finite-topological-spaces files replaced by a single finite-topological-space.lisp
This commit is contained in:
Julián Cuevas-Rozo
parent
0eb1ea06d3
commit
fdf8f49efc
@ -59,10 +59,7 @@
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(:file "smith")
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(:file "smith")
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(:file "vf-order")
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(:file "vf-order")
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(:file "sage-interface")
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(:file "sage-interface")
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(:file "finite-topological-spaces-aux")
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(:file "finite-topological-spaces")
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(:file "finite-topological-spaces-class")
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(:file "finite-topological-spaces-core")
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(:file "finite-topological-spaces-homology")
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(:module "anromero"
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(:module "anromero"
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:components
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:components
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((:file "resolutions")
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((:file "resolutions")
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@ -1,262 +0,0 @@
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;;;; -*- Mode: Lisp; Syntax: ANSI-Common-Lisp; Base: 10 -*
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;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
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;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
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;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
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(IN-PACKAGE #:cat)
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(PROVIDE "finite-topological-spaces-aux")
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;;
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;; Auxiliary functions (most of them in 'NewSmith')
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;;
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(DEFUN MAJTERME (pl pc val)
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#| Same 'maj-terme' but changing '=' by 'eq' |#
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(if (eq val 0)
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(if (eq (left pl) (up pc)) (supprimer-terme pl pc))
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(if (eq (left pl) (up pc))
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(setf (val (left pl)) val)
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(inserer-terme pl pc val))))
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(DEFUN EQUALMATRIX (mtrx1 mtrx2)
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#| Same 'equal-matrix' but changing 'line-number' by 'nlig' and 'column-number' by 'ncol' |#
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(declare (type matrice mtrx1 mtrx2))
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(the boolean
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(let ((line-number (nlig mtrx1)))
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(declare (type fixnum line-number))
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(unless (eql line-number (nlig mtrx2))
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(return-from equalmatrix +false+))
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(unless (eql (ncol mtrx1) (ncol mtrx2))
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(return-from equalmatrix +false+))
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(do ((il 1 (1+ il)))
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((> il line-number))
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(declare (type fixnum il))
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(let ((p10 (baselig mtrx1 il))
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(p20 (baselig mtrx2 il)))
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(declare (type t-mat p10 p20))
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(do ((p1 (left p10) (left p1))
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(p2 (left p20) (left p2)))
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(nil)
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(declare (type t-mat p1 p2))
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(when (eq p1 p10)
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(unless (eq p2 p20)
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(return-from equalmatrix +false+))
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(return))
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(when (eq p2 p20)
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(unless (eq p1 p10)
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(return-from equalmatrix +false+)))
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(unless (eql (icol p1) (icol p2))
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(return-from equalmatrix +false+))
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(unless (eql (val p1) (val p2))
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(return-from equalmatrix +false+)))))
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(return-from equalmatrix +true+))))
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(DEFUN MATRICE-PRDC (mtrx1 mtrx2)
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#| Same 'mtrx-prdc' but changing 'line-number' by 'nlig' and 'column-number' by 'ncol' |#
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(declare (type matrice mtrx1 mtrx2))
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(the matrice
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(let ((nl (nlig mtrx1))
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(nc (ncol mtrx2))
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(n (ncol mtrx1)))
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(declare (type fixnum nl nc n))
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(assert (eql n (nlig mtrx2)))
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(let ((rslt (creer-matrice nl nc)))
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(declare (type matrice rslt))
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(do ((il 1 (1+ il)))
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((> il nl))
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(declare (type fixnum il))
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(do ((pl01 (baselig mtrx1 il))
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(pl0r (baselig rslt il))
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(ic 1 (1+ ic)))
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((> ic nc))
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(declare (type t-mat pl01 pl0r) (type fixnum ic))
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(let ((pl (left pl01))
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(pc (up (basecol mtrx2 ic)))
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(sum 0))
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(declare (type t-mat pl pc) (type fixnum sum))
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(loop
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(let ((ilic (icol pl))
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(icil (ilig pc)))
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(declare (type fixnum ilic icil))
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(when (zerop ilic) (return))
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(when (zerop icil) (return))
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(cond ((eql ilic icil)
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(incf sum (safe-* (val pl) (val pc)))
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(setf pl (left pl) pc (up pc)))
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((> ilic icil)
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(setf pl (left pl)))
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(t
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(setf pc (up pc))))))
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(unless (zerop sum)
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(inserer-terme pl0r (basecol rslt ic) sum)))))
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rslt))))
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(DEFUN MATRICE-TO-LMTRX (mtrx)
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(let* ((column-n (ncol mtrx))
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(rslt (make-array column-n)))
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(dotimes (j column-n)
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(let ((rsltj '())
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(columnj-pair-list
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(let ((ptc (basecol mtrx (1+ j)))
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(res '()))
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(do ((pc (up ptc) (up pc)))
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((eq pc ptc))
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(push (list (ilig pc) (val pc)) res))
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res)))
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(mapcar #'(lambda (pair)
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(push (list (1- (first pair)) (second pair)) rsltj))
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columnj-pair-list)
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(setf (svref rslt j) (nreverse rsltj) )))
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rslt))
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(DEFUN SAFE-* (arg1 arg2)
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#| This is in 'NewSmith' |#
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(declare (type fixnum arg1 arg2))
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(let ((rslt (* arg1 arg2)))
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(declare (type integer rslt))
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(if (typep rslt 'fixnum)
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rslt
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(error "Fixnum-overflow in (safe-* ~D ~D)." arg1 arg2))))
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(DEFUN SAFE-+ (arg1 arg2)
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#| This is in 'NewSmith' |#
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(declare (type fixnum arg1 arg2))
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(let ((rslt (+ arg1 arg2)))
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(declare (type integer rslt))
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(if (typep rslt 'fixnum)
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rslt
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(error "Fixnum-overflow in (safe-+ ~D ~D)." arg1 arg2))))
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(DEFUN SAFE-- (arg)
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#| This is in 'NewSmith' |#
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(declare (type fixnum arg))
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(let ((rslt (- arg)))
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(declare (type integer rslt))
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(if (typep rslt 'fixnum)
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rslt
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(error "Fixnum-overflow in (SAFE-- ~D)." arg))))
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(DEFUN 0NEW-COLUMN (mtrx icol list)
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#| This is 'new-column' in 'NewSmith' |#
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(declare (type matrice mtrx) (type fixnum icol) (type list list))
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(the matrice
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(let ((peigne (peigne-hor mtrx (baselig mtrx 0) icol))
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(pc0 (basecol mtrx icol)))
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(declare (type list peigne) (type t-mat pc0))
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(map nil #'(lambda (item)
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(declare (type t-mat item))
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(when (eq (up pc0) (left item))
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(supprimer-terme item pc0)))
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peigne)
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(do ((markp (nreverse peigne) (cdr markp))
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(ilig 1 (1+ ilig))
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(markc list))
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((endp markc))
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(declare (type list markp markc) (type fixnum ilig))
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(when (eql (caar markc) ilig)
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(inserer-terme (car markp) pc0 (cadar markc))
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(setf markc (cdr markc))))
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mtrx)))
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(DEFUN 0COLUMN-OP (mtrx lambda icol1 icol2)
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#| This is 'column-op' in 'NewSmith' |#
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(declare
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(type matrice mtrx)
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(type fixnum lambda icol1 icol2))
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(the matrice
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(let ((mark1 (extract-column mtrx icol1))
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(mark2 (extract-column mtrx icol2))
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(new-column2 +empty-list+))
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(declare (type list mark1 mark2 new-column2))
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(loop
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(when (endp mark1)
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(setf new-column2 (nreconc new-column2 mark2))
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(return))
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(when (endp mark2)
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(setf new-column2
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(nreconc new-column2
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(mapcar #'(lambda (item)
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(declare (type list item))
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(list (first item)
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(safe-* lambda (second item))))
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mark1)))
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(return))
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(let ((ilig1 (caar mark1))
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(ilig2 (caar mark2)))
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(declare (type fixnum ilig1 ilig2))
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(cond ((< ilig1 ilig2)
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(push (list ilig1 (safe-* lambda (second (pop mark1))))
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new-column2))
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((> ilig1 ilig2)
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(push (list ilig2 (second (pop mark2))) new-column2))
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(t (let ((new-val (safe-+ (safe-* lambda (second (pop mark1)))
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(second (pop mark2)))))
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(declare (type fixnum new-val))
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(unless (zerop new-val)
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(push (list ilig1 new-val) new-column2)))))))
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(0new-column mtrx icol2 new-column2)
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mtrx)))
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(DEFUN 0COLUMN-SWAP (mtrx icol1 icol2)
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#| This is 'column-swap' in 'NewSmith' |#
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(declare
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(type matrice mtrx) (type fixnum icol1 icol2))
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(the matrice
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(let ((new-column1 (extract-column mtrx icol2))
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(new-column2 (extract-column mtrx icol1)))
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(declare (type list new-column1 new-column2))
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(0new-column mtrx icol1 new-column1)
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(0new-column mtrx icol2 new-column2)
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mtrx)))
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(DEFUN 0COLUMN-MINUS (mtrx icol)
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#| This is 'column-minus' in 'NewSmith' |#
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(declare (type matrice mtrx) (type fixnum icol))
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(the matrice
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(0new-column mtrx icol
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(mapcar #'(lambda (item)
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(declare (type list item))
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(the list
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(list (first item)
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(safe-- (second item)))))
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(extract-column mtrx icol)))))
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(DEFUN EXTRACT-COLUMN (mtrx icol)
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#| This is in 'NewSmith' |#
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(declare (type matrice mtrx) (type fixnum icol))
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(the list
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(let ((pc0 (basecol mtrx icol)))
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(declare (type t-mat pc0))
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(do ((pc (up pc0) (up pc))
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(rslt +empty-list+ (cons (list (ilig pc) (val pc)) rslt)))
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((eq pc pc0) rslt)
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(declare (type t-mat pc) (type list rslt))))))
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(DEFUN EXTRACT-LINE (mtrx ilig)
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#| This is in 'NewSmith' |#
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(declare (type matrice mtrx) (type fixnum ilig))
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(the list
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(let ((pl0 (baselig mtrx ilig)))
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(declare (type t-mat pl0))
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(do ((pl (left pl0) (left pl))
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(rslt +empty-list+ (cons (list (icol pl) (val pl)) rslt)))
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((eq pl pl0) rslt)
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(declare (type t-mat pl) (type list rslt))))))
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@ -1,522 +0,0 @@
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;;;; -*- Mode: Lisp; Syntax: ANSI-Common-Lisp; Base: 10 -*
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;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
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;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
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;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
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(IN-PACKAGE #:cat)
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(PROVIDE "finite-topological-spaces-class")
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;;
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;; Finite topological spaces
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;;
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(DEFMACRO INSERT-TERM (mat ilig icol val)
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#| Insert the value 'val' in the ('ilig' 'icol')-entry of 'mat' |#
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`(majterme (chercher-hor (baselig ,mat ,ilig) ,icol)
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(chercher-ver (basecol ,mat ,icol) ,ilig)
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,val))
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(DEFUN CONVERTARRAY (array)
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#| Convert an 'array' to a 'matrice' |#
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(let* ((numfil (array-dimension array 0))
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(numcol (array-dimension array 1))
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(rslt (creer-matrice numfil numcol)))
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(dotimes (j numcol)
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(dotimes (i numfil)
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(insert-term rslt (1+ i) (1+ j) (aref array i j))))
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rslt))
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(DEFUN EXTRACT-COLUMN2 (mtrx icol list)
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#| Modification of 'EXTRACT-COLUMN' in order to extract only the elements in the column 'icol' whose row indexes are in the list 'list' |#
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(declare (type matrice mtrx) (type fixnum icol) (type list list))
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(the list
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(let ((pc0 (basecol mtrx icol))
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(lst list))
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(declare (type t-mat pc0))
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(do ((pc (up pc0) (up pc))
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(rslt +empty-list+ (if (find (ilig pc) lst)
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(progn
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(setf lst (remove (ilig pc) lst))
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(cons (list (ilig pc) (val pc)) rslt))
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rslt)))
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((eq pc pc0) rslt)
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(declare (type t-mat pc) (type list rslt))))))
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(DEFUN SUB-MATRIX (mtrx rows cols)
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#| Extract the submatrix of 'mtrx' formed by the rows whose indexes are in 'rows' the columns whose indexes are in 'cols' |#
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(declare (type matrice mtrx) (type list rows cols))
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(let ((rslt (creer-matrice (length rows) (length cols))))
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(do ((k 1 (1+ k))
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(columnas cols (cdr columnas)))
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((endp columnas) rslt)
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(0new-column rslt k (let ((valor NIL))
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(do ((j (length rows) (1- j))
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(rslt2 +empty-list+ (if (setf valor (second (find (nth (1- j) rows) (extract-column2 mtrx (car columnas) rows) :key #'first)))
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(cons (list j valor) rslt2)
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rslt2)))
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((< j 1) rslt2)))))))
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(DEFUN NILPOT (matrix)
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(declare (type matrice matrix))
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(let ((rslt (copier-matrice matrix)))
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(loop for k from 1 to (nlig rslt)
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do (insert-term rslt k k 0))
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rslt))
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(DEFUN NILPOT-1 (matrix)
|
|
||||||
(declare (type matrice matrix))
|
|
||||||
(let ((rslt (copier-matrice matrix)))
|
|
||||||
(loop for k from 1 to (nlig rslt)
|
|
||||||
do (insert-term rslt k k 1))
|
|
||||||
rslt))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN ADD-ROWS (matrice pos num)
|
|
||||||
#| Add 'num' rows from position 'pos' |#
|
|
||||||
(let ((rslt (creer-matrice (+ (n-lig matrice) num) (n-col matrice))))
|
|
||||||
(do ((i 1 (1+ i)))
|
|
||||||
((eq i pos))
|
|
||||||
(do ((ptl1 (baselig matrice i))
|
|
||||||
(pl1 (left (baselig matrice i)) (left pl1))
|
|
||||||
(pl2 (baselig rslt i) (left pl2)))
|
|
||||||
((eq pl1 ptl1))
|
|
||||||
(inserer-terme pl2 (basecol rslt (icol pl1)) (val pl1))))
|
|
||||||
|
|
||||||
(do ((i pos (1+ i)))
|
|
||||||
((> i (n-lig matrice)) rslt)
|
|
||||||
(do ((ptl1 (baselig matrice i))
|
|
||||||
(pl1 (left (baselig matrice i)) (left pl1))
|
|
||||||
(pl2 (baselig rslt (+ i num)) (left pl2)))
|
|
||||||
((eq pl1 ptl1))
|
|
||||||
(inserer-terme pl2 (basecol rslt (icol pl1)) (val pl1))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN ADD-COLS (matrice pos num)
|
|
||||||
#| Add 'num' columns from position 'pos' |#
|
|
||||||
(let ((rslt (creer-matrice (n-lig matrice) (+ (n-col matrice) num))))
|
|
||||||
(do ((i 1 (1+ i)))
|
|
||||||
((eq i pos))
|
|
||||||
(do ((ptc1 (basecol matrice i))
|
|
||||||
(pc1 (up (basecol matrice i)) (up pc1))
|
|
||||||
(pc2 (basecol rslt i) (up pc2)))
|
|
||||||
((eq pc1 ptc1))
|
|
||||||
(inserer-terme (baselig rslt (ilig pc1)) pc2 (val pc1))))
|
|
||||||
|
|
||||||
(do ((i pos (1+ i)))
|
|
||||||
((> i (n-col matrice)) rslt)
|
|
||||||
(do ((ptc1 (basecol matrice i))
|
|
||||||
(pc1 (up (basecol matrice i)) (up pc1))
|
|
||||||
(pc2 (basecol rslt (+ i num)) (up pc2)))
|
|
||||||
((eq pc1 ptc1))
|
|
||||||
(inserer-terme (baselig rslt (ilig pc1)) pc2 (val pc1))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMACRO ADD-POINTS (matrice pos num)
|
|
||||||
#| Add 'num' points from position 'pos' |#
|
|
||||||
`(add-cols (add-rows ,matrice ,pos ,num) ,pos ,num))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN STONGMAT (topogenous)
|
|
||||||
#| Stong matrice from the topogenous matrice 'topogenous' |#
|
|
||||||
(declare (type matrice topogenous))
|
|
||||||
(let* ((dim (nlig topogenous))
|
|
||||||
(rslt (identite dim)))
|
|
||||||
(declare (type fixnum dim))
|
|
||||||
(if (or (eq dim 1) (eq dim 2))
|
|
||||||
(return-from stongmat topogenous)
|
|
||||||
|
|
||||||
(do ((i 1 (1+ i))) ((> i dim) rslt)
|
|
||||||
(do ((j (1+ i) (1+ j))) ((> j dim))
|
|
||||||
(cond ((eq j (1+ i)) (insert-term rslt i j (terme topogenous i j)))
|
|
||||||
((eq (terme topogenous i j) 0))
|
|
||||||
(T (let ((parada 0))
|
|
||||||
(do ((k (1+ i) (1+ k))) ((or (> k (1- j)) (eq parada 1)))
|
|
||||||
(cond ((and (eq (terme topogenous i k) 1) (eq (terme topogenous k j) 1)) (setf parada 1))
|
|
||||||
((and (eq k (1- j)) (eq parada 0)) (insert-term rslt i j 1))))))))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN TOPMAT (stong)
|
|
||||||
#| Topogenous matrice from the Stong matrice 'stong' |#
|
|
||||||
(declare (type matrice stong))
|
|
||||||
(let* ((dim (nlig stong))
|
|
||||||
(rslt (identite dim)))
|
|
||||||
(declare (type fixnum dim))
|
|
||||||
(if (or (eq dim 1) (eq dim 2))
|
|
||||||
(return-from topmat stong)
|
|
||||||
|
|
||||||
(do ((k 2 (1+ k))) ((> k dim) rslt)
|
|
||||||
(if (eq k 2)
|
|
||||||
(do ((i 1 (1+ i))) ((> i (1- dim)))
|
|
||||||
(insert-term rslt i (1+ i) (terme stong i (1+ i))))
|
|
||||||
|
|
||||||
(do ((i 1 (1+ i))) ((> i (1+ (- dim k))))
|
|
||||||
|
|
||||||
(if (eq (terme stong i (1- (+ i k))) 1)
|
|
||||||
(insert-term rslt i (1- (+ i k)) 1)
|
|
||||||
|
|
||||||
(if (eq (let ((indicator 0))
|
|
||||||
(do ((r (1+ i) (1+ r))) ((or (> r (- (+ i k) 2)) (eq indicator 1)))
|
|
||||||
(if (and (eq (terme rslt i r) 1) (eq (terme rslt r (1- (+ i k))) 1))
|
|
||||||
(setf indicator 1))) indicator) 1)
|
|
||||||
(insert-term rslt i (1- (+ i k)) 1)))))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN RANDOMTOP (dim dens)
|
|
||||||
#| A 'dim' x 'dim' random topogenous matrice |#
|
|
||||||
(declare (fixnum dim))
|
|
||||||
(let ((limite (truncate (/ (* dens (- dim 2) (- dim 1)) 2)))
|
|
||||||
(rslt (identite dim))
|
|
||||||
(contador 1)
|
|
||||||
(base (make-array dim)))
|
|
||||||
(unless (= dim 1)
|
|
||||||
(do () ((> contador limite))
|
|
||||||
(let* ((j1 (1+ (random (1- dim))))
|
|
||||||
(i1 (random j1)))
|
|
||||||
(if (find i1 (aref base j1))
|
|
||||||
(incf contador) ; Avoiding an infinite loop...
|
|
||||||
(progn
|
|
||||||
(push i1 (aref base j1))
|
|
||||||
(setf (aref base j1) (union (aref base j1) (aref base i1)))
|
|
||||||
(loop for k in (>a-b< j1 dim)
|
|
||||||
if (find j1 (aref base k))
|
|
||||||
do (and (pushnew i1 (aref base k))
|
|
||||||
(setf (aref base k) (union (aref base k) (aref base i1))) ; Improve...
|
|
||||||
(incf contador)))))))
|
|
||||||
(loop for j in (<a-b< 1 dim)
|
|
||||||
do (mapcar #'(lambda (elem) (insert-term rslt (1+ elem) (1+ j) 1)) (aref base j))))
|
|
||||||
rslt))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMACRO RANDOMSTONG (dim dens)
|
|
||||||
#| A 'dim' x 'dim' random Stong matrice |#
|
|
||||||
`(stongmat (randomtop ,dim ,dens)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN HEIGHTS-AUX (stong lst)
|
|
||||||
(if (null lst)
|
|
||||||
NIL
|
|
||||||
(let ((minimals (loop for n in lst
|
|
||||||
if (null (loop for i from 0 to (1- (position n lst))
|
|
||||||
thereis (eq (terme stong (nth i lst) n) 1)))
|
|
||||||
collect n)))
|
|
||||||
(cons minimals (heights-aux stong (set-difference lst minimals)))))) ; 'set-difference' must be in ascending order
|
|
||||||
|
|
||||||
(DEFMETHOD HEIGHTS ((stong matrice))
|
|
||||||
#| List of elements separated by heights |#
|
|
||||||
(heights-aux stong (<a-b> 1 (ncol stong))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFCLASS FINITE-SPACE ()
|
|
||||||
;; TOPogenous matrix
|
|
||||||
((top :type matrice :initarg :top :reader top)
|
|
||||||
;; STONG matrix
|
|
||||||
(stong :type matrice :initarg :stong :reader stong)
|
|
||||||
;; HEIGHTS
|
|
||||||
(heights :type list :initarg :heights :reader heights)
|
|
||||||
;; IDentification NuMber
|
|
||||||
(idnm :type fixnum :initform (incf *idnm-counter*) :reader idnm)
|
|
||||||
;; ORiGiN
|
|
||||||
(orgn :type list :initarg :orgn :reader orgn)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD SLOT-UNBOUND (class (finspace finite-space) (slot-name (eql 'heights)))
|
|
||||||
(declare (ignore class))
|
|
||||||
(the list
|
|
||||||
(setf (slot-value finspace 'heights) (heights (stong finspace)))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD SLOT-UNBOUND (class (finspace finite-space) (slot-name (eql 'top)))
|
|
||||||
(declare (ignore class))
|
|
||||||
(the matrice
|
|
||||||
(setf (slot-value finspace 'top) (topmat (stong finspace)))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD SLOT-UNBOUND (class (finspace finite-space) (slot-name (eql 'stong)))
|
|
||||||
(declare (ignore class))
|
|
||||||
(the matrice
|
|
||||||
(setf (slot-value finspace 'stong) (stongmat (top finspace)))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD SLOT-UNBOUND (class (finspace finite-space) (slot-name (eql 'orgn)))
|
|
||||||
(declare (ignore class))
|
|
||||||
(the list
|
|
||||||
(setf (slot-value finspace 'orgn) `(FINITE-SPACE ,(idnm finspace))))) ;(1+ *idnm-counter*)
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD INITIALIZE-INSTANCE :after ((finspace FINITE-SPACE) &rest rest)
|
|
||||||
(set (intern (format nil "K~D" (idnm finspace))) finspace))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFVAR *FINITE-SPACE-LIST*)
|
|
||||||
(SETF *FINITE-SPACE-LIST* +empty-list+)
|
|
||||||
(PUSHNEW '*FINITE-SPACE-LIST* *list-list*)
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD PRINT-OBJECT ((finspace finite-space) stream)
|
|
||||||
(the finite-space
|
|
||||||
(progn
|
|
||||||
(format stream "[K~D Finite-Space]" (idnm finspace))
|
|
||||||
finspace)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN BUILD-FINITE-SPACE (&key top stong heights orgn)
|
|
||||||
(the finite-space
|
|
||||||
(progn
|
|
||||||
(let ((already (find orgn *finite-space-list* :test #'equal :key #'orgn)))
|
|
||||||
(declare (type (or finite-space null) already))
|
|
||||||
(when already
|
|
||||||
(return-from build-finite-space already)))
|
|
||||||
(let ((finspace (make-instance 'finite-space)))
|
|
||||||
(declare (type finite-space finspace))
|
|
||||||
(if top (setf (slot-value finspace 'top) top))
|
|
||||||
(if stong (setf (slot-value finspace 'stong) stong))
|
|
||||||
(if heights (setf (slot-value finspace 'heights) heights))
|
|
||||||
(if orgn (setf (slot-value finspace 'orgn) orgn))
|
|
||||||
(push finspace *finite-space-list*)
|
|
||||||
finspace))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN TOPOLOGY (dmns dens)
|
|
||||||
#| Random Finite-Space of size 'dmns' and density 'dens' |#
|
|
||||||
(declare (fixnum dmns))
|
|
||||||
(unless (plusp dmns)
|
|
||||||
(error "In TOPOLOGY, the dimension ~D should be positive." dmns))
|
|
||||||
(build-finite-space :top (randomtop dmns dens)
|
|
||||||
:orgn `(RANDOM-TOPOLOGY ,(1+ *idnm-counter*))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN ADMISSIBLE (topogenous i j)
|
|
||||||
#| 'T' if Hat-Uj-{i} is contractible (the edge (i j) is admissible) |#
|
|
||||||
(if (and (> j i) (eq (terme topogenous i j) 1))
|
|
||||||
(the boolean
|
|
||||||
(eq (length (core_list topogenous
|
|
||||||
(loop for k from 1 to (1- j)
|
|
||||||
unless (or (zerop (terme topogenous k j)) (eq k i))
|
|
||||||
collect k))) 1))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD ADMISSIBLE-P ((topogenous matrice))
|
|
||||||
(the boolean
|
|
||||||
(let ((fin T)
|
|
||||||
(stong (stongmat topogenous)))
|
|
||||||
(do ((j 2 (1+ j))) ((or (null fin) (> j (ncol topogenous))) fin)
|
|
||||||
(do ((i 1 (1+ i))) ((or (null fin) (> i (1- j))))
|
|
||||||
(if (= (terme stong i j) 1)
|
|
||||||
(if (null (admissible topogenous i j))
|
|
||||||
(setf fin NIL))))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD ADMISSIBLE-P ((finspace finite-space))
|
|
||||||
(the boolean
|
|
||||||
(let ((fin T))
|
|
||||||
(do ((j 2 (1+ j))) ((or (null fin) (> j (ncol (top finspace)))) fin)
|
|
||||||
(do ((i 1 (1+ i))) ((or (null fin) (> i (1- j))))
|
|
||||||
(if (= (terme (stong finspace) i j) 1)
|
|
||||||
(if (null (admissible (top finspace) i j))
|
|
||||||
(setf fin NIL))))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD DVFIELD ((finspace finite-space))
|
|
||||||
#| Discrete vector field on 'finspace' |#
|
|
||||||
(declare (finite-space finspace))
|
|
||||||
(let* ((m_stong (matrice-to-lmtrx (nilpot (stong finspace))))
|
|
||||||
(m_top (matrice-to-lmtrx (nilpot (top finspace))))
|
|
||||||
(rown (length m_stong))
|
|
||||||
(status (make-array rown :initial-element '()))
|
|
||||||
(used nil)
|
|
||||||
(vf '()))
|
|
||||||
(dotimes (i rown) ; Here it is working on the columns. 'rown' is the dimension of the space
|
|
||||||
(unless (member i used)
|
|
||||||
(let ((coli_stong (svref m_stong i))
|
|
||||||
(coli_top (svref m_top i)))
|
|
||||||
(when coli_stong
|
|
||||||
(let ((rowilist (mapcar #'car coli_stong))
|
|
||||||
(rowilist_top (mapcar #'car coli_top)))
|
|
||||||
(declare (type list rowilist rowilist_top))
|
|
||||||
(dolist (rowi rowilist)
|
|
||||||
(declare (type fixnum rowi))
|
|
||||||
(let ((rowistatus (svref status rowi)))
|
|
||||||
(unless (eql 1 rowistatus)
|
|
||||||
(unless (member rowi used)
|
|
||||||
(when (and (admissible (top finspace) (1+ rowi) (1+ i))
|
|
||||||
(null-intersection-p rowistatus rowilist))
|
|
||||||
(setf (svref status rowi) 1)
|
|
||||||
(setf rowistatus (insert rowi rowistatus))
|
|
||||||
(push (list (1+ rowi) (1+ i)) vf)
|
|
||||||
(push i used)
|
|
||||||
(push rowi used)
|
|
||||||
(dolist (item rowilist_top)
|
|
||||||
(unless (= item rowi)
|
|
||||||
(case (svref status item)
|
|
||||||
(1 (dotimes (rowj rown)
|
|
||||||
(let ((rowjstatus (svref status rowj)))
|
|
||||||
(unless (eql 1 rowjstatus)
|
|
||||||
(when (member item rowjstatus)
|
|
||||||
(setf (svref status rowj)
|
|
||||||
(union-merge rowistatus rowjstatus)))))))
|
|
||||||
(otherwise
|
|
||||||
(setf (svref status item)
|
|
||||||
(union-merge (member item rowilist_top) (union-merge rowistatus (svref status item))))))))
|
|
||||||
(return)))))))))))
|
|
||||||
(return-from DVFIELD (nreverse vf))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD DVFIELD ((topogenous matrice))
|
|
||||||
#| Discrete vector field on a matrice 'topogenous' |#
|
|
||||||
(dvfield (make-instance 'finite-space
|
|
||||||
:top topogenous)))
|
|
||||||
|
|
||||||
|
|
||||||
;;
|
|
||||||
;; Barycentric subdivision
|
|
||||||
;;
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN RELAC (topogenous)
|
|
||||||
#| Chains of length 2 |#
|
|
||||||
(declare (type matrice topogenous))
|
|
||||||
(let* ((dim (nlig topogenous))
|
|
||||||
(rslt (creer-matrice dim dim)))
|
|
||||||
(declare (type fixnum dim))
|
|
||||||
(do ((i 1 (1+ i))) ((> i dim) rslt)
|
|
||||||
(do ((j (1+ i) (1+ j))) ((> j dim))
|
|
||||||
(if (eq (terme topogenous i j) 1)
|
|
||||||
(insert-term rslt i j (list (list i j))))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN BOUNDARYOPERATORS (topogenous)
|
|
||||||
(let* ((relac (relac topogenous))
|
|
||||||
(diferenciales NIL)
|
|
||||||
(nuevo relac)
|
|
||||||
(dim (nlig topogenous))
|
|
||||||
(parada 0)
|
|
||||||
(dim_n 0)
|
|
||||||
(Cn NIL))
|
|
||||||
|
|
||||||
(do ((i 1 (1+ i))) ((> i (1- dim)))
|
|
||||||
(do ((j (1+ i) (1+ j))) ((> j dim))
|
|
||||||
(unless (eq (terme topogenous i j) 0)
|
|
||||||
(setf Cn (append Cn (list (list i j)))))))
|
|
||||||
|
|
||||||
(setf dim_n (length Cn))
|
|
||||||
|
|
||||||
(push (let ((D1 (creer-matrice dim dim_n)))
|
|
||||||
(dotimes (i dim)
|
|
||||||
(dotimes (j dim_n)
|
|
||||||
(if (find (1+ i) (nth j Cn))
|
|
||||||
(insert-term D1 (1+ i) (1+ j) 1))))
|
|
||||||
D1) diferenciales)
|
|
||||||
|
|
||||||
(if (> dim 1)
|
|
||||||
(do ((long 2 (1+ long))) ((or (> long dim) (eq parada 1)))
|
|
||||||
(let ((dim_n-1 dim_n)
|
|
||||||
(Cn-1 Cn)
|
|
||||||
(anterior nuevo))
|
|
||||||
|
|
||||||
(setf dim_n 0 Cn NIL nuevo (creer-matrice dim dim))
|
|
||||||
|
|
||||||
(do ((i 1 (1+ i))) ((> i (- (1+ dim) long)))
|
|
||||||
(do ((j (1+ i) (1+ j))) ((> j dim))
|
|
||||||
(let ((cadenasij NIL))
|
|
||||||
(do ((r i (1+ r))) ((> r j))
|
|
||||||
(let ((termeir (terme anterior i r)))
|
|
||||||
(unless (or (eq termeir 0) (eq (terme relac r j) 0))
|
|
||||||
(setf cadenasij (append cadenasij (mapcar #'(lambda (x) (append x (list j))) termeir))))))
|
|
||||||
(if cadenasij
|
|
||||||
(progn (insert-term nuevo i j cadenasij)
|
|
||||||
(setf Cn (append Cn cadenasij)))))))
|
|
||||||
|
|
||||||
(setf dim_n (length Cn))
|
|
||||||
|
|
||||||
(if (eq dim_n 0)
|
|
||||||
(setf parada 1)
|
|
||||||
(push (let ((Dn (creer-matrice dim_n-1 dim_n)))
|
|
||||||
(dotimes (i dim_n-1)
|
|
||||||
(dotimes (j dim_n)
|
|
||||||
(if (subsetp (nth i Cn-1) (nth j Cn))
|
|
||||||
(insert-term Dn (1+ i) (1+ j) 1))))
|
|
||||||
Dn) diferenciales)))))
|
|
||||||
(return-from BOUNDARYOPERATORS (reverse diferenciales))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN BLOCKS (list)
|
|
||||||
(let ((rslt (identite (let ((suma (nlig (car list))))
|
|
||||||
(dolist (x list)
|
|
||||||
(setf suma (+ suma (ncol x))))
|
|
||||||
suma))))
|
|
||||||
(do* ((lst list (cdr lst))
|
|
||||||
(kfilas 0 (if (null lst) 0 (+ kfilas (nlig dif))))
|
|
||||||
(kcolumnas (nlig (car list)) (if (null lst) 0 (+ kcolumnas (ncol dif))))
|
|
||||||
(dif (car lst) (car lst))) ((endp lst))
|
|
||||||
|
|
||||||
(do ((i 1 (1+ i))) ((> i (nlig dif)))
|
|
||||||
(do ((j 1 (1+ j))) ((> j (ncol dif)))
|
|
||||||
(unless (eq (terme dif i j) 0)
|
|
||||||
(insert-term rslt (+ i kfilas) (+ j kcolumnas) 1)))))
|
|
||||||
rslt))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD BAR_SUBDIVISION ((topogenous matrice))
|
|
||||||
#| Topogenous matrice of the barycentric subdivision of 'topogenous' |#
|
|
||||||
(topmat (blocks (boundaryoperators topogenous))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD BAR_SUBDIVISION ((finspace finite-space))
|
|
||||||
#| Finite-Space whose 'top' is the barycentric subdivision of (top 'finspace') |#
|
|
||||||
(let ((already (find `(BARYCENTRIC-SUBDIVISION ,finspace) *finite-space-list* :test #'equal :key #'orgn)))
|
|
||||||
(declare (type (or finite-space null) already))
|
|
||||||
(if already
|
|
||||||
already
|
|
||||||
(build-finite-space :orgn `(BARYCENTRIC-SUBDIVISION ,finspace)
|
|
||||||
:stong (blocks (boundaryoperators (top finspace)))))))
|
|
||||||
|
|
||||||
|
|
||||||
;;
|
|
||||||
;; Special examples of Finite topological spaces
|
|
||||||
;;
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN FINITE-MODEL-SPHERE (dmns)
|
|
||||||
#| Minimal finite model of the 'dmns'-dimensional sphere |#
|
|
||||||
(declare (fixnum dmns))
|
|
||||||
(if (minusp dmns)
|
|
||||||
(error "In FINITE-MODEL-SPHERE, the dimension ~D must be non-negative integer." dmns))
|
|
||||||
(build-finite-space
|
|
||||||
:stong (let ((rslt (identite (+ (* 2 dmns) 2))))
|
|
||||||
(unless (= dmns 0)
|
|
||||||
(do ((i 1 (1+ i))) ((> i (* 2 dmns)))
|
|
||||||
(insert-term rslt i (+ i 2) 1)
|
|
||||||
(if (= (mod i 2) 0)
|
|
||||||
(insert-term rslt i (+ i 1) 1)
|
|
||||||
(insert-term rslt i (+ i 3) 1))))
|
|
||||||
rslt)
|
|
||||||
:heights (let ((rslt (<a-b> 1 (+ (* 2 dmns) 2))))
|
|
||||||
(dotimes (q (1+ dmns))
|
|
||||||
(setf rslt (append (cddr rslt) (list (list (pop rslt) (pop rslt))))))
|
|
||||||
rslt)
|
|
||||||
:orgn `(FINITE-MODEL-SPHERE ,dmns)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD FINITE-SUSPENSION ((topogenous matrice))
|
|
||||||
#| Non-Hausdorff suspension of 'topogenous' |#
|
|
||||||
(let* ((nlig+1 (1+ (nlig topogenous)))
|
|
||||||
(rslt (add-points topogenous nlig+1 2)))
|
|
||||||
(maj-colonne rslt nlig+1 (loop for x in (<a-b> 1 nlig+1)
|
|
||||||
collect (list x 1)))
|
|
||||||
(maj-colonne rslt (1+ nlig+1) (loop for x in (<a-b> 1 (1- nlig+1))
|
|
||||||
collect (list x 1)))
|
|
||||||
(insert-term rslt (1+ nlig+1) (1+ nlig+1) 1)
|
|
||||||
rslt))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD FINITE-SUSPENSION ((finspace finite-space))
|
|
||||||
(build-finite-space :top (finite-suspension (top finspace))
|
|
||||||
:orgn `(FINITE-SUSPENSION ,(idnm finspace))))
|
|
||||||
@ -1,132 +0,0 @@
|
|||||||
;;;; -*- Mode: Lisp; Syntax: ANSI-Common-Lisp; Base: 10 -*
|
|
||||||
|
|
||||||
;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
|
|
||||||
;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
|
|
||||||
;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
|
|
||||||
|
|
||||||
(IN-PACKAGE #:cat)
|
|
||||||
|
|
||||||
(PROVIDE "finite-topological-spaces-core")
|
|
||||||
|
|
||||||
;;
|
|
||||||
;; Point reductions: beat points and weak beat points
|
|
||||||
;;
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN DOWNBP (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| T if Xn is a down beat point of the submatrix 'list'x'list' |#
|
|
||||||
(the boolean
|
|
||||||
(let ((maximal (loop for k in (reverse (subseq list 0 (position n list)))
|
|
||||||
thereis (and (eq (terme topogenous k n) 1) k))))
|
|
||||||
|
|
||||||
(unless (or (null maximal)
|
|
||||||
(loop for i in (subseq list 0 (position n list))
|
|
||||||
thereis (not (eq (terme topogenous i maximal) (terme topogenous i n)))))
|
|
||||||
+TRUE+))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN UPBP (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| T if Xn is an up beat point of the submatrix 'list'x'list' |#
|
|
||||||
(the boolean
|
|
||||||
(let ((minimal (loop for k in (subseq list (1+ (position n list)))
|
|
||||||
thereis (and (eq (terme topogenous n k) 1) k))))
|
|
||||||
(unless (or (null minimal)
|
|
||||||
(loop for i in (subseq list (1+ (position n list)))
|
|
||||||
thereis (not (eq (terme topogenous minimal i) (terme topogenous n i)))))
|
|
||||||
+TRUE+))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN BEATPOINT (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| T if Xn is a beat point of the submatrix 'list'x'list' |#
|
|
||||||
(the boolean
|
|
||||||
(if (< (1+ n) (/ (ncol topogenous) 2))
|
|
||||||
(if (downbp topogenous n list)
|
|
||||||
+TRUE+
|
|
||||||
(upbp topogenous n list))
|
|
||||||
(if (upbp topogenous n list)
|
|
||||||
+TRUE+
|
|
||||||
(downbp topogenous n list)))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN CORE_LIST (topogenous &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| List of the elements of the core of the submatrix 'list'x'list' |#
|
|
||||||
(let ((eliminar NIL))
|
|
||||||
(setf eliminar (loop for n in list
|
|
||||||
thereis (and (beatpoint topogenous n list) n)))
|
|
||||||
(if (null eliminar)
|
|
||||||
(return-from core_list list)
|
|
||||||
(core_list topogenous (remove eliminar list)))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN Un-N (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| List of the elements in Un-{Xn} |#
|
|
||||||
(loop for i in (subseq list 0 (position n list))
|
|
||||||
when (eq (terme topogenous i n) 1)
|
|
||||||
collect i))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN Fn-N (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| List of the elements in Fn-{Xn} |#
|
|
||||||
(loop for j in (subseq list (1+ (position n list)))
|
|
||||||
when (eq (terme topogenous n j) 1)
|
|
||||||
collect j))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN LINK_LIST (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| List of the elements in the link of Xn |#
|
|
||||||
(append (Un-N topogenous n list) (Fn-N topogenous n list)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN WEAKPOINT (topogenous n &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| T if Xn is a weak beat point of the submatrix 'list'x'list' |#
|
|
||||||
(the boolean
|
|
||||||
(or (eq (length (core_list topogenous (Un-N topogenous n list))) 1)
|
|
||||||
(eq (length (core_list topogenous (Fn-N topogenous n list))) 1))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN WEAKCORE_LIST (topogenous &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| List of the elements of a "weak core" of the submatrix 'list'x'list' |#
|
|
||||||
(let ((eliminar NIL))
|
|
||||||
(setf eliminar (loop for n in list
|
|
||||||
thereis (and (or (beatpoint topogenous n list) (weakpoint topogenous n list)) n)))
|
|
||||||
(if (null eliminar)
|
|
||||||
(return-from weakcore_list list)
|
|
||||||
(weakcore_list topogenous (remove eliminar list)))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD CORE ((topogenous matrice) &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| Matrice of the core of 'topogenous' |#
|
|
||||||
(the matrice
|
|
||||||
(let ((corelist (core_list topogenous list)))
|
|
||||||
(sub-matrix topogenous corelist corelist))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD CORE ((finspace finite-space) &optional list)
|
|
||||||
#| Finite-Space whose 'top' is the topogenous matrix of the core of (top 'finspace') |#
|
|
||||||
(let ((already (find (if list `(CORE ,finspace ,list) `(CORE ,finspace)) *finite-space-list* :test #'equal :key #'orgn)))
|
|
||||||
(declare (type (or finite-space null) already))
|
|
||||||
(if already
|
|
||||||
already
|
|
||||||
(let ((list2 (or list (<a-b> 1 (nlig (top finspace))))))
|
|
||||||
(build-finite-space :orgn (if list `(CORE ,finspace ,list) `(CORE ,finspace))
|
|
||||||
:top (core (top finspace) list2))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD WEAKCORE ((topogenous matrice) &optional (list (<a-b> 1 (nlig topogenous))))
|
|
||||||
#| Matrice of a "weak core" of 'topogenous' |#
|
|
||||||
(the matrice
|
|
||||||
(let ((weakcorelist (weakcore_list topogenous (core_list topogenous list))))
|
|
||||||
(sub-matrix topogenous weakcorelist weakcorelist))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD WEAKCORE ((finspace finite-space) &optional list)
|
|
||||||
#| Finite-Space whose 'top' is the topogenous matrix of a "weak core" of (top 'finspace') |#
|
|
||||||
(let ((already (find (if list `(WEAK-CORE ,finspace ,list) `(WEAK-CORE ,finspace)) *finite-space-list* :test #'equal :key #'orgn)))
|
|
||||||
(declare (type (or finite-space null) already))
|
|
||||||
(if already
|
|
||||||
already
|
|
||||||
(let ((list2 (or list (<a-b> 1 (nlig (top finspace))))))
|
|
||||||
(build-finite-space :orgn (if list `(WEAK-CORE ,finspace ,list) `(WEAK-CORE ,finspace))
|
|
||||||
:top (weakcore (top finspace) list2))))))
|
|
||||||
|
|
||||||
|
|
||||||
@ -1,301 +0,0 @@
|
|||||||
;;;; -*- Mode: Lisp; Syntax: ANSI-Common-Lisp; Base: 10 -*
|
|
||||||
|
|
||||||
;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
|
|
||||||
;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
|
|
||||||
;; FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES FINITE-TOPOLOGICAL-SPACES
|
|
||||||
|
|
||||||
(IN-PACKAGE #:cat)
|
|
||||||
|
|
||||||
(PROVIDE "finite-topological-spaces-homology")
|
|
||||||
|
|
||||||
;;
|
|
||||||
;; Homology of h-regular spaces
|
|
||||||
;;
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN COLUMN-J (mtrx j)
|
|
||||||
(declare (type matrix mtrx)
|
|
||||||
(type fixnum j))
|
|
||||||
(assert (< j (column-number mtrx)))
|
|
||||||
(the list
|
|
||||||
(let ((line-n (line-number mtrx)))
|
|
||||||
(declare (type fixnum line-n))
|
|
||||||
(mapcar
|
|
||||||
#'(lambda (i)
|
|
||||||
(declare (type fixnum i))
|
|
||||||
(aref mtrx i j))
|
|
||||||
(<a-b> 0 (1- line-n))))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN KERNEL (mtrx)
|
|
||||||
(declare (type matrix mtrx))
|
|
||||||
(the list
|
|
||||||
(let* ((smith-list (smith mtrx))
|
|
||||||
(m (third smith-list))
|
|
||||||
(q (fourth smith-list))
|
|
||||||
(min (min (line-number mtrx) (column-number mtrx)))
|
|
||||||
(rslt nil))
|
|
||||||
(declare
|
|
||||||
(type list smith-list rslt)
|
|
||||||
(type matrix m q)
|
|
||||||
(type fixnum min))
|
|
||||||
(progn
|
|
||||||
(do ((j (1- (column-number mtrx)) (1- j)))
|
|
||||||
((< j min))
|
|
||||||
(declare (type fixnum j))
|
|
||||||
(setq rslt (nconc (list (column-j q j)) rslt)))
|
|
||||||
(do ((i (1- min) (1- i)))
|
|
||||||
((or (< i 0) (not (eql 0 (aref m i i)))))
|
|
||||||
(declare (type fixnum i))
|
|
||||||
(setq rslt (nconc (list (column-j q i)) rslt)))
|
|
||||||
rslt))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD H-REGULAR-DIF ((finspace finite-space))
|
|
||||||
(let ((diferenciales NIL)
|
|
||||||
(aristas (matrice-to-lmtrx (nilpot (stong finspace))))
|
|
||||||
(alturas (heights finspace)))
|
|
||||||
(declare (type list diferenciales))
|
|
||||||
(dotimes (dimension (length alturas))
|
|
||||||
(let* ((Cn (nth dimension alturas))
|
|
||||||
(dim_n (length Cn)))
|
|
||||||
(if (zerop dimension)
|
|
||||||
(push (creer-matrice 0 (length Cn)) diferenciales)
|
|
||||||
(let* ((Cn-1 (nth (1- dimension) alturas))
|
|
||||||
(dim_n-1 (length Cn-1))
|
|
||||||
(rslt (creer-matrice dim_n-1 dim_n)))
|
|
||||||
(case dimension
|
|
||||||
(1 (progn (push (do ((group Cn (cdr group))
|
|
||||||
(posicion 1 (1+ posicion)))
|
|
||||||
((endp group) rslt)
|
|
||||||
(let ((colj (aref aristas (1- (car group)))))
|
|
||||||
(insert-term rslt (1+ (position (1+ (car (first colj))) Cn-1)) posicion -1)
|
|
||||||
(insert-term rslt (1+ (position (1+ (car (second colj))) Cn-1)) posicion 1)))
|
|
||||||
diferenciales)))
|
|
||||||
|
|
||||||
(otherwise (push (let ((Cn-2 (<a-b> 1 (length (nth (- dimension 2) alturas))))
|
|
||||||
(dn-1 (first diferenciales))
|
|
||||||
(group Cn))
|
|
||||||
(do ((posicion 1 (1+ posicion)))
|
|
||||||
((null group) rslt)
|
|
||||||
(let* ((maxUj (mapcar #'(lambda (v) (1+ (car v))) (aref aristas (1- (pop group)))))
|
|
||||||
(cols (posiciones-1 maxUj Cn-1))
|
|
||||||
(ker (car (kernel (make-array (list (length Cn-2) (length cols))
|
|
||||||
:element-type 'fixnum
|
|
||||||
:initial-contents (loop for i in Cn-2
|
|
||||||
collect (loop for j in cols
|
|
||||||
collect (terme dn-1 i j))))))))
|
|
||||||
(do ((ker ker (cdr ker))
|
|
||||||
(cols cols (cdr cols)))
|
|
||||||
((endp cols))
|
|
||||||
(insert-term rslt (car cols) posicion (car ker))))))
|
|
||||||
diferenciales)))))))
|
|
||||||
(return-from H-REGULAR-DIF (reverse diferenciales))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD H-REGULAR-DIF ((topogenous matrice))
|
|
||||||
(let ((finspace (build-finite-space :top topogenous)))
|
|
||||||
(H-REGULAR-DIF finspace)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN POSICIONES (pos list)
|
|
||||||
(loop for x in pos
|
|
||||||
collect (nth (1- x) list)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN POSICIONES-1 (list1 list2) ; 'list1' is a sublist of 'list2'
|
|
||||||
(loop for x in list1
|
|
||||||
collect (1+ (position x list2 :test #'equal))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN D21-1 (blocks size)
|
|
||||||
#| Modify 'blocks' in order to obtain an identity matrix in the submatrix 'size'x'size' |#
|
|
||||||
(declare (type fixnum size))
|
|
||||||
(the matrice
|
|
||||||
(let ((rslt (copier-matrice blocks)))
|
|
||||||
(unless (or (< (nlig rslt) size) (< (ncol rslt) size) (= size 0))
|
|
||||||
(loop for k from 1 to size
|
|
||||||
do (progn
|
|
||||||
;(if (eq (terme rslt k k) 0)
|
|
||||||
;(0column-swap rslt k (loop for j from (1+ k) to size
|
|
||||||
; when (not (eq (terme rslt k j) 0))
|
|
||||||
; return j)))
|
|
||||||
(unless (eq (terme rslt k k) 1)
|
|
||||||
(0column-op rslt (1- (terme rslt k k)) k k))
|
|
||||||
(loop for j from 1 to size
|
|
||||||
if (not (eq j k))
|
|
||||||
do (unless (eq (terme rslt k j) 0)
|
|
||||||
(0column-op rslt (- (terme rslt k j)) k j))))))
|
|
||||||
rslt)))
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN RESTA (mtrx1 mtrx2)
|
|
||||||
(let ((rslt (creer-matrice (nlig mtrx1) (ncol mtrx2))))
|
|
||||||
(loop for i from 1 to (nlig mtrx1)
|
|
||||||
do (loop for j from 1 to (ncol mtrx1)
|
|
||||||
do (insert-term rslt i j (- (terme mtrx1 i j) (terme mtrx2 i j)))))
|
|
||||||
rslt))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFUN FINAL (matrix corte) ; 'matrix' is the result of the function D21-1 and 'corte' is the 'size' in D21-1 function
|
|
||||||
(let ((d31 (sub-matrix matrix
|
|
||||||
(>a-b> corte (nlig matrix))
|
|
||||||
(<a-b> 1 corte)))
|
|
||||||
(d23 (sub-matrix matrix
|
|
||||||
(<a-b> 1 corte )
|
|
||||||
(>a-b> corte (ncol matrix))))
|
|
||||||
(d33 (sub-matrix matrix
|
|
||||||
(>a-b> corte (nlig matrix))
|
|
||||||
(>a-b> corte (ncol matrix)))))
|
|
||||||
(resta d33 (matrice-prdc d31 d23))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFSTRUCT (TSC (:conc-name nil))
|
|
||||||
name diferencial group targets sources critical)
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMACRO DESCOMP (name)
|
|
||||||
`(setf ,name (make-TSC)
|
|
||||||
(sources ,name) (reverse (intersection sou summands))
|
|
||||||
(targets ,name) (reverse (intersection tar summands))
|
|
||||||
(critical ,name) (let ((cri summands))
|
|
||||||
(dolist (x (append (targets ,name) (sources ,name)))
|
|
||||||
(setf cri (remove x cri)))
|
|
||||||
cri)))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD DVF-H-REGULAR-DIF ((finspace finite-space) &key sou tar)
|
|
||||||
(let* ((groups NIL)
|
|
||||||
(diferenciales NIL)
|
|
||||||
(dn-3 NIL)
|
|
||||||
(dn-2 NIL)
|
|
||||||
(dn-1 NIL)
|
|
||||||
(dn NIL)
|
|
||||||
(alturas (heights finspace))
|
|
||||||
(height (length alturas)))
|
|
||||||
(declare (type list groups diferenciales)
|
|
||||||
(type fixnum height))
|
|
||||||
(setf dn-3 (make-TSC))
|
|
||||||
(dotimes (dimension height)
|
|
||||||
(let ((summands (nth dimension alturas)))
|
|
||||||
(case dimension
|
|
||||||
(0 (progn (descomp dn-2)
|
|
||||||
;;; Computing C0':
|
|
||||||
(push (mapcar #'(lambda (u) (list (list 1 u))) summands) groups)
|
|
||||||
;;; Computing d0:
|
|
||||||
(push (creer-matrice 0 (length (critical dn-2))) diferenciales)))
|
|
||||||
|
|
||||||
(1 (progn (descomp dn-1)
|
|
||||||
;;; Computing C1':
|
|
||||||
(push (loop for x in summands
|
|
||||||
collect (let* ((primer1 (find-if #'(lambda (y) (= (terme (top finspace) y x) 1))
|
|
||||||
(<a-b< 1 (nlig (top finspace)))))
|
|
||||||
(segundo1 (find-if #'(lambda (y) (= (terme (top finspace) y x) 1))
|
|
||||||
(>a-b> primer1 (nlig (top finspace))))))
|
|
||||||
(list (list 1 segundo1 x) (list -1 primer1 x)))) groups)
|
|
||||||
|
|
||||||
;;; Computing d1'':
|
|
||||||
(push (let ((rslt (creer-matrice (length (second groups)) (length summands))))
|
|
||||||
(dolist (x (apply #'append (first groups)))
|
|
||||||
(insert-term rslt (1+ (position (second x) (first alturas) :test #'equal))
|
|
||||||
(1+ (position (third x) (second alturas) :test #'equal))
|
|
||||||
(first x)))
|
|
||||||
rslt) diferenciales)))
|
|
||||||
|
|
||||||
(otherwise (progn (descomp dn)
|
|
||||||
(let ((rslt NIL)
|
|
||||||
(Cn-1 (first groups))
|
|
||||||
(Cn-2 (second groups)))
|
|
||||||
|
|
||||||
;;; Cálculo de Cn' (rslt):
|
|
||||||
(dolist (x (reverse summands))
|
|
||||||
(let ((pseudo NIL)
|
|
||||||
(list_fil NIL)
|
|
||||||
(list_col NIL)
|
|
||||||
(kernel NIL))
|
|
||||||
|
|
||||||
(setf list_fil (loop for k from 0 to (1- (length Cn-2))
|
|
||||||
when (= (terme (top finspace) (car (last (first (nth k Cn-2)))) x) 1)
|
|
||||||
collect k)
|
|
||||||
list_col (loop for k from 0 to (1- (length Cn-1))
|
|
||||||
when (= (terme (top finspace) (car (last (first (nth k Cn-1)))) x) 1)
|
|
||||||
collect k)
|
|
||||||
|
|
||||||
kernel (car (kernel (convertmatrice (sub-matrix (first diferenciales)
|
|
||||||
(mapcar #'(lambda (x) (1+ x)) list_fil)
|
|
||||||
(mapcar #'(lambda (x) (1+ x)) list_col))))))
|
|
||||||
|
|
||||||
(do ((lst list_col (cdr lst))
|
|
||||||
(ker kernel (cdr ker)))
|
|
||||||
((endp lst))
|
|
||||||
(unless (equal (car ker) 0)
|
|
||||||
(let ((actualizar (nth (car lst) Cn-1)))
|
|
||||||
(dolist (z actualizar)
|
|
||||||
(push (reverse (cons x (reverse (cons (* (car ker) (car z)) (cdr z))))) pseudo)))))
|
|
||||||
|
|
||||||
(push pseudo rslt)))
|
|
||||||
|
|
||||||
;;; Computing dn'' (rslt2):
|
|
||||||
(push (let ((rslt2 (creer-matrice (length Cn-1) (length summands))))
|
|
||||||
(dotimes (j (length summands) rslt2)
|
|
||||||
(let ((next-to-last 0))
|
|
||||||
(do ((tj (nth j rslt) (remove-if #'(lambda (elto)
|
|
||||||
(equal next-to-last (second (reverse elto))))
|
|
||||||
tj)))
|
|
||||||
((null tj))
|
|
||||||
|
|
||||||
(setf next-to-last (second (reverse (first tj))))
|
|
||||||
(let* ((g (nth (position next-to-last (nth (1- dimension) alturas)) Cn-1))
|
|
||||||
(ui (car (last g))))
|
|
||||||
(dolist (l tj)
|
|
||||||
(if (equal (cdr ui) (reverse (cdr (reverse (cdr l)))))
|
|
||||||
(progn
|
|
||||||
(insert-term rslt2 (1+ (position g Cn-1)) (1+ j) (* (first ui) (first l)))
|
|
||||||
(return))))))))) diferenciales)
|
|
||||||
(setf groups (list (car groups)))
|
|
||||||
(push rslt groups))
|
|
||||||
|
|
||||||
(unless (= dimension 2)
|
|
||||||
(setf (third diferenciales)
|
|
||||||
(final
|
|
||||||
(d21-1
|
|
||||||
(sub-matrix (third diferenciales)
|
|
||||||
(posiciones-1 (append (sources dn-3) (critical dn-3)) (nth (- dimension 3) alturas))
|
|
||||||
(posiciones-1 (append (targets dn-2) (critical dn-2)) (nth (- dimension 2) alturas)))
|
|
||||||
(length (targets dn-2)))
|
|
||||||
(length (targets dn-2)))))
|
|
||||||
|
|
||||||
(setf dn-3 dn-2
|
|
||||||
dn-2 dn-1
|
|
||||||
dn-1 dn))))))
|
|
||||||
|
|
||||||
;;; Modify the last 2 matrices
|
|
||||||
(unless (= height 1)
|
|
||||||
(unless (= height 2)
|
|
||||||
(setf (second diferenciales)
|
|
||||||
(final
|
|
||||||
(d21-1
|
|
||||||
(sub-matrix (second diferenciales)
|
|
||||||
(posiciones-1 (append (sources dn-3) (critical dn-3)) (nth (- height 3) alturas))
|
|
||||||
(posiciones-1 (append (targets dn-2) (critical dn-2)) (nth (- height 2) alturas)))
|
|
||||||
(length (targets dn-2)))
|
|
||||||
(length (targets dn-2)))))
|
|
||||||
|
|
||||||
(setf (first diferenciales)
|
|
||||||
(final
|
|
||||||
(d21-1
|
|
||||||
(sub-matrix (first diferenciales)
|
|
||||||
(posiciones-1 (append (sources dn-2) (critical dn-2)) (nth (- height 2) alturas))
|
|
||||||
(posiciones-1 (append (targets dn-1) (critical dn-1)) (nth (- height 1) alturas)))
|
|
||||||
(length (targets dn-1)))
|
|
||||||
(length (targets dn-1)))))
|
|
||||||
|
|
||||||
(return-from DVF-H-REGULAR-DIF (reverse diferenciales))))
|
|
||||||
|
|
||||||
|
|
||||||
(DEFMETHOD DVF-H-REGULAR-DIF ((topogenous matrice) &key sou tar)
|
|
||||||
(let ((finspace (build-finite-space :top topogenous
|
|
||||||
:stong (stongmat topogenous))))
|
|
||||||
(DVF-H-REGULAR-DIF finspace :sou sou :tar tar)))
|
|
||||||
|
|
||||||
1280
src/finite-topological-spaces.lisp
Normal file
1280
src/finite-topological-spaces.lisp
Normal file
File diff suppressed because it is too large
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Reference in New Issue
Block a user