409 lines
11 KiB
Common Lisp
409 lines
11 KiB
Common Lisp
;;; DELTA DELTA DELTA DELTA DELTA DELTA DELTA DELTA DELTA
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;;; DELTA DELTA DELTA DELTA DELTA DELTA DELTA DELTA DELTA
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;;; DELTA DELTA DELTA DELTA DELTA DELTA DELTA DELTA DELTA
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(IN-PACKAGE "CAT")
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(PROVIDE "delta")
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(DEFMETHOD PRINT-KEYCONS ((car (eql :delt)) cdr stream)
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(format stream "~A" (hyphenize-list (dlop-int-ext cdr)))
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(cons car cdr))
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(DEFUN SOFT-DELTA-CMPR (gmsm1 gmsm2)
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(f-cmpr (cdr gmsm1) (cdr gmsm2)))
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#|
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(soft-delta-cmpr (d 12) (d 23))
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|#
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(DEFUN DELTA-FACE (indx dmns gmsm)
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(declare
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(fixnum indx gmsm)
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(ignore dmns))
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(the absm
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(do ((pmark 1 (ash pmark 1))
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(bmark indx)
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(gmsm2 gmsm (ash gmsm2 -1)))
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(nil)
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(declare (fixnum pmark bmark gmsm2))
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(when (oddp gmsm2)
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(when (minusp (decf bmark))
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(return-from delta-face (absm 0 (logxor gmsm pmark))))))))
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(DEFUN SOFT-DELTA-FACE (indx dmns gmsm)
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(declare
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(fixnum indx dmns)
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(type soft-dlop gmsm))
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(absm 0 (d (gmsm (delta-face indx dmns (cdr gmsm))))))
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#|
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(dotimes (i 4)
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(print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 1 2 3)))))))
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(dotimes (i 4)
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(print (dlop-int-ext (gmsm (delta-face i 3 (dlop-ext-int '(0 2 4 6))))))))
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(dotimes (i 4)
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(print (soft-delta-face i 3 (d (mask 4)))))
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(dotimes (i 4)
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(print (soft-delta-face i 3 (d (dlop-ext-int '(0 2 4 6))))))
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|#
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(DEFUN DELTA-dffr (dmns gmsm)
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(declare (fixnum dmns gmsm))
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(the cmbn
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(if (zerop dmns)
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+zero-negative-cmbn+
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(make-cmbn
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:degr (1- dmns)
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:list (do ((rslt +empty-list+)
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(gmsm2 gmsm (ash gmsm2 -1))
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(pmark 1 (ash pmark +1))
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(sign 1))
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((zerop gmsm2) rslt)
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(declare
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(list rslt)
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(fixnum gmsm2 pmark sign))
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(when (oddp gmsm2)
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(push (term sign (logxor gmsm pmark)) rslt)
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(setf sign (- sign))))))))
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(DEFUN SOFT-DELTA-dffr (dmns gmsm)
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(declare
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(fixnum dmns)
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(type soft-dlop gmsm))
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(make-cmbn
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:degr (1- dmns)
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:list (mapcar #'(lambda (term)
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(with-term (cffc gmsm) term
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(term cffc (d gmsm))))
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(cmbn-list (delta-dffr dmns (cdr gmsm))))))
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#|
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(delta-dffr 0 4)
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(delta-dffr 1 3)
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(delta-dffr 1 5)
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(delta-dffr 1 10)
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(delta-dffr 5 63)
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(soft-delta-dffr 5 (d (mask 6)))
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|#
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(DEFUN DELTA-CPRD (dmns gmsm)
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(declare (fixnum dmns gmsm))
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(the cmbn
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(make-cmbn
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:degr dmns
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:list (do ((rslt +empty-list+)
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(ldegr dmns)
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(indx (1- (integer-length gmsm)) (1- indx)))
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((minusp indx))
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(declare
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(list rslt)
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(fixnum indx))
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(when (logbitp indx gmsm)
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(push (term 1 (tnpr
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ldegr (logand gmsm (mask (1+ indx)))
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(- dmns ldegr) (logandc2 gmsm (mask indx))))
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rslt)
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(when (minusp (decf ldegr))
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(return rslt)))))))
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(DEFUN SOFT-DELTA-CPRD (dmns gmsm)
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(declare
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(fixnum dmns)
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(type soft-dlop gmsm))
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(make-cmbn :degr dmns
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:list (mapcar
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#'(lambda (term)
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(with-term (cffc tnpr) term
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(with-tnpr (degr1 gmsm1 degr2 gmsm2) tnpr
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(term cffc
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(tnpr degr1 (d gmsm1) degr2 (d gmsm2))))))
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(cmbn-list (delta-cprd dmns (cdr gmsm))))))
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#|
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(delta-cprd 3 15)
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(delta-cprd 3 170)
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(soft-delta-cprd 3 (d (dlop-ext-int '(1 3 5 7))))
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(delta-cprd 0 64)
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|#
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(DEFUN DELTA-INFINITY ()
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(the simplicial-set
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(simplicial-set
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:cmpr #'f-cmpr
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:basis :locally-effective
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:bsgn 1
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:face #'delta-face
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:cprd-intr #'delta-cprd
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:cprd-strt :gnrt
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:dffr-intr #'delta-dffr
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:dffr-strt :gnrt
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:dfnt '(delta-infinity))))
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#|
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(cmpr (delta-infinity) 2 4)
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(cmpr (delta-infinity) 4 4)
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(cmpr (delta-infinity) 8 4)
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(basis (delta-infinity) 1) ;;; => error
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(face (delta-infinity) 1 2 21)
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(cprd (delta-infinity) 3 15)
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(cprd (delta-infinity) 3 15)
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(? (delta-infinity) 2 21))
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|#
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(DEFUN SOFT-DELTA-INFINITY ()
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(the simplicial-set
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(simplicial-set
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:cmpr #'soft-delta-cmpr
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:basis :locally-effective
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:bsgn (d 1)
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:face #'soft-delta-face
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:cprd-intr #'soft-delta-cprd :cprd-strt :gnrt
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:dffr-intr #'soft-delta-dffr :dffr-strt :gnrt
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:dfnt '(soft-delta-infinity))))
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#|
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(cat-init)
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(cmpr (soft-delta-infinity) (d 2) (d 4))
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(face (soft-delta-infinity) 1 2 (d (dlop-ext-int '(1 3 5))))
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(cprd (soft-delta-infinity) 3 (d 15))
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(cprd (soft-delta-infinity) 3 (d 15))
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(? (soft-delta-infinity) 2 (d (dlop-ext-int '(0 2 4))))
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|#
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(DEFUN DELTA-N-BASIS (n)
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(declare (fixnum n dmns))
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(flet ((rslt (dmns)
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(when (> dmns n)
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(return-from rslt +empty-list+))
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(setf dmns (1+ dmns))
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(do ((rslt +empty-list+)
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(count (binomial-n-p (1+ n) dmns))
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(gmsm (mask (1+ n)) (1- gmsm)))
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((zerop count) rslt)
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(when (= (logcount gmsm) dmns)
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(push gmsm rslt)
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(decf count)))))
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(the basis #'rslt)))
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(DEFUN SOFT-DELTA-N-BASIS (n)
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(declare (fixnum n))
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(flet ((rslt (dmns)
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(when (> dmns n)
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(return-from rslt +empty-list+))
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(setf dmns (1+ dmns))
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(do ((rslt +empty-list+)
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(count (binomial-n-p (1+ n) dmns))
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(gmsm (mask (1+ n)) (1- gmsm)))
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((zerop count) rslt)
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(when (= (logcount gmsm) dmns)
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(push (d gmsm) rslt)
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(decf count)))))
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(the basis #'rslt)))
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#|
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(setf basis (delta-n-basis 3))
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(setf soft-basis (soft-delta-n-basis 3))
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(dotimes (i 5)
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(print (funcall basis i)))
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(dotimes (i 5)
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(print (funcall soft-basis i)))))
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|#
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(DEFUN DELTA (dmns)
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(declare (fixnum dmns))
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(the simplicial-set
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(simplicial-set
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:cmpr #'f-cmpr
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:basis (delta-n-basis dmns)
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:bsgn 1
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:face #'delta-face
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:cprd-intr #'delta-cprd
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:cprd-strt :gnrt
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:dffr-intr #'delta-dffr
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:dffr-strt :gnrt
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:dfnt `(delta ,dmns))))
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#|
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(cat-init)
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(setf d3 (delta 3))
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(cmpr d3 2 4)
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(cmpr d3 4 4)
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(cmpr d3 8 4)
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(basis d3 1)
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(cprd d3 3 15)
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(face d3 1 2 21)
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(? d3 2 13)
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(setf d (delta-infinity))
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(basis d)
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(setf d (delta-infinity)))
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|#
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(DEFUN SOFT-DELTA (dmns)
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(declare (fixnum dmns))
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(the simplicial-set
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(simplicial-set
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:cmpr #'soft-delta-cmpr
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:basis (soft-delta-n-basis dmns)
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:bsgn (d 1)
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:face #'soft-delta-face
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:cprd-intr #'soft-delta-cprd :cprd-strt :gnrt
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:dffr-intr #'soft-delta-dffr :dffr-strt :gnrt
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:dfnt `(soft-delta ,dmns))))
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#|
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(cat-init)
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(setf d3 (soft-delta 3))
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(cmpr d3 (d 2) (d 4))
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(basis d3 1)
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(cprd d3 3 (d 15))
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(face d3 1 2 (d 21))
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(? d3 2 (d 13))
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|#
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#| For comparison with EAT.
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In
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(setf delta (delta-infinity))
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(setf d (dffr delta))
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(setf s14 (mask 15))
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(cmbn-? d (gnrt-? d 14 s14))
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(defun t1 (n)
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(time (dotimes (i n) (cmbn-? d (gnrt-? d 14 s14)))))
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(compile 't1)
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(t1 500)
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(setf +too-much-time+ -1)
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(t1 500)
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|#
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#|
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In EAT:
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(setf delta *delta*)
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(setf d (cc-d (ss-cc delta)))
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(setf s14 (<a-b> 0 14))
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(??? d (? d 14 s14))
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(defun t1 (n)
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(time (dotimes (i n) (??? d (? d 14 s14)))))
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(compile 't1)
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(t1 500)
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|#
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(DEFUN DELTAB-CMPR (gmsm1 gmsm2)
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(declare (fixnum gmsm1 gmsm2))
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(if (= 1 (logcount gmsm1))
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:equal
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(f-cmpr gmsm1 gmsm2)))
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(DEFUN DELTAB-dffr (dmns gmsm)
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(declare (fixnum dmns gmsm))
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(the cmbn
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(if (< dmns 2)
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(zero-cmbn (1- dmns))
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(make-cmbn
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:degr (1- dmns)
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:list (do ((rslt +empty-list+)
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(gmsm2 gmsm (ash gmsm2 -1))
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(pmark 1 (ash pmark +1))
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(sign 1))
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((zerop gmsm2) rslt)
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(declare
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(list rslt)
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(fixnum gmsm2 pmark sign))
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(when (oddp gmsm2)
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(push (term sign (logxor gmsm pmark)) rslt)
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(setf sign (- sign))))))))
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(DEFUN DELTAB2-FACE (indx dmns gmsm)
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(declare
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(fixnum indx dmns gmsm))
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(the absm
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(progn
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(when (= 2 dmns)
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(return-from deltab2-face (absm 1 1)))
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(do ((pmark 1 (ash pmark 1))
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(bmark indx)
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(gmsm2 gmsm (ash gmsm2 -1)))
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(nil)
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(declare (fixnum pmark bmark gmsm2))
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(when (oddp gmsm2)
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(when (minusp (decf bmark))
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(return-from deltab2-face (absm 0 (logxor gmsm pmark)))))))))
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(DEFUN DELTAB2-cprd (dmns gmsm)
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(declare (fixnum dmns gmsm))
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(the cmbn
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(make-cmbn
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:degr dmns
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:list (if (zerop dmns)
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(list (term 1 (tnpr 0 gmsm 0 gmsm)))
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(do ((rslt +empty-list+)
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(ldegr dmns)
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(indx (1- (integer-length gmsm)) (1- indx)))
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((minusp indx))
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(declare
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(list rslt)
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(fixnum indx))
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(when (logbitp indx gmsm)
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(push (term 1 (tnpr
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ldegr (logand gmsm (mask (1+ indx)))
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(- dmns ldegr) (logandc2 gmsm (mask indx))))
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rslt)
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(when (minusp (decf ldegr))
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(setf rslt (delete 1 rslt :key #'caaddr))
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(setf (gnrt1 (gnrt (first rslt)))
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(setf (gnrt2 (gnrt (car (last rslt))))
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1))
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(return (delete 1 rslt :key #'cadddr)))))))))
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#|
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(dotimes (i 7)
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(print (deltab2-cprd i (mask (1+ i)))))
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|#
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(DEFUN DELTAB2-dffr (dmns gmsm)
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(declare (fixnum dmns gmsm))
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(the cmbn
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(if (< dmns 3)
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(zero-cmbn (1- dmns))
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(make-cmbn
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:degr (1- dmns)
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:list (do ((rslt +empty-list+)
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(gmsm2 gmsm (ash gmsm2 -1))
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(pmark 1 (ash pmark +1))
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(sign 1))
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((zerop gmsm2) rslt)
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(declare
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(list rslt)
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(fixnum gmsm2 pmark sign))
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(when (oddp gmsm2)
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(push (term sign (logxor gmsm pmark)) rslt)
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(setf sign (- sign))))))))
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#|
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(deltab-dffr 1 5)
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(deltab-dffr 3 15)
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|#
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(DEFUN DELTAB ()
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(the simplicial-set
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(simplicial-set
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:cmpr #'deltab-cmpr
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:basis :locally-effective
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:bsgn 1
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:face #'delta-face
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:cprd-intr #'delta-cprd
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:cprd-strt :gnrt
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:dfnt '(deltab))))
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(DEFUN DELTAB2 ()
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(the simplicial-set
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(simplicial-set
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:cmpr #'f-cmpr
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:basis :locally-effective
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:bsgn 1
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:face #'deltab2-face
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:cprd-intr #'deltab2-cprd
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:cprd-strt :gnrt
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:dfnt '(deltab2))))
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