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grgmater.sl
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grgmater.sl
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%==========================================================================%
% GRGmater.sl Matter fields: EM, YM, Scalar, Dirac, Fluid %
%==========================================================================%
% GRG 3.2 Standard Lisp Source Code (C) 1988-96 Vadim V. Zhytnikov %
%==========================================================================%
% This file is distributed without any warranty. You may modify it but you %
% are not allowed to remove author's name and/or distribute modified file. %
%==========================================================================%
%---------- YM field. 09.96 -----------------------------------------------
(de sconst!> (wa wb wc)
(gets0!> !#!S!C!O!N!S!T (list3 wa wb wc) '((a 1 2 3)) 0))
% FFYM = d AYM + AYM/\AYM
(de ffymfromaym!> nil
(prog (w wc)
(makebox!> '!#!F!F!Y!M)
(for!> x (0 1 9) do (progn
(setq w (ncons (dex!> (getel1!> !#!A!Y!M x))))
(for!> y (0 1 9) do (for!> z (0 1 9) do
(progn
(setq wc (sconst!> x y z))
(cond (wc
(setq w (cons
(fndfpr!> (list 'quotient wc 2)
(dfprod2!> (getel1!> !#!A!Y!M y)
(getel1!> !#!A!Y!M z))) w)))))))
(putel1!> (evalform!> (dfsum!> w)) !#!F!F!Y!M x)))
(return t)))
% First YM equation ...
(de firstym!> nil
(prog (w wc)
(makebox!> '!#!Y!M!F!q)
(for!> x (0 1 9) do (progn
(setq w (ncons (dex!> (dual!> (getel1!> !#!F!F!Y!M x)))))
(for!> y (0 1 9) do (for!> z (0 1 9) do
(progn
(setq wc (sconst!> x y z))
(cond (wc
(setq w (cons
(fndfpr!> wc (dfprod2!>
(getel1!> !#!A!Y!M y)
(dual!>(getel1!> !#!F!F!Y!M z)))) w)))))))
(putel1!> (equation!> (evalform!> (dfsum!> w)) nil) !#!Y!M!F!q x)))
(return t)))
% Second YM equation ...
(de secondym!> nil
(prog (w wc)
(makebox!> '!#!Y!M!S!q)
(for!> x (0 1 9) do (progn
(setq w (ncons (dex!> (getel1!> !#!F!F!Y!M x))))
(for!> y (0 1 9) do (for!> z (0 1 9) do
(progn
(setq wc (sconst!> x y z))
(cond (wc
(setq w (cons
(fndfpr!> wc (dfprod2!>
(getel1!> !#!A!Y!M y)
(getel1!> !#!F!F!Y!M z))) w)))))))
(putel1!> (equation!> (evalform!> (dfsum!> w)) nil) !#!Y!M!S!q x)))
(return t)))
% YMACT = -1/8/pi FFYM/\*FFYM
(de ymact!> nil
(prog (w)
(for!> x (0 1 9) do (progn
(setq w (cons (dfprod2!> (getel1!> !#!F!F!Y!M x)
(dual!> (getel1!> !#!F!F!Y!M x))) w))))
(setq w (evalform!>
(fndfpr!> '(quotient (minus 1) (times 8 pi))
(dfsum!> w))))
(setq !#!Y!M!A!C!T (ncons w))))
% FFYM = 1/2 FTYM.a.b S'a'b
(de ffymfromftym!> nil
(prog (w)
(makebox!> '!#!F!F!Y!M)
(for!> x (0 1 9) do (progn
(setq w nil)
(fordim!> a do (fordim!> b do (cond ((lessp a b)
(setq w (cons (fndfpr!> (getel!> !#!F!T!Y!M (list x a b))
(getel2!> !#!S a b)) w))))))
(putel1!> (evalform!> (dfsum!> w)) !#!F!F!Y!M x)))))
% FTYM.a.b = D.b _| D.a _| FFYM
(de ftymfromffym!> nil
(prog nil
(makebox!> '!#!F!T!Y!M)
(for!> x (0 1 9) do
(fordim!> a do (fordim!> b do (cond ((lessp a b)
(putel!> (evalalg!>
(vform1!> (getiframe!> b)
(vform!> (getiframe!> a) (getel1!> !#!F!F!Y!M x))))
!#!F!T!Y!M (list3 x a b)))))))
(return t)))
% TYM
(de tymbydef!> nil
(prog (w wr)
(setq !#!T!Y!M (mkt!> 2))
(setq w (list 'times -1 ![sigprod!] (car ![sgn!])
(duald!> (car !#!Y!M!A!C!T))))
(fordim!> a do (fordim!> b do (cond ((leq a b)
(setq wr (ncons (list 'times (getmetr!> a b) w)))
(fordim!> m do (for!> x (0 1 9) do
(setq wr (cons (list 'times -1
(list 'quotient (car ![sgn!]) '(times 4 pi))
(getm!> '!#!F!T!Y!M nil (list3 x a m) '(nil nil nil))
(getm!> '!#!F!T!Y!M nil (list3 x b m) '(nil nil 1)))
wr))))
(putel!> (evalalg!> (cons 'plus wr)) !#!T!Y!M (list2 a b))))))))
%---------- EM field. 09.96 -----------------------------------------------
% FF = d A
(de fffroma!> nil
(setq !#!F!F (ncons (evalform!> (dex!> (car !#!A))))))
% FF = 1/2 FT.a.b S'a'b
(de fffromft!> nil
(prog (w)
(fordim!> a do (fordim!> b do (cond ((lessp a b)
(setq w (cons (fndfpr!> (getel2!> !#!F!T a b)
(getel2!> !#!S a b)) w))))))
(setq !#!F!F (ncons (evalform!> (dfsum!> w))))))
% FT.a.b = D.b _| D.a _| FF
(de ftfromff!> nil
(prog nil
(setq !#!F!T (mkt!> 2))
(fordim!> a do (fordim!> b do (cond ((lessp a b)
(putel!> (evalalg!>
(vform1!> (getiframe!> b)
(vform!> (getiframe!> a) (car !#!F!F))))
!#!F!T (list2 a b))))))
(return t)))
% EMACT = -1/8/pi FF/\*FF
(de emact!> nil
(setq !#!E!M!A!C!T (ncons (evalform!>
(fndfpr!> '(quotient (minus 1) (times 8 pi))
(dfprod2!> (car !#!F!F) (dual!> (car !#!F!F))))))))
% TEM
(de tembydef!> nil
(prog (w wr)
(setq !#!T!E!M (mkt!> 2))
(setq w (list 'times -1 ![sigprod!] (car ![sgn!])
(duald!> (car !#!E!M!A!C!T))))
(fordim!> a do (fordim!> b do (cond ((leq a b)
(setq wr (ncons (list 'times (getmetr!> a b) w)))
(fordim!> m do
(setq wr (cons (list 'times -1
(list 'quotient (car ![sgn!]) '(times 4 pi))
(getasy2!> !#!F!T a m nil)
(getm!> '!#!F!T nil (list2 b m) '(nil 1)))
wr)))
(putel!> (evalalg!> (cons 'plus wr)) !#!T!E!M (list2 a b))))))))
% d # FF = # J
(de firstmw!> nil
(setq !#!M!W!F!q (ncons
(equation!> (evalform!> (dex!> (dual!> (car !#!F!F))))
(cond
((not !#!J) nil)
(t (evalform!> (fndfpr!> (list 'times 4 'pi (car ![sgn!])
(list 'expt -1
(difference ![dim!] 2)))
(dual!> (car !#!J))))))
))))
% d FF = 0
(de secondmw!> nil
(setq !#!M!W!S!q (ncons
(equation!> (evalform!> (dex!> (car !#!F!F))) nil))))
% d # J =0
(de contineq!> nil
(setq !#!C!O!q (ncons
(equation!> (evalform!> (dex!> (dual!> (car !#!J)))) nil))))
% First scalar ...
(de firstscal!> nil
(setq !#!S!C!F (ncons (evalalg!> (chsigna!> (duald!>
(dfprod2!> (car !#!F!F) (dual!> (car !#!F!F)))))))))
% Second scalar ...
(de secondscal!> nil
(setq !#!S!C!S (ncons (evalalg!> (duald!>
(dfprod2!> (car !#!F!F) (car !#!F!F)))))))
% FFU = FF - i #FF
(de ffufromff!> nil
(setq !#!F!F!U (ncons (evalform!>
(dfsum2!> (car !#!F!F)
(fndfpr!> '(minus i) (dual!> (car !#!F!F))))))))
% FFU = 2 FIU_AB SU^AB
(de ffufromfiu!> nil
(setq !#!F!F!U (ncons (evalform!> (fndfpr!> 2 (dfsum!> (list
(fndfpr!> (getel1!> !#!F!I!U 0) (getel1!> !#!S!U 2))
(fndfpr!> (getel1!> !#!F!I!U 2) (getel1!> !#!S!U 0))
(fndfpr!> -2 (fndfpr!> (getel1!> !#!F!I!U 1) (getel1!> !#!S!U 1))))))))))
% FF= 1/2 (FFU + ~FFU)
(de fffromffu!> nil
(setq !#!F!F (ncons (evalform!> (fndfpr!> '(quotient 1 2)
(dfsum2!> (car !#!F!F!U) (coform!> (car !#!F!F!U))))))))
% FIU_AB = -i/2 # ( FFU/\SU_AB )
(de fiufromffu!> nil
(prog nil
(makebox!> '!#!F!I!U)
(for!> a (0 1 2) do
(putel1!> (evalalg!> (list 'times '(quotient (minus i) 2)
(duald!>
(dfprod2!> (car !#!F!F!U)
(getel1!> !#!S!U a)))))
!#!F!I!U a ))))
% FIU_AB = -i # ( FF/\SU_AB )
(de fiufromff!> nil
(prog nil
(makebox!> '!#!F!I!U)
(for!> a (0 1 2) do
(putel1!> (evalalg!> (list 'times '(minus i)
(duald!>
(dfprod2!> (car !#!F!F)
(getel1!> !#!S!U a)))))
!#!F!I!U a ))))
% SCU = 2 FIU_AB FIU^AB
(de scufromfiu!> nil
(setq !#!S!C!U (ncons (evalalg!> (list 'times 4 (list 'plus
(list 'times (getel1!> !#!F!I!U 2) (getel1!> !#!F!I!U 0))
(list 'times -1 (getel1!> !#!F!I!U 1) (getel1!> !#!F!I!U 1)) ))))))
% SCU = -i/2 #( FFU/\FFU )
(de scufromffu!> nil
(setq !#!S!C!U (ncons (evalalg!> (list 'times '(quotient (minus i) 2)
(duald!> (dfprod2!> (car !#!F!F!U) (car !#!F!F!U))))))))
% TEMS.AA.BB
(de tems!> nil
(prog nil
(makebox!> '!#!T!E!M!S)
(for!> a (0 1 2) do (for!> b (0 1 2) do (cond ((leq a b)
(putel!> (evalalg!> (list 'times '(quotient 1 (times 2 pi))
(getel1!> !#!F!I!U a)
(coalg!> (getel1!> !#!F!I!U b))))
!#!T!E!M!S (list2 a b))))))))
% d FFU = i #J
(de complexmw!> nil
(setq !#!M!W!U!q (ncons
(equation!> (evalform!> (dex!> (car !#!F!F!U)))
(cond
((not !#!J) nil)
(t (evalform!> (fndfpr!> (list 'times -4 'i 'pi
(car ![sgn!]))
(dual!> (car !#!J))))))
))))
% FIU/\SD_AA = 0
(de sduality!> nil
(prog nil
(makebox!> '!#!S!D!q)
(for!> a (0 1 2) do
(putel1!> (equation!> (evalform!>
(dfprod2!> (car !#!F!F!U)
(getel1!> !#!S!D a))) nil)
!#!S!D!q a))))
%---------- Scalar field. 01.91, 09.96 ------------------------------------
% Scalar field action (minimal interaction) ...
(de sactmin!> nil
(prog (w wr wss)
(setq w (car !#!F!I))
(fordim!> a do (fordim!> b do
(setq wr (cons (list 'times (dfisign!>)
(list 'df w (x!> a))
(list 'df w (x!> b))
(gimetr!> a b)) wr))))
(setq wr (cons (list 'times '(expt !S!M!A!S!S 2) w w) wr))
(setq wr (cons 'plus wr))
(setq !#!S!A!C!T!M!I!N (ncons (evalform!>
(fndfpr!> '(quotient -1 2) (fndfpr!> wr (car !#!V!O!L))))))
(return t)))
(de dfisign!> nil
(cond ((lessp (car ![sgn!]) 0) 1 )
(t -1 )))
% Scalar field action ...
(de sact!> nil
(prog (w wr wss)
(setq w (car !#!F!I))
(fordim!> a do (fordim!> b do
(setq wr (cons (list 'times (dfisign!>)
(list 'df w (x!> a))
(list 'df w (x!> a))
(gimetr!> a b)) wr))))
(setq wr (cons (list 'times '(expt !S!M!A!S!S 2) w w) wr))
(cond (!*nonmin
(setq wr (cons (list 'times (car !#!A!C!O!N!S!T)
(car !#!R!R)
w w ) wr))))
(setq wr (cons 'plus wr))
(setq !#!S!A!C!T (ncons (evalform!>
(fndfpr!> '(quotient -1 2) (fndfpr!> wr (car !#!V!O!L))))))
(return t)))
% Scalar field equation ...
(de kgeq!> nil
(prog (w wf)
(setq wf (car !#!F!I))
(setq w (list 'plus
(list 'times (dfisign!>) ![sigprod!] (list 'expt -1 ![dim1!])
(duald!> (dex!> (dual!> (dfun!> wf)))) )
(list 'times -1 wf (list 'plus '(expt !S!M!A!S!S 2)
(cond (!*nonmin (list 'times
(car !#!A!C!O!N!S!T)
(car !#!R!R)))
(t 0)))) ))
(setq !#!S!C!q (ncons (equation!> (evalalg!> w) nil)))
(return t)))
% Scalar energy-momentum tensor (minimal interaction) ...
(de tsclmin!> nil
(prog (w)
(setq !#!T!S!C!L!M!I!N (mkt!> 2))
(setq w (duald!> (car !#!S!A!C!T!M!I!N)))
(setq w (evalalg!> (list 'times -1 ![sigprod!] (car ![sgn!]) w)))
(fordim!> wa do (fordim!> wb do
(cond ((leq wa wb)
(putel!> (evalalg!> (list 'plus
(list 'times (vfun!> (getiframe!> wa) (car !#!F!I))
(vfun!> (getiframe!> wb) (car !#!F!I)))
(list 'times (getmetr!> wa wb) w)))
!#!T!S!C!L!M!I!N (list2 wa wb))))))
(return t)))
%---------- Dirac field. 12.90, 9.96 ------------------------------------
% Current 1-form from Dirac spinor ...
(de dcurr!> nil
(progn
(setq !#!J (ncons (evalform!>
(fndfpr!> (list 'times (mp!> 1) '(sqrt 2) '!E!C!O!N!S!T)
(dfsum!> (list2 (spintetr!> !#!C!H!I)
(spintetr!> !#!P!H!I) ))))))
t))
(de spintetr!> (wss)
(dfsum!> (list
(fndfpr!> (getel1!> wss 0)
(fndfpr!> (coalg!>(getel1!> wss 0)) (getframe!> 1)))
(fndfpr!> (getel1!> wss 1)
(fndfpr!> (coalg!>(getel1!> wss 1)) (getframe!> 0)))
(fndfpr!> (getel1!> wss 0)
(fndfpr!> (coalg!>(getel1!> wss 1)) (getframe!> 3)))
(fndfpr!> (getel1!> wss 1)
(fndfpr!> (coalg!>(getel1!> wss 0)) (getframe!> 2))) )))
% Covariant derivative with ieA and 1/2 Q terms ...
% wi - index, wss - spinor, bool=t - 1/2 Q term must be included
% wc=t +i for phi and wc=nil -i for chi
(de dexcs!> (wi wss bool wc)
(prog (w)
(setq w (list (dfun!>(getel1!> wss wi))
(chsign!> t (fndfpr!> (getel1!> wss 0)
(pmf!>(getel1!> !#!o!m!e!g!a!u (add1 wi)))))
(fndfpr!> (getel1!> wss 1)
(pmf!>(getel1!> !#!o!m!e!g!a!u wi)))))
(cond (!#!A
(setq w (cons (fndfpr!> (list 'times '!E!C!O!N!S!T
(cond (wc 'i) (t '(minus i))))
(fndfpr!> (getel1!> wss wi) (car !#!A))) w))))
(cond ((and bool !*torsion)
(setq w (cons (fndfpr!> '(quotient -1 2)
(fndfpr!> (getel1!> wss wi) (car !#!Q!Q))) w))))
(return(dfsum!> w))))
% Dirac equation ...
(de dequ!> (wa wb we wc)
(prog nil
(set we (mkbox!> we))
(for!> a (0 1 1) do
(putel1!> (equation!>
(evalalg!> (list 'plus
(list 'times '(sqrt 2) (mpa!> 'i) (dfcs!> a wa wc))
(list 'times '(minus !D!M!A!S!S) (coalg!>(getel1!> wb a)))))
nil)
(eval we) a))
(return t)))
(de dfcs!> (wi wss wc)
(list 'plus (vform1!> (getiframe!> (cond ((eqn wi 0) 2) (t 0)))
(dexcs!> 0 wss t wc))
(vform1!> (getiframe!> (cond ((eqn wi 0) 1) (t 3)))
(chsign!> t (dexcs!> 1 wss t wc)))))
% Dirac action 4-form ...
(de dact!> nil
(prog (www)
(setq www (list
(fndfpr!> '(quotient i (sqrt 2)) (sdstetr!> !#!P!H!I t))
(fndfpr!> '(quotient (minus i) (sqrt 2)) (sdstetr!> !#!C!H!I nil))
(fndfpr!> '(minus !D!M!A!S!S)
(fndfpr!> (scaldir!>) (car !#!V!O!L))) ))
(setq www (append www (mapcar www (function coform!>))))
(setq !#!D!A!C!T (ncons(evalform!>(dfsum!> www))))
(return t)))
(de sdstetr!> (wss wc)
(dfsum!> (list
(dfprod2!> (dual!>(dexcs!> 0 wss nil wc))
(fndfpr!> (coalg!>(getel1!> wss 0)) (getframe!> 1)))
(dfprod2!> (dual!>(dexcs!> 1 wss nil wc))
(fndfpr!>(coalg!>(getel1!> wss 1)) (getframe!> 0)))
(dfprod2!> (dual!>(dexcs!> 0 wss nil wc))
(fndfpr!>(coalg!>(getel1!> wss 1)) (getframe!> 3)))
(dfprod2!> (dual!>(dexcs!> 1 wss nil wc))
(fndfpr!>(coalg!>(getel1!> wss 0)) (getframe!> 2))) )))
(de scaldir!> nil
(list 'plus
(list 'times (getel1!> !#!P!H!I 0) (getel1!> !#!C!H!I 1))
(list 'times -1 (getel1!> !#!P!H!I 1) (getel1!> !#!C!H!I 0))))
% Dirac spin 3-form ...
(de spinsd!> nil
(prog (w)
(setq !#!S!P!D!I!U (mkbox!> '!#!S!P!D!I!U))
(setq w '(quotient i (sqrt 8)))
(putel1!> (evalform!> (fndfpr!> w (dual!> (dfsum!> (list
(sst!> !#!P!H!I 0 1 0 nil)
(sst!> !#!P!H!I 0 0 2 nil)
(sst!> !#!C!H!I 0 1 0 t)
(sst!> !#!C!H!I 0 0 2 t))))))
!#!S!P!D!I!U 0)
(putel1!> (evalform!> (fndfpr!> w (dual!>
(fndfpr!> '(quotient 1 2) (dfsum!> (list
(sst!> !#!P!H!I 1 1 0 nil)
(sst!> !#!P!H!I 1 0 2 nil)
(sst!> !#!C!H!I 1 1 0 t)
(sst!> !#!C!H!I 1 0 2 t)
(sst!> !#!P!H!I 0 1 3 t)
(sst!> !#!P!H!I 0 0 1 t)
(sst!> !#!C!H!I 0 1 3 nil)
(sst!> !#!C!H!I 0 0 1 nil)))))))
!#!S!P!D!I!U 1)
(putel1!> (evalform!> (fndfpr!> w (dual!> (dfsum!> (list
(sst!> !#!P!H!I 1 1 3 t)
(sst!> !#!P!H!I 1 0 1 t)
(sst!> !#!C!H!I 1 1 3 nil)
(sst!> !#!C!H!I 1 0 1 nil))))))
!#!S!P!D!I!U 2)))
(de sst!> (wss wa wb wt bool)
(prog (w)
(setq w
(fndfpr!> (getel1!> wss wa)
(fndfpr!> (coalg!>(getel1!> wss wb)) (getframe!> wt))))
(return (cond (bool w) (t (chsign!> t w))))))
% Dirac energy-momentum tensor ...
(de tdi!> nil
(prog (w wa)
(setq !#!T!D!I (mkt!> 2))
(setq w (mkt!> 1))
(for!> a (0 1 3) do
(putel1!>
(dfsum!> (list
(chsign!> t (vform!> (getiframe!> a) (car !#!D!A!C!T)))
(pmf!>(ddss!> !#!P!H!I a t t))
(pmf!>(coform!> (ddss!> !#!P!H!I (ccin!> a) t t)))
(pmf!>(ddss!> !#!C!H!I a nil nil))
(pmf!>(coform!> (ddss!> !#!C!H!I (ccin!> a) nil nil)))))
w a))
(cond
(!*torsion
(for!> a (0 1 3) do (for!> b (0 1 3) do
(progn
(setq wa (dfprod2!> (getlo!> !#!T b) (getel1!> w a)))
(putel!> (evalalg!> (duald!> (pmf!> wa)))
!#!T!D!I (list2 a b))))) )
(t(for!> a (0 1 3) do (for!> b (0 1 3) do
(cond ((leq a b) (progn
(setq wa nil)
(setq wa (cons (dfprod2!> (getlo!> !#!T b) (getel1!> w a)) wa))
(setq wa (cons (dfprod2!> (getlo!> !#!T a) (getel1!> w b)) wa))
(putel!> (evalalg!> (duald!> (fndfpr!> '(quotient -1 2)
(mpf!> (dfsum!> wa)))))
!#!T!D!I (list2 a b))))))) ))
(return t)))
(de ddss!> (wss wa bool wc)
(prog (w)
(setq w (cond
((eqn wa 0) (fndfpr!> (coalg!>(getel1!> wss 1))
(dexcs!> 1 wss nil wc)))
((eqn wa 1) (fndfpr!> (coalg!>(getel1!> wss 0))
(dexcs!> 0 wss nil wc)))
((eqn wa 2) (fndfpr!> (coalg!>(getel1!> wss 0))
(dexcs!> 1 wss nil wc)))
((eqn wa 3) (fndfpr!> (coalg!>(getel1!> wss 1))
(dexcs!> 0 wss nil wc)))))
(setq w (fndfpr!> (mpa!> '(quotient i (sqrt 2)))
(dual!> w)))
(return (cond (bool w) (t (chsign!> t w))))))
(de ccin!> (w)
(cond ((eqn w 2) 3)
((eqn w 3) 2)
(t w)))
%---- Total Energy-Momentun and Spin. 10.96 -------------------------------
(de tenmom!> nil
(prog (w wc wr wss)
(makebox!> '!#!T!E!N!M!O!M)
(fordim!> a do (fordim!> b do (cond ((leq a b)
(setq w ![tlst!])
(setq wr nil)
(while!> w
(setq wc (eval(car w)))
(setq wss (get (car w) '!=sidxl))
(cond (wc (setq wr (cons (getelsyc!> wc wss a b) wr))))
(setq w (cdr w)))
(cond (wr (putel!> (evalalg!> (cons 'plus wr))
!#!T!E!N!M!O!M (list2 a b))))
))))))
(de getelsyc!> (w wss wa wb)
(cond (wss (getel2!> w wa wb))
(t (list 'times '(quotient 1 2)
(list 'plus (getel2!> w wa wb)
(getel2!> w wb wa))))))
(de spinu!> nil
(prog (w wc wr)
(makebox!> '!#!S!P!I!N!U)
(for!> a (0 1 2) do (progn
(setq w ![slst!])
(setq wr nil)
(while!> w
(setq wc (eval(car w)))
(cond (wc (setq wr (cons (getel1!> wc a) wr))))
(setq w (cdr w)))
(cond (wr (putel1!> (evalform!> (dfsum!> wr))
!#!S!P!I!N!U a)))
))))
(de tenmomt!> nil
(prog (w)
(fordim!> m do
(setq w (cons (getm!> '!#!T!E!N!M!O!M nil (list2 m m) '(1 nil)) w)))
(setq !#!T!E!N!M!O!M!T (ncons (evalalg!> (cond (w (cons 'plus w))
(t nil)))))))
(de tenmoms!> nil
(prog nil
(makebox!> '!#!T!E!N!M!O!M!S)
(putel!> (tenmomc!> 1 1) !#!T!E!N!M!O!M!S (list2 0 0))
(putel!> (tenmomc!> 1 3) !#!T!E!N!M!O!M!S (list2 0 1))
(putel!> (tenmomc!> 3 3) !#!T!E!N!M!O!M!S (list2 0 2))
(putel!> (tenmomc!> 0 1) !#!T!E!N!M!O!M!S (list2 1 1))
(putel!> (tenmomc!> 0 3) !#!T!E!N!M!O!M!S (list2 1 2))
(putel!> (tenmomc!> 0 0) !#!T!E!N!M!O!M!S (list2 2 2))
))
(de tenmomc!> (wa wb)
(evalalg!> (list 'plus (getel2s!> !#!T!E!N!M!O!M wa wb)
(list 'times '(quotient -1 4) (getmetr!> wa wb)
(car !#!T!E!N!M!O!M!T)))))
%----- Ideal Fluid. 10.96 -------------------------------------------------
(de tfli!> nil
(prog (w)
(setq !#!T!I!F!L (mkt!> 2))
(fordim!> a do (fordim!> b do (cond ((leq a b)
(setq w (tfli0!> a b))
(putel!> (evalalg!> w) !#!T!I!F!L (list2 a b))))))))
(de tfli0!> (a b)
(list 'plus (list 'times -1 (car !#!P!R!E!S) (car !#!U!S!Q)
(getmetr!> a b))
(list 'times (list 'plus (car !#!E!N!E!R) (car !#!P!R!E!S))
(getloa!> !#!U!U a) (getloa!> !#!U!U b))))
%----- Spin Fluid. 11.96 --------------------------------------------------
(de spfl!> nil
(prog (w)
(fordim!> a do (fordim!> b do (cond ((lessp a b)
(setq w (cons (fndfpr!> (getel2!> !#!S!P!F!L!T a b)
(getel2!> !#!S a b)) w))))))
(setq !#!S!P!F!L (ncons (evalform!> (dfsum!> w))))))
(de spflt!> nil
(prog nil
(setq !#!S!P!F!L!T (mkt!> 2))
(fordim!> a do (fordim!> b do (cond ((leq a b)
(putel!> (evalalg!> (vform1!> (getiframe!> b)
(vform!> (getiframe!> a)
(car !#!S!P!F!L))))
!#!S!P!F!L!T (list2 a b))))))))
(de frenkel!> nil
(prog (w)
(setq w (evalform!> (vform!> (car !#!U!V) (car !#!S!P!F!L))))
(cond (w (msg!> 6702)))
(setq !#!F!C!o (ncons (equation!> w nil)))))
(de spflu!> nil
(prog (w)
(fordim!> a do
(setq w (cons (fndfpr!> (getloa!> !#!U!U a) (getframe!> a)) w)))
(setq w (evalform!> (dual!> (dfsum!> w))))
(makebox!> '!#!S!P!F!L!U)
(putel1!> (evalform!>
(fndfpr!> (getel2!> !#!S!P!F!L!T 1 3) w))
!#!S!P!F!L!U 0)
(putel1!> (evalform!> (fndfpr!> '(quotient 1 2) (fndfpr!>
(list 'difference (getel2!> !#!S!P!F!L!T 2 3)
(getel2!> !#!S!P!F!L!T 0 1)) w)))
!#!S!P!F!L!U 1)
(putel1!> (evalform!>
(chsign!> t (fndfpr!> (getel2!> !#!S!P!F!L!T 0 2) w)))
!#!S!P!F!L!U 2)
))
(de tsfluid!> nil
(progn
(setq !#!T!S!F!L (mkt!> 2))
(cond (!*torsion (tsfluidq!>))
(t (tsfluidq0!>)))))
(de tsfluidq0!> nil
(prog (w)
(fordim!> a do (fordim!> b do (cond ((leq a b)
(setq w (list 'plus (tfli0!> a b) (sdeltq0!> a b)))
(putel!> (evalalg!> w) !#!T!S!F!L (list2 a b))))))))
(de spin3!> (a b c)
(multa!> (getloa!> !#!U!U a) (getasy2!> !#!S!P!F!L!T b c nil)))
(de spin2!> (b c)
(getasy2!> !#!S!P!F!L!T b c nil))
(de dspin3!> (a b c d)
(prog (w)
(setq w (ncons (chsign!> t (dfun!> (spin3!> b c d)))))
(fordim!> m do
(setq w (append w (list
(fndfpr!> (spin3!> m c d) (getel2!> !#!o!m!e!g!a m b))
(fndfpr!> (spin3!> b m d) (getel2!> !#!o!m!e!g!a m c))
(fndfpr!> (spin3!> b c m) (getel2!> !#!o!m!e!g!a m d)) ))))
(setq w (dfsum!> w))
(return (evalalg!> (vform1!> (getiframe!> a) w)))))
(de projq0!> (a b)
(list 'plus (getimetr!> a b)
(list 'quotient (multa!> (getel1!> !#!U!U a)
(getel1!> !#!U!U b))
(car !#!U!S!Q))))
(de sdeltq0!> (a b)
(prog (w)
(fordim!> c do (fordim!> d do
(setq w (cons (list 'times (projq0!> c d)
(list 'plus (dspin3!> c a b d)
(dspin3!> c b a d))) w))))
(return (cons 'plus w))))
(de tsfluidq!> nil
(prog (w)
(fordim!> a do (fordim!> b do (progn
(setq w (list 'plus (tfli0!> a b) (sdeltq!> a b)))
(putel!> (evalalg!> w) !#!T!S!F!L (list2 a b)))))))
(de sdeltq!> (a b)
(prog (w)
(fordim!> d do
(setq w (cons (list 'times
(list 'quotient -2 (car !#!U!S!Q))
(getloa!> !#!U!U a)
(getel1!> !#!U!U d)
(dspin2!> b d)) w)))
(return (cons 'plus w))))
(de dspin2!> (a b)
(prog (w)
(setq w (ncons (chsign!> t (dfun!> (spin2!> a b)))))
(fordim!> m do
(setq w (append w (list
(fndfpr!> (spin2!> m b) (getel2!> !#!o!m!e!g!a m a))
(fndfpr!> (spin2!> a m) (getel2!> !#!o!m!e!g!a m b)) ))))
(setq w (dfsum!> w))
(return (evalalg!> (vform1!> (car !#!U!V) w)))))
%========= End of GRGmater.sl =============================================%