn (degr1 gnrt1) brgn1
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(with-brgn (degr2 gnrt2) brgn2
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(let ((sign (-1-expt-n degr1))
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(aprd-brgn1-brgn2
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(gnrt-? aprd
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(+ degr1 degr2 -2)
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(tnpr (1- degr1)
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gnrt1
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(1- degr2)
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gnrt2)))
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(aprd-rest1 (rslt
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(- degr degr1)
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rest1)))
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(declare
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(type cmbn aprd-brgn1-brgn2)
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(type icmbn aprd-rest1))
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(with-cmbn (degr12 icmbn12)
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aprd-brgn1-brgn2
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(incf degr12)
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(nconc
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(mapcar
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#'(lambda (term2)
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(declare (type term
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term2))
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(with-term (cffc2 iabar2)
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term2
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(term (* sign cffc2)
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(cons brgn1
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iabar2))))
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aprd-rest1)
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(mapcar
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#'(lambda (term1)
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(declare (type term
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term1))
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(with-term (cffc1 gnrt12)
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term1
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(term (* sign cffc1)
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(cons (brgn
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degr12
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gnrt12)
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rest2))))
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icmbn12)))))))))))
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(the intr-mrph
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#'(lambda (degr abar)
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(declare
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(fixnum degr)
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(type abar abar))
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(the cmbn
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(make-cmbn :degr (1- degr)
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:list (mapcar #'(lambda (term)
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(declare (type term term))
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(with-term (cffc iabar) term
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(term cffc
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(make-abar
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:list iabar))))
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(rslt degr (abar-list abar)))))))))
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(DEFUN BAR-HRZN-DFFR (algb)
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(declare (type algebra algb))
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(the morphism
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(with-slots (aprd) algb
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(declare (type morphism aprd))
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(build-mrph
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:sorc (vrtc-bar algb) :trgt (vrtc-bar algb) :degr -1
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:intr (bar-intr-hrzn-dffr aprd) :strt :gnrt
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:orgn `(bar-hrzn-dffr ,algb)))))
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(DEFUN BAR-INTR-DFFR (vrtc-dffr hrzn-dffr)
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(declare (type morphism vrtc-dffr hrzn-dffr))
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(flet ((rslt (degr abar)
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(declare
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(fixnum degr)
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(type abar abar))
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(make-cmbn :degr (1- degr)
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:list (append ;;; and not nconc, otherwise a terrible bug,
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;;; when the first result is stored in memory
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(cmbn-list (gnrt-? hrzn-dffr degr abar))
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(cmbn-list (gnrt-? vrtc-dffr degr abar))))))
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(the intr-mrph #'rslt)))
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(DEFGENERIC BAR (algebra-or-hmeq))
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(DEFMETHOD BAR ((algebra algebra))
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(let ((vrtc-bar (vrtc-bar algebra))
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(bar-hrzn-dffr (bar-hrzn-dffr algebra)))
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(declare (type chain-complex vrtc-bar)
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(type morphism bar-hrzn-dffr))
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(the chain-complex
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(let ((rslt (build-chcm
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:cmpr (cmpr vrtc-bar)
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:basis (basis vrtc-bar)
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:bsgn +null-abar+
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:intr-dffr (bar-intr-dffr (dffr vrtc-bar) bar-hrzn-dffr)
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:strt :gnrt
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:orgn `(add ,vrtc-bar ,bar-hrzn-dffr))))
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(declare (type chain-complex rslt))
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(setf (slot-value rslt 'grmd) (grmd vrtc-bar))
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rslt))))
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(DEFUN CMBN-ABAR-CMBN-TNPR (cmbn abar-cmbn)
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(declare (type cmbn cmbn abar-cmbn))
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(the cmbn
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(with-cmbn (degr1 list1) cmbn
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(incf degr1) ;; because abar organization
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(with-cmbn (degrr listr) abar-cmbn
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(make-cmbn
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:degr (+ degr1 degrr)
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:list
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(mapcan
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#'(lambda (term1)
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(declare (type term term1))
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(with-term (cffc1 gnrt1) term1
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(let ((brgn1 (brgn degr1 gnrt1)))
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(declare (type brgn brgn1))
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(mapcar
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#'(lambda (termr)
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(declare (type term
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termr))
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(with-term (cffcr abarr)
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termr
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(term
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(* cffc1 cffcr)
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(make-abar
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:list (cons
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brgn1
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(abar-list
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abarr))))))
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listr))))
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list1))))))
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(DEFUN NCMBN-BAR (cmbn-list)
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(declare (list cmbn-list))
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(the cmbn
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(progn
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(unless cmbn-list
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(return-from ncmbn-bar (cmbn 0 1 +null-abar+)))
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(cmbn-abar-cmbn-tnpr
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(first cmbn-list)
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(ncmbn-bar (rest cmbn-list))))))
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(DEFUN MRPH-VRTC-BAR-INTR (mrph)
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(declare (type morphism mrph))
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(flet ((rslt (degr abar)
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(declare
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(ignore degr)
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(type abar abar))
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(the cmbn
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(ncmbn-bar
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(mapcar #'(lambda (brgn)
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(declare (type brgn brgn))
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(with-brgn (degr gnrt) brgn
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(gnrt-? mrph (1- degr) gnrt)))
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(abar-list abar))))))
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(the intr-mrph #'rslt)))
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(DEFMETHOD VRTC-BAR ((mrph morphism))
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(the morphism
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(if (eq (first (orgn mrph)) 'idnt-mrph)
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(idnt-mrph (vrtc-bar (sorc mrph)))
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(build-mrph
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:sorc (vrtc-bar (sorc mrph))
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:trgt (vrtc-bar (trgt mrph))
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:degr 0
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:intr (mrph-vrtc-bar-intr mrph)
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:strt :gnrt
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:orgn `(vrtc-bar ,mrph)))))
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(DEFUN HMTP-VRTC-BAR-INTR (h gf)
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(declare (type morphism h gf))
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(labels ((rslt (degr iabar)
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(declare
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(fixnum degr)
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(type iabar iabar))
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(unless iabar
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(return-from rslt +empty-list+))
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(let ((brgn1 (first iabar))
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(rest2 (rest iabar)))
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(declare
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(type brgn brgn1)
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(list rest2))
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(with-brgn (degr1 gnrt1) brgn1
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(let ((h-gnrt1 (cmbn-list (gnrt-? h (1- degr1)
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gnrt1)))
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(h-rest2 (rslt (- degr degr1) rest2))
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(degr1+1 (1+ degr1))
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(rest-sign (-1-expt-n degr1))
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(gf-gnrt1 (cmbn-list (gnrt-? gf (1- degr1)
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gnrt1))))
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(declare
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(fixnum degr1+1 rest-sign)
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(type icmbn h-gnrt1 h-rest2 gf-gnrt1))
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(nconc
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(mapcan
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#'(lambda (term1)
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(declare (type term term1))
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(with-term (cffc1 gnrt11) term1
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(mapcar
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#'(lambda (term2)
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(declare (type term term2))
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(with-term (cffc2 iabar2)
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term2
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(term (* rest-sign cffc1
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cffc2)
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(cons
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(brgn degr1 gnrt11)
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iabar2))))
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h-rest2)))
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gf-gnrt1)
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(mapcar
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#'(lambda (term1)
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(declare (type term term1))
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(with-term (cffc1 gnrt11) term1
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(term (- cffc1)
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(cons
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(brgn degr1+1 gnrt11)
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rest2))))
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h-gnrt1)))))))
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(the intr-mrph
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#'(lambda (degr abar)
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(declare
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(fixnum degr)
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(type abar abar))
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(make-cmbn
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:degr (1+ degr)
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:list (mapcar
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#'(lambda (term)
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(declare (type term term))
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(with-term (cffc iabar) term
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(declare
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(fixnum cffc)
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(type iabar iabar))
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(term cffc (make-abar :list iabar))))
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(rslt degr (abar-list abar))))))))
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(DEFUN HMTP-VRTC-BAR (h gf)
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(declare (type morphism h gf))
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(unless (and (= +1 (degr h))
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(= +0 (degr gf)))
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(error "In HMTP-VRTC-BAR, the morphism degrees are not the right ones."))
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(unless (and (eq (sorc h) (trgt h))
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(eq (trgt h) (sorc gf))
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(eq (sorc gf) (trgt gf)))
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(error "In HMTP-VRTC-BAR, fg-h sources and targets are not the same."))
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(the morphism
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(if (eq (first (orgn h)) 'zero-mrph)
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(zero-mrph (vrtc-bar (sorc h)))
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(build-mrph
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:sorc (vrtc-bar (sorc h)) :trgt (vrtc-bar (sorc h)) :degr +1
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:intr (hmtp-vrtc-bar-intr h gf)
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:strt :gnrt
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:orgn `(hmtp-vrtc-bar ,h ,gf)))))
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(DEFMETHOD VRTC-BAR ((rdct reduction))
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(the reduction
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(if (eq (first (orgn rdct)) 'trivial-rdct)
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(trivial-rdct (vrtc-bar (bcc rdct)))
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(with-slots (f g h) rdct
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(build-rdct
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:f (vrtc-bar f)
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:g (vrtc-bar g)
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:h (hmtp-vrtc-bar h (cmps g f))
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:orgn `(vrtc-bar ,rdct))))))
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|
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(DEFMETHOD VRTC-BAR ((hmeq homotopy-equivalence))
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(the homotopy-equivalence
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(if (eq (first (orgn hmeq)) 'trivial-hmeq)
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(trivial-hmeq (vrtc-bar (lbcc hmeq)))
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|
(with-slots (lrdct rrdct) hmeq
|
|
(build-hmeq
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|
:lrdct (vrtc-bar lrdct)
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|
:rrdct (vrtc-bar rrdct)
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|
:orgn `(vrtc-bar ,hmeq))))))
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|
|
|
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(DEFMETHOD BAR ((hmeq homotopy-equivalence))
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|
(unless (typep (lbcc hmeq) 'algebra)
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(error "In (BAR HMEQ), the LBCC should be a algebra."))
|
|
(the homotopy-equivalence
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|
(if (eq (first (orgn hmeq)) 'trivial-hmeq)
|
|
(trivial-hmeq (bar (lbcc hmeq)))
|
|
(add (vrtc-bar hmeq) (bar-hrzn-dffr (lbcc hmeq))))))
|