461 lines
16 KiB
Common Lisp
461 lines
16 KiB
Common Lisp
;;; CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP
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;;; CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP
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;;; CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP CHCM-ELEMENTARY-OP
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(IN-PACKAGE "CAT")
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(PROVIDE "chcm-elementary-op")
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(DEFUN Z-CHCM ()
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(the chain-complex
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(chain-complex
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:cmpr #'(lambda (gnrt1 gnrt2)
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(declare (ignore gnrt1 gnrt2))
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(the cmpr :equal))
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:basis #'(lambda (n)
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(declare (type fixnum n))
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(the list
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(if (zerop n)
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(list :Z-gnrt)
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+empty-list+)))
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:bsgn :Z-gnrt
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:dffr-intr #'zero-dffr-intr
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:dffr-strt :cmbn
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:dfnt '(Z-chcm))))
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(DEFUN ZERO-MRPH (chcm1 &optional (chcm2 chcm1) (degr 0))
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(declare (type chain-complex chcm1 chcm2)
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(type fixnum degr))
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(the morphism
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(morphism
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:sorc chcm1 :trgt chcm2 :degr degr
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:intr #'(lambda (cmbn)
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(declare (type cmbn cmbn))
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(zero-cmbn (+ (cmbn-degr cmbn) degr)))
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:strt :cmbn
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:dfnt `(zero-mrph ,chcm1 ,chcm2 ,degr))))
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#|
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(cat-init)
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(setf z (zero-mrph (Z-chcm) (Z-chcm) 2))
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(gnrt-? z 0 :z-gnrt)
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(cmbn-? z (cmbn 3))
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(setf z2 (zero-mrph (Z-chcm) (Z-chcm) 2))
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(eq z z2)
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(setf z3 (zero-mrph (Z-chcm) (Z-chcm) 3))
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(gnrt-? z3 0 :z-gnrt)
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(eq z z3))
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|#
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(DEFUN IDNT-MRPH (chcm)
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(declare (type chain-complex chcm))
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(the morphism
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(morphism
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:sorc chcm :trgt chcm :degr 0
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:intr #'identity
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:strt :cmbn
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:dfnt `(idnt-mrph ,chcm))))
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#|
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(setf zi (idnt-mrph (Z-chcm)))
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(gnrt-? zi 0 :z-gnrt)
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(setf zi2 (idnt-mrph (Z-chcm)))
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(eq zi zi2))
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|#
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(DEFUN OPPS (mrph)
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(declare (type morphism mrph))
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(the morphism
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(with-slots (sorc trgt degr) mrph
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(morphism
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:sorc sorc :trgt trgt :degr degr
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:intr #'(lambda (cmbn)
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(declare (type cmbn cmbn))
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(cmbn-opps (cmbn-? mrph cmbn)))
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:strt :cmbn
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:dfnt `(opps ,mrph)))))
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#|
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(cat-init)
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(setf -zi (opps (idnt-mrph (Z-chcm))))
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(gnrt-? -zi 0 :z-gnrt)
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(setf -zi2 (opps (idnt-mrph (Z-chcm))))
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(eq -zi -zi2))
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|#
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(DEFMETHOD CMPS ((chcm1 chain-complex) (chcm2 chain-complex) &optional strt)
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(declare (type (or strt null) strt))
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(the morphism
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(cmps (dffr chcm1) (dffr chcm2) strt)))
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(DEFMETHOD CMPS ((chcm1 chain-complex) (mrph2 morphism) &optional strt)
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(declare (type (or strt null) strt))
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(the morphism
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(cmps (dffr chcm1) mrph2 strt)))
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(DEFMETHOD CMPS ((mrph1 morphism) (chcm2 chain-complex) &optional strt)
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(declare (type (or strt null) strt))
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(the morphism
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(cmps mrph1 (dffr chcm2) strt)))
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(DEFMETHOD CMPS ((mrph1 morphism) (mrph2 morphism) &optional strt)
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(declare (type (or strt null) strt))
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(the morphism
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(with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
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(declare
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(type chain-complex sorc1 trgt1)
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(fixnum degr1)
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(type strt strt1))
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(with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
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(declare
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(type chain-complex sorc2 trgt2)
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(fixnum degr2)
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(type strt strt2))
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(unless (eq (grmd sorc1) (grmd trgt2))
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(error "In 2MRPH-CMPS, the morphisms ~A and ~A may not be composed (cf source and target)."
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mrph1 mrph2))
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(unless strt
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(setf strt (if (and (eq strt1 :gnrt)
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(eq strt2 :gnrt))
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:gnrt
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:cmbn)))
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(when (or (eq (first (dfnt mrph1)) 'zero-mrph)
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(eq (first (dfnt mrph2)) 'zero-mrph))
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(return-from cmps
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(zero-mrph sorc2 trgt1 (+ degr1 degr2))))
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(when (eq (first (dfnt mrph1)) 'idnt-mrph)
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(return-from cmps mrph2))
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(when (eq (first (dfnt mrph2)) 'idnt-mrph)
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(return-from cmps mrph1))
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(ecase strt
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(:cmbn (morphism
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:sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
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:intr #'(lambda (cmbn)
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(declare (type cmbn cmbn))
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(the cmbn
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(cmbn-? mrph1 (cmbn-? mrph2 cmbn))))
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:strt :cmbn :dfnt `(2mrph-cmps ,mrph1 ,mrph2 ,strt)))
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(:gnrt (morphism
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:sorc sorc2 :trgt trgt1 :degr (+ degr1 degr2)
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:intr #'(lambda (degr gnrt)
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(declare
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(type fixnum degr)
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(type gnrt gnrt))
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(the cmbn
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(cmbn-? mrph1 (gnrt-? mrph2 degr gnrt))))
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:strt :gnrt :dfnt `(2mrph-cmps ,mrph1 ,mrph2 ,strt))))))))
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#|
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(cat-init)
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(setf cc (chain-complex :cmpr #'f-cmpr
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:basis :locally-effective
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:bsgn 0
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:dffr-intr #'(lambda (cmbn)
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(cmbn (1- (cmbn-degr cmbn))))
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:dffr-strt :cmbn
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:dfnt '(Z of Z)))
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(setf *n* 5)
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(defun ff (degr i)
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(do ((*2n* (ash *n* 1))
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(rslt +empty-list+
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(cons (cons (let ((cffc (- (random *2n*) *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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(make-cmbn
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:degr 0
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:list rslt))))
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(setf mrph (morphism :sorc cc :trgt cc :degr 0
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:intr #'ff :strt :gnrt :dfnt '(test)))
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(setf mrph2 (2mrph-cmps mrph mrph :gnrt))
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(gnrt-? mrph2 0 0)
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(dotimes (i 5)
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(print (gnrt-? mrph2 0 i)))
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(setf mrph (morphism :sorc cc :trgt cc :degr 0
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:intr #'ff :strt :gnrt :dfnt '(test)))
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(setf mrph3 (cmps mrph mrph :cmbn))
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(gnrt-? mrph3 0 0)
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(dotimes (i 5)
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(print (gnrt-? mrph3 0 i)))
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(setf mrph33 (cmps mrph mrph :cmbn))
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(eq mrph3 mrph33))
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|#
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(DEFUN N-MRPH-INTR (n mrph)
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(declare
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(fixnum n)
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(type morphism mrph))
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(flet ((rslt (cmbn)
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(declare (type cmbn cmbn))
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(n-cmbn n (cmbn-? mrph cmbn))))
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(the intr #'rslt)))
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(DEFUN N-MRPH (n mrph)
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(declare
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(fixnum n)
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(type morphism mrph))
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(the morphism
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(with-slots (sorc trgt degr) mrph
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(declare
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(type chain-complex sorc trgt)
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(fixnum degr))
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(morphism
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:sorc sorc :trgt trgt :degr degr
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:intr (n-mrph-intr n mrph) :strt :cmbn
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:dfnt `(n-mrph ,n ,mrph)))))
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#|
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(setf s3 (sphere 3))
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(setf ch3 (chml-clss s3 3))
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(setf 2ch3 (n-mrph 2 ch3))
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(setf f3 (z-whitehead s3 2ch3))
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(setf x (fibration-total f3))
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(homology x 0 10)
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(setf k (k-z 3))
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(setf ch3 (chml-clss k 3))
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(setf 2ch3 (n-mrph 2 ch3))
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(setf f3 (z-whitehead k 2ch3))
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(setf x (fibration-total f3))
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(homology x 0 10)
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|#
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(DEFMETHOD ADD ((mrph1 morphism) (mrph2 morphism) &optional strt)
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(declare (type (or null strt) strt))
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(the morphism
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(with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
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(declare
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(type chain-complex sorc1 trgt1)
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(fixnum degr1)
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(type strt strt1))
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(with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
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(declare
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(type chain-complex sorc2 trgt2)
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(fixnum degr2)
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(type strt strt2))
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(unless (and (eq (grmd sorc1) (grmd sorc2))
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(eq (grmd trgt1) (grmd trgt2))
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(= degr1 degr2))
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(error "In 2MRPH-ADD, ~A and ~A may not be added." mrph1 mrph2))
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(when (eq (first (dfnt mrph1)) 'zero-mrph)
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(return-from add mrph2))
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(when (eq (first (dfnt mrph2)) 'zero-mrph)
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(return-from add mrph1))
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(unless strt
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(setf strt
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(if (and (eq strt1 :gnrt)
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(eq strt2 :gnrt))
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:gnrt
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:cmbn)))
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(when (or (eq (first (dfnt mrph1)) 'idnt-mrph)
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(eq (first (dfnt mrph2)) 'idnt-mrph))
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(setf strt :cmbn))
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(let ((cmpr (cmpr trgt1)))
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(declare (type cmprf cmpr))
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(ecase strt
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(:gnrt (morphism
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:sorc sorc1 :trgt trgt1 :degr degr1
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:intr #'(lambda (degr gnrt)
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(declare (type fixnum degr) (type gnrt gnrt))
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(2cmbn-add cmpr
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(gnrt-? mrph1 degr gnrt)
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(gnrt-? mrph2 degr gnrt)))
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:strt :gnrt
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:dfnt `(2mrph-add ,mrph1 ,mrph2 ,strt)))
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(:cmbn (morphism
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:sorc sorc1 :trgt trgt1 :degr degr1
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:intr #'(lambda (cmbn)
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(declare (type cmbn cmbn))
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(2cmbn-add cmpr
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(cmbn-? mrph1 cmbn)
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(cmbn-? mrph2 cmbn)))
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:strt :cmbn
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:dfnt `(2mrph-add ,mrph1 ,mrph2 ,strt)))))))))
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#|
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(cat-init)
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(setf cc (chain-complex :cmpr #'f-cmpr
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:basis :locally-effective
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:bsgn 0
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:dffr-intr #'(lambda (cmbn)
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(cmbn (1- (cmbn-degr cmbn))))
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:dffr-strt :cmbn
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:dfnt '(Z of Z)))
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(setf *n* 10)
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(defun ff (degr i)
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(do ((*2n* (ash *n* 1))
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(rslt +empty-list+
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(cons (cons (let ((cffc (- (random *2n*) *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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(make-cmbn
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:degr 0
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:list rslt))))
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(setf mrph1 (morphism :sorc cc :trgt cc :degr 0
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:intr #'ff :strt :gnrt :dfnt '(test)))
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(setf mrph2 (morphism :sorc cc :trgt cc :degr 0
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:intr #'ff :strt :gnrt :dfnt '(test2)))
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(setf mrph3 (add mrph1 mrph2 :gnrt))
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(setf +too-much-time+ -1)
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(gnrt-? mrph1 0 0)
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(gnrt-? mrph2 0 0)
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(gnrt-? mrph3 0 0)
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(setf mrph4 (add mrph1 mrph2 :cmbn))
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(gnrt-? mrph4 0 0)
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(setf mrph44 (add mrph1 mrph2 :cmbn))
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(eq mrph4 mrph44))
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|#
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(DEFMETHOD SBTR ((mrph1 morphism) (mrph2 morphism) &optional strt)
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(declare (type (or null strt) strt))
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(the morphism
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(with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr) (strt1 strt)) mrph1
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(declare
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(type chain-complex sorc1 trgt1)
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(fixnum degr1)
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(type strt strt1))
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(with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr) (strt2 strt)) mrph2
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(declare
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(type chain-complex sorc2 trgt2)
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(fixnum degr2)
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(type strt strt2))
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(unless (and (eq (grmd sorc1) (grmd sorc2))
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(eq (grmd trgt1) (grmd trgt2))
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(= degr1 degr2))
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(error "In 2MRPH-SBTR, ~A and ~A may not be subtracteded." mrph1 mrph2))
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(when (eq (first (dfnt mrph1)) 'zero-mrph)
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(return-from sbtr mrph2))
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(when (eq (first (dfnt mrph2)) 'zero-mrph)
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(return-from sbtr mrph1))
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(unless strt
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(setf strt
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(if (and (eq strt1 :gnrt)
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(eq strt2 :gnrt))
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:gnrt
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:cmbn)))
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(when (or (eq (first (dfnt mrph1)) 'idnt-mrph)
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(eq (first (dfnt mrph2)) 'idnt-mrph))
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(setf strt :cmbn))
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(let ((cmpr (cmpr trgt1)))
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(declare (type cmprf cmpr))
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(ecase strt
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(:gnrt (morphism
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:sorc sorc1 :trgt trgt1 :degr degr1
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:intr #'(lambda (degr gnrt)
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(declare (type fixnum degr) (type gnrt gnrt))
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(2cmbn-sbtr cmpr
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(gnrt-? mrph1 degr gnrt)
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(gnrt-? mrph2 degr gnrt)))
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:strt :gnrt
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:dfnt `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))
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(:cmbn (morphism
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:sorc sorc1 :trgt trgt1 :degr degr1
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:intr #'(lambda (cmbn)
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(declare (type cmbn cmbn))
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(2cmbn-sbtr cmpr
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(cmbn-? mrph1 cmbn)
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(cmbn-? mrph2 cmbn)))
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:strt :cmbn
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:dfnt `(2mrph-sbtr ,mrph1 ,mrph2 ,strt)))))))))
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#|
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(cat-init)
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(setf cc (chain-complex :cmpr #'f-cmpr
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:basis :locally-effective
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:bsgn 0
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:dffr-intr #'(lambda (cmbn)
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(cmbn (1- (cmbn-degr cmbn))))
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:dffr-strt :cmbn
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:dfnt '(Z of Z)))
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(setf *n* 10)
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(defun ff (degr i)
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(do ((*2n* (ash *n* 1))
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(rslt +empty-list+
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(cons (cons (let ((cffc (- (random *2n*) *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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(make-cmbn
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:degr 0
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:list rslt))))
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(setf mrph1 (morphism :sorc cc :trgt cc :degr 0
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:intr #'ff :strt :gnrt :dfnt '(test)))
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(setf mrph2 (morphism :sorc cc :trgt cc :degr 0
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:intr #'ff :strt :gnrt :dfnt '(test2)))
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(setf mrph3 (sbtr mrph1 mrph2 :gnrt))
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(setf +too-much-time+ -1)
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(gnrt-? mrph1 0 0)
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(gnrt-? mrph2 0 0)
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(gnrt-? mrph3 0 0)
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(setf mrph4 (sbtr mrph1 mrph2 :cmbn))
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(gnrt-? mrph4 0 0)
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(setf mrph44 (sbtr mrph1 mrph2 :cmbn))
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(eq mrph4 mrph44))
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|#
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(DEFUN CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
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(declare
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(type morphism mrph)
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(type (or null chain-complex) new-sorc new-trgt))
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(the morphism
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(with-slots (sorc trgt degr intr strt) mrph
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(morphism
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:sorc (or new-sorc sorc)
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:trgt (or new-trgt trgt)
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:degr degr
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:intr intr
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:strt strt
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:dfnt `(change-sorc-trgt ,mrph ,new-sorc ,new-trgt)))))
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(DEFUN DSTR-CHANGE-SORC-TRGT (mrph &key new-sorc new-trgt)
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(declare
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(type morphism mrph)
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(type (or null chain-complex) new-sorc new-trgt)
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(list new-dfnt))
|
|
(the morphism
|
|
(with-slots (sorc trgt) mrph
|
|
(when new-sorc
|
|
(setf sorc new-sorc))
|
|
(when new-trgt
|
|
(setf trgt new-trgt))
|
|
mrph)))
|
|
|
|
(DEFMETHOD ADD ((chcm chain-complex) (perturbation morphism) &optional strt)
|
|
(declare (type (or strt null) strt))
|
|
(the chain-complex
|
|
(with-slots (cmpr basis bsgn dffr) chcm
|
|
(declare
|
|
(type cmprf cmpr)
|
|
(type basis basis)
|
|
(type morphism dffr))
|
|
(with-slots (sorc trgt degr) perturbation
|
|
(declare
|
|
(type chain-complex sorc trgt)
|
|
(fixnum degr))
|
|
(unless (and (eq (grmd sorc) (grmd chcm))
|
|
(eq (grmd trgt) (grmd chcm))
|
|
(= degr -1))
|
|
(error "In (METHOD ADD CHAIN-COMPLEX MORPHISM), the data are not coherent."))
|
|
(let ((new-dffr (add dffr perturbation strt)))
|
|
(declare (type morphism new-dffr))
|
|
(let ((new-chcm (chain-complex
|
|
:cmpr cmpr
|
|
:basis basis
|
|
:dffr-intr (intr new-dffr)
|
|
:dffr-strt (strt new-dffr)
|
|
:dfnt `(add ,chcm ,perturbation))))
|
|
(declare (type chain-complex new-chcm))
|
|
(if (slot-boundp chcm 'bsgn)
|
|
(setf (slot-value new-chcm 'bsgn) bsgn)
|
|
(slot-makunbound new-chcm 'bsgn))
|
|
(setf (slot-value new-chcm 'grmd) (grmd chcm))
|
|
new-chcm)))))) |