369 lines
13 KiB
Common Lisp
369 lines
13 KiB
Common Lisp
;;; TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS
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;;; TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS
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;;; TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS TENSOR-PRODUCTS
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(IN-PACKAGE "COMMON-LISP-USER")
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(PROVIDE "tensor-products")
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(DEFVAR *TNPR-WITH-DEGREES* nil)
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(DEFUN TNPR-PRINT (tnpr stream depth)
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(declare
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(type tnpr tnpr) (stream stream)
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(ignore depth))
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(the tnpr
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(progn
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(with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
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(format stream
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"<TnPr~:[~*~; ~D~] ~A~:[~*~; ~D~] ~A>"
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*tnpr-with-degrees* degr1 gnrt1
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*tnpr-with-degrees* degr2 gnrt2))
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tnpr)))
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#|
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(tnpr 2 'a 3 'b)
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(setf *tnpr-with-degrees* t)
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(tnpr 2 'a 3 'b)
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(setf *tnpr-with-degrees* nil)
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|#
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(DEFUN 2CMBN-TNPR (cmbn1 cmbn2)
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(declare (type cmbn cmbn1 cmbn2))
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(the cmbn
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(with-cmbn (degr1 list1) cmbn1
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(with-cmbn (degr2 list2) cmbn2
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(make-cmbn
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:degr (+ degr1 degr2)
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:list (mapcan
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#'(lambda (term1)
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(declare (type term term1))
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(the list
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(with-term (cffc1 gnrt1) term1
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(mapcar
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#'(lambda (term2)
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(declare (type term term2))
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(the term
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(term
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(* cffc1 (cffc term2))
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(tnpr degr1 gnrt1 degr2 (gnrt term2)))))
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list2))))
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list1))))))
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#|
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(setf *tnpr-with-degrees* t)
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(2cmbn-tnpr (cmbn 2 3 'a 4 'b -5 'c) (cmbn 3 4 'x -3 'y 2 'z)))
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|#
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#|
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(DEFUN TNSR-PRDC-CMPR (cmpr1 cmpr2)
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(declare (type cmprf cmpr1 cmpr2))
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(flet ((rslt (tnpr1 tnpr2)
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(declare (type tnpr tnpr1 tnpr2))
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(let ((left-cons-1 (cadr tnpr1))
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(left-cons-2 (cadr tnpr2)))
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(declare (cons left-cons-1 left-cons-2))
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(lexico
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(f-cmpr (car left-cons-1) (car left-cons-2))
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(funcall cmpr1 (cdr left-cons-1) (cdr left-cons-2))
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(funcall cmpr2 (gnrt2 tnpr1) (gnrt2 tnpr2))))))
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(the cmprf #'rslt)))
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|#
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(DEFUN TNSR-PRDC-CMPR (cmpr1 cmpr2)
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(declare (type cmprf cmpr1 cmpr2))
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(flet ((rslt (tnpr1 tnpr2)
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(declare (type tnpr tnpr1 tnpr2))
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(the cmpr
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(lexico
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(f-cmpr (degr1 tnpr1) (degr1 tnpr2))
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(funcall cmpr1 (gnrt1 tnpr1) (gnrt1 tnpr2))
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(funcall cmpr2 (gnrt2 tnpr1) (gnrt2 tnpr2))))))
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(the cmprf #'rslt)))
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#|
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(setf cmpr (tnsr-prdc-cmpr #'s-cmpr #'s-cmpr))
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(funcall cmpr (tnpr 2 'a 3 'b) (tnpr 3 'a 2 'b))
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(funcall cmpr (tnpr 3 'a 2 'b) (tnpr 2 'a 3 'b))
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(funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'b 3 'b))
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(funcall cmpr (tnpr 2 'b 3 'b) (tnpr 2 'a 3 'b))
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(funcall cmpr (tnpr 2 'a 3 'a) (tnpr 2 'a 3 'b))
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(funcall cmpr (tnpr 2 'a 3 'c) (tnpr 2 'a 3 'b))
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(funcall cmpr (tnpr 2 'a 3 'b) (tnpr 2 'a 3 'b)))
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|#
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(DEFUN TNSR-PRDC-BASIS (basis1 basis2)
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(declare (type basis basis1 basis2))
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(when (or (eq basis1 :locally-effective)
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(eq basis2 :locally-effective))
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(return-from tnsr-prdc-basis :locally-effective))
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(flet ((rslt (degr)
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(declare (fixnum degr))
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(the list
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(progn
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(when (minusp degr)
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(return-from rslt +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* ((basis1 (funcall basis1 degr1))
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(degr2 (- degr degr1))
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(basis2 (funcall basis2 degr2)))
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(declare
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(fixnum degr2)
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(list basis1 basis2))
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(the list
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(mapcan
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#'(lambda (gnrt1)
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(declare (type gnrt gnrt1))
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(the list
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(mapcar
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#'(lambda (gnrt2)
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(declare (type gnrt gnrt2))
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(the tnpr
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(tnpr degr1 gnrt1 degr2 gnrt2)))
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basis2)))
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basis1))))
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(<a-b> 0 degr))))))
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(the basis #'rslt)))
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#|
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(defun bas (degr)
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(case degr
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(0 '(a b c))
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(1 '(d))
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(2 nil)
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(3 '(x y))))
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(setf bas (tnsr-prdc-basis #'bas #'bas))
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(dotimes (i 8)
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(print (funcall bas i))))
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|#
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(DEFUN TNSR-PRDC-INTR-DFFR (dffr1 dffr2)
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(declare (type morphism dffr1 dffr2))
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(flet ((rslt (degr tnpr)
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(declare
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(fixnum degr)
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(type tnpr tnpr))
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(the cmbn
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(with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
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(let ((degr1-1 (1- degr1))
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(degr2-1 (1- degr2))
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(sign (oddp degr1))
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(list1 (cmbn-list (gnrt-? dffr1 degr1 gnrt1)))
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(list2 (cmbn-list (gnrt-? dffr2 degr2 gnrt2))))
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(declare
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(fixnum degr1-1 degr2-1 sign)
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(list list1 list2))
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(make-cmbn
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:degr (1- degr)
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:list (nconc
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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 gnrt1) term1
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(term cffc1
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(tnpr degr1-1 gnrt1 degr2 gnrt2))))
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list1)
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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 gnrt2) term2
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(term (if sign (- cffc2) cffc2)
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(tnpr degr1 gnrt1 degr2-1 gnrt2))))
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list2))))))))
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(the intr-mrph #'rslt)))
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#|
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(cat-init)
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(setf chcm (build-chcm :cmpr #'s-cmpr :strt :gnrt :orgn '(test-1)))
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(setf dffr (build-mrph :sorc chcm :trgt chcm :degr -1
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:intr #'(lambda (degr gnrt)
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(ecase gnrt
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(a (cmbn (1- degr) 2 'd1a -3 'd2a))
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(b (cmbn (1- degr) 3 'd1b -4 'd2b))))
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:strt :gnrt :orgn '(test-2)))
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(setf rslt (tnsr-prdc-intr-dffr dffr dffr))
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(funcall rslt 4 (tnpr 2 'a 2 'b))
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(funcall rslt 5 (tnpr 3 'a 2 'b))
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(funcall rslt 5 (tnpr 2 'a 3 'b))
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(funcall rslt 6 (tnpr 3 'a 3 'b)))
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|#
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(DEFMETHOD TNSR-PRDC ((chcm1 chain-complex) (chcm2 chain-complex))
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(the chain-complex
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(with-slots ((cmpr1 cmpr) (basis1 basis) (dffr1 dffr)) chcm1
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(declare
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(type cmprf cmpr1)
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(type basis basis1)
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(type morphism dffr1))
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(with-slots ((cmpr2 cmpr) (basis2 basis) (dffr2 dffr)) chcm2
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(declare
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(type cmprf cmpr2)
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(type basis basis2)
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(type morphism dffr2))
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(let ((rslt
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(build-chcm
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:cmpr (tnsr-prdc-cmpr cmpr1 cmpr2)
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:basis (tnsr-prdc-basis basis1 basis2)
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:intr-dffr (tnsr-prdc-intr-dffr dffr1 dffr2)
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:strt :gnrt
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:orgn `(tnsr-prdc ,chcm1 ,chcm2))))
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(declare (type chain-complex rslt))
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(if (and (slot-boundp chcm1 'bsgn)
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(slot-boundp chcm2 'bsgn))
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(setf (slot-value rslt 'bsgn)
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(tnpr 0 (bsgn chcm1) 0 (bsgn chcm2)))
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(slot-makunbound rslt 'bsgn))
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rslt)))))
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#|
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(setf dd (tnsr-prdc (delta 2) (delta 3)))
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(cmpr dd (tnpr 2 7 2 11) (tnpr 2 7 2 14))
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(basis dd 3)
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(? dd 4 (tnpr 2 7 2 14))
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(? dd 3 (tnpr 1 6 2 14))
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(? dd (? dd 4 (tnpr 2 7 2 14)))
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(? dd (? dd 3 (tnpr 1 6 2 14))))
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|#
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(DEFUN TNSR-PRDC-INTR (mrph1 mrph2)
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(declare
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(type morphism mrph1 mrph2))
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(let ((mrph2-sign (oddp (degr mrph2))))
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(declare (type boolean mrph2-sign))
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(flet ((rslt (degr tnpr)
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(declare
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(ignore degr)
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(type tnpr tnpr))
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(with-tnpr (degr1 gnrt1 degr2 gnrt2) tnpr
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(let ((rslt (2cmbn-tnpr
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(gnrt-? mrph1 degr1 gnrt1)
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(gnrt-? mrph2 degr2 gnrt2))))
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(declare (type cmbn rslt))
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(when (and mrph2-sign
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(oddp degr1))
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(mapc #'(lambda (term)
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(declare (type term term))
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(setf (the fixnum (cffc term))
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(the fixnum (- (cffc term)))))
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(cmbn-list rslt)))
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rslt))))
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(the intr-mrph #'rslt))))
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#|
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(cat-init)
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(setf chcm (build-chcm :cmpr #'s-cmpr :strt :gnrt :orgn '(test-1)))
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(setf mrph (build-mrph :sorc chcm :trgt chcm :degr 0
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:intr #'(lambda (degr gnrt)
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(ecase gnrt
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(a (cmbn degr 2 'd1a -3 'd2a))
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(b (cmbn degr 3 'd1b -4 'd2b))))
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:strt :gnrt :orgn '(test-2)))
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(setf rslt (tnsr-prdc-intr mrph mrph))
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(funcall rslt 6 (tnpr 2 'a 4 'b))
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(funcall rslt 5 (tnpr 3 'a 2 'b))
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(setf mrph (build-mrph :sorc chcm :trgt chcm :degr 1
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:intr #'(lambda (degr gnrt)
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(ecase gnrt
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(a (cmbn (1+ degr) 2 'd1a -3 'd2a))
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(b (cmbn (1+ degr) 3 'd1b -4 'd2b))))
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:strt :gnrt :orgn '(test-3)))
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(setf rslt (tnsr-prdc-intr mrph mrph))
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(funcall rslt 6 (tnpr 2 'a 4 'b))
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(funcall rslt 5 (tnpr 3 'a 2 'b)))
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|#
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(DEFMETHOD TNSR-PRDC ((mrph1 morphism) (mrph2 morphism))
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(the morphism
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(with-slots ((sorc1 sorc) (trgt1 trgt) (degr1 degr)) mrph1
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(with-slots ((sorc2 sorc) (trgt2 trgt) (degr2 degr)) mrph2
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(the morphism
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(progn
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(when (and (eq 'idnt-mrph (first (orgn mrph1)))
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(eq 'idnt-mrph (first (orgn mrph2))))
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(return-from tnsr-prdc
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(idnt-mrph (tnsr-prdc sorc1 sorc2))))
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(when (or (eq 'zero-mrph (first (orgn mrph1)))
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(eq 'zero-mrph (first (orgn mrph2))))
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(return-from tnsr-prdc
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(zero-mrph (tnsr-prdc sorc1 sorc2)
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(tnsr-prdc trgt1 trgt2)
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(+ degr1 degr2))))
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(build-mrph
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:sorc (tnsr-prdc sorc1 sorc2)
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:trgt (tnsr-prdc trgt1 trgt2)
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:degr (+ degr1 degr2)
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:intr (tnsr-prdc-intr mrph1 mrph2)
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:strt :gnrt
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:orgn `(tnsr-prdc ,mrph1 ,mrph2))))))))
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#|
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(cat-init)
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(setf d (dffr (delta-infinity)))
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(setf dd (tnsr-prdc d d))
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(eq (sorc dd) (tnsr-prdc (delta-infinity) (delta-infinity)))
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(? dd 5 (tnpr 2 7 3 15))
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(? dd 5 (tnpr 3 15 2 7))
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(? dd (? dd 5 (tnpr 2 7 3 15)))
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(? dd (? dd 5 (tnpr 3 15 2 7)))
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(setf ddd (cmps dd dd))
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(? ddd 5 (tnpr 2 7 3 15))
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(? ddd 5 (tnpr 3 15 2 7))
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|#
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(DEFMETHOD TNSR-PRDC ((rdct1 reduction) (rdct2 reduction))
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(the reduction
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(progn
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(when (and (eq 'trivial-rdct (first (orgn rdct1)))
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(eq 'trivial-rdct (first (orgn rdct2))))
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(return-from tnsr-prdc
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(trivial-rdct (tnsr-prdc (bcc rdct1) (bcc rdct2)))))
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(with-slots ((tcc1 tcc) (bcc1 bcc) (f1 f) (g1 g) (h1 h)) rdct1
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(declare
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(type chain-complex tcc1 bcc1)
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(type morphism f1 g1 h1))
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(with-slots ((tcc2 tcc) (bcc2 bcc) (f2 f) (g2 g) (h2 h)) rdct2
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(declare
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(type chain-complex tcc2 bcc2)
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(type morphism f2 g2 h2))
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(build-rdct
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:f (tnsr-prdc f1 f2)
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:g (tnsr-prdc g1 g2)
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:h (add
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(tnsr-prdc h1 (cmps g2 f2))
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(tnsr-prdc (idnt-mrph tcc1) h2))
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:orgn `(tnsr-prdc ,rdct1 ,rdct2)))))))
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#|
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(cat-init)
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(setf r (ez (delta-infinity) (delta-infinity)))
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(setf r2 (tnsr-prdc r r))
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(setf *bc* (cmbn 4 1 (tnpr 2 (tnpr 1 3 1 3) 2 (tnpr 1 3 1 3)))
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*tc* (cmbn 2 1 (tnpr 1 (crpr 0 3 0 3) 1 (crpr 0 3 0 3))))
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(pre-check-rdct r2)
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(check-rdct)
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|#
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(DEFMETHOD TNSR-PRDC ((hmeq1 homotopy-equivalence)
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(hmeq2 homotopy-equivalence))
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(the homotopy-equivalence
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(build-hmeq
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:lrdct (tnsr-prdc (lrdct hmeq1) (lrdct hmeq2))
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:rrdct (tnsr-prdc (rrdct hmeq1) (rrdct hmeq2))
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:orgn `(tnsr-prdc ,hmeq1 ,hmeq2))))
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(DEFMETHOD SEARCH-EFHM (chcm (orgn (eql 'tnsr-prdc)))
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(declare (type chain-complex chcm))
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(the homotopy-equivalence
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(tnsr-prdc (efhm (second (orgn chcm)))
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(efhm (third (orgn chcm))))))
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#|
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(cat-init)
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(setf k (k-z 2))
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(setf k2 (tnsr-prdc k k))
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(homology k2 0 10)
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|# |