Essays/Torsion Tensor/TorsionTensor04
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NB. ... script torsiontensor.ijs ... B2kt1=: (0 3 1|:])"4@Gamdx B2kt2=: -@(0 1 3|:])"4@Gamdx B2kt3=:Gam (0 2 1|:])@([smx 0|:])"3 3 Gam B2kt4=:Gam-@(0 1 2|:])@([smx 0|:])"3 3 Gam B2k =:B2kt1+B2kt2+B2kt3+B2kt4 B2kdxt1=: (0 3 1 4|:])"5@Gamdxdx B2kdxt2=: -@(0 1 3 4|:])"5@Gamdxdx B2kdxt3=:Gam (0 2 1 4|:])@(( [)smx 0|:])"3 4 Gamdx B2kdxt4=:Gamdx (0 3 1 2|:])@((2|:[)smx 0|:])"4 3 Gam B2kdxt5=:Gam -@(0 1 2 4|:])@(( [)smx 0|:])"3 4 Gamdx B2kdxt6=:Gamdx-@(0 1 3 2|:])@((2|:[)smx 0|:])"4 3 Gam B2kdx =:B2kdxt1+B2kdxt2+B2kdxt3+B2kdxt4+B2kdxt5+B2kdxt6
NB. ... execute (ijx) ...
gXcme =:( 1.5 0.45 0.754 )"_
gXpAll=:( 6 _1.4 1.7 )"_
gXqAll=:( 1 1 _1 )"_
gXwAll=:( 1.25 _ _ )"_
yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_
NB. ... B2k is a tensor ...
B2kBox=:([B2k hkAx);xcdy;([(0|:])"2@:ycdx xfromy);[B2k hkAy
B2kChk=:[(>@(0{])(((2^_43);2^_41)qteq[;])"4>@(1{])smx"2 4>@(2{])([smx"2 4[smx"2 4 smx"2 4)>@(3{]))B2kBox
(gXT B2kChk]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... derivatives ...
(gXT(([B2kdx hkAy)(((2^_15);2^_12)qteq[;])"5(0|:[:(gXT([B2k hkAy)])D.1])"_ 1)]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... script torsiontensor.ijs ... B2kcvt1=: ( 0|:])@((0|:[)smx 0|:]) B2kcvt2=:-@(0 3 4 1|:])@(( [)smx 1|:]) B2kcvt3=:-@( 0 4 1|:])@(( [)smx 2|:]) B2kcvt4=:-@( 0 1|:])@(( [)smx ]) B2kcv =:B2kdx+Gam(B2kcvt1+B2kcvt2+B2kcvt3+B2kcvt4)"3 4 B2k
NB. ... execute (ijx) ...
gXcme =:( 1.5 0.45 0.754 )"_
gXpAll=:( 6 _1.4 1.7 )"_
gXqAll=:( 1 1 _1 )"_
gXwAll=:( 1.25 _ _ )"_
yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_
NB. ... B2kcv is a tensor ...
B2kcvBox=:([B2kcv hkAx);xcdy;([(0|:])"2@:ycdx xfromy);[B2kcv hkAy
B2kcvChk=:[(>@(0{])(((2^_37);2^_36)qteq[;])"5>@(1{])smx"2 5>@(2{])([smx"2 5[smx"2 5[smx"2 5 smx"2 5)>@(3{]))B2kcvBox
(gXT B2kcvChk]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... script torsiontensor.ijs ... NB. ... utility verb ... BB2kcv=:B2kcv+S(0 1 4|:])@smx"3 4 B2k
NB. ... execute (ijx) ...
gXcme =:( 1.5 0.45 0.754 )"_
gXpAll=:( 6 _1.4 1.7 )"_
gXqAll=:( 1 1 _1 )"_
gXwAll=:( 1.25 _ _ )"_
yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_
NB. ... utility verb BB2kcv is a tensor ...
BB2kcvBox=:([BB2kcv hkAx);xcdy;([(0|:])"2@:ycdx xfromy);[BB2kcv hkAy
BB2kcvChk=:[(>@(0{])(((2^_37);2^_36)qteq[;])"5>@(1{])smx"2 5>@(2{])([smx"2 5[smx"2 5[smx"2 5 smx"2 5)>@(3{]))BB2kcvBox
(gXT BB2kcvChk]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... Bianchi Identity ...
*./^:5"5 (0=]) ((2^_36)qtsz]) (gXT([(]+(2|:])+2 3|:])"5@BB2kcv hkAy)]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
*./^:5"5 (0=]) ((2^_37)qtsz]) (gXT([(]+(2|:])+2 3|:])"5@BB2kcv hkAx)]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... script torsiontensor.ijs ... Fcv=:+/"1@((<0 1)|:])"5@BB2kcv
NB. ... execute (ijx) ...
gXcme =:( 1.5 0.45 0.754 )"_
gXpAll=:( 6 _1.4 1.7 )"_
gXqAll=:( 1 1 _1 )"_
gXwAll=:( 1.25 _ _ )"_
yCpts=:0.3 2 50,(0.1,(1p1-0.1),28),0 2p1 50,:1 8 50"_
NB. ... Maxwell's equation ...
*./^:3"3 (0=]) ((2^_36)qtsz]) (gXT([(]+(0|:])+0 1|:])"3@Fcv hkAy)]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
*./^:3"3 (0=]) ((2^_37)qtsz]) (gXT([(]+(0|:])+0 1|:])"3@Fcv hkAx)]) (50 yCrandom yCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... example ...
NB.
NB. ... Fcv in frame of reference which is not rotating ...
NB. ... Fcv in frame of reference which is rotating ...
(gXT(([((2^_36)qtsz])@Fcv hkAy),:[((2^_37)qtsz])@Fcv hkAx)]) (1 yCrandom yCpts)''
0 0 0 0
0 0 0 0
0 0 0 0
252.997 0 0 9874.99
0 0 0 0
0 0 0 0
0 0 0 0
0 48.987 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 40.8337 0
_252.997 0 0 _9874.99
0 _48.987 0 0
0 0 _40.8337 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
252.997 0 0 9874.99
0 0 0 0
0 0 0 0
0 0 0 0
0 48.987 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 40.8337 51.0421
_252.997 0 0 _9874.99
0 _48.987 0 0
0 0 _40.8337 _51.0421
0 0 0 0
Download: File:LTT0400C.txt
Download: File:LTT0401C.txt
Download: File:LTT0402C.txt
Download: File:LTT0403C.txt
Download MoinMoin source: File:TorsionTensor04.ijs
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Contributed by Tom Allen