User:Tom Allen/TensorExperimentsZ06

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GTEZ0600C.jpg


NB. ... script experimentalZ.ijs ...

J3=:+/"1@((<0 1)|:])"5@R

J1cv=:+/"1@((<0 2)|:])"3@(mcn([smx 0|:])"2 3 J3)

J1cn=:mcn smx"2 1 J1cv

J1cncv=:mcn([smx 0|:])"2 B2kEMr2+SBkEMr2


NB. ... execute (ijx) ...

   gXcw  =:  1.2  0    _  _    _    _"_
   gXbAll=: _0.6  3.5  3  1.3  1.2  0"_

   xCpts=:_ 1 3 27,_ 0 1p1 27,_ 0 2p1 27,:_ 0 2 27"_

NB. ... xRef ...

NB. ... a tensor ...

   vA =:[J3 xRef
   vB0=:((0|:[)smx])"2 3
   vB1=:((0|:[)smx])"2 3
   vB2=:((0|:[)smx])"2 3
   vB =:[(zdx vB2 zdx vB1 zdx vB0 J3)zRef

   A=:(gXZ([vA hkxM)]) ((0.1;50"_)pTRandom xCpts)''
   B=:(gXZ([vB hkxM)]) ((0.1;50"_)pTRandom xCpts)''

   A (((2^_35);2^_42)qteq[;])"3 B
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. ...

   A=:(gXZ([J3 xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''

NB. ... EM ...

   *./^:3"3 (0=]) ((2^_44)qtsz]) (]+0|:])"2 (0 1|:])"3 A
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. ... Maxwell's equation ...

   *./^:3"3 (0=]) ((2^_39)qtsz]) (]+(0|:])+0 1|:])"3 A
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. ... zRef ...

NB. ... a tensor ...

   vA =:[J3 zRef
   vB0=:((0|:[)smx])"2 3
   vB1=:((0|:[)smx])"2 3
   vB2=:((0|:[)smx])"2 3
   vB =:[(xdz vB2 xdz vB1 xdz vB0 J3)xRef

   A=:(gXZ([vA hkxM)]) ((0.1;50"_)pTRandom xCpts)''
   B=:(gXZ([vB hkxM)]) ((0.1;50"_)pTRandom xCpts)''

   A (((2^_37);2^_43)qteq[;])"3 B
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. ...

   B=:(gXZ([J3 zRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''

NB. ... EM ...

   *./^:3"3 (0=]) ((2^_38)qtsz]) (]+0|:])"2 (0 1|:])"3 B
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. ... Maxwell's equation ...

   *./^:3"3 (0=]) ((2^_38)qtsz]) (]+(0|:])+0 1|:])"3 B
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. ... sum of 2 ...

   A=:(gXZ([J1cv             xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''
   B=:(gXZ([(B2kEMr1+SBkEMr1)xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''

   A -:"1 B
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. ... a tensor ...

   vA=:[J1cn xRef
   vB=:[(xdz smx"2 1 J1cn)zRef

   A=:(gXZ([vA hkxM)]) ((0.1;50"_)pTRandom xCpts)''
   B=:(gXZ([vB hkxM)]) ((0.1;50"_)pTRandom xCpts)''

   A (((2^_38);2^_43)qteq[;])"1 B
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. ... a tensor ...

   vA=:[J1cn zRef
   vB=:[(zdx smx"2 1 J1cn)xRef

   A=:(gXZ([vA hkxM)]) ((0.1;50"_)pTRandom xCpts)''
   B=:(gXZ([vB hkxM)]) ((0.1;50"_)pTRandom xCpts)''

   A (((2^_44);2^_39)qteq[;])"1 B
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


GTEZ0601C.jpg


NB. ... script experimentalZ.ijs ...

F  =:+/"1@((<0 1)|:])"4@B2k
Fdc=:+/"1@((<0 1)|:])"5@B2kdc

JBt0=:                                 Fdc
JBt1=:-@(  1|:])"3@(Gam([smx 0|:])"3 2 F  )
JBt2=:-@(0 1|:])"3@(Gam([smx    ])"3 2 F  )
JB  =:JBt0+JBt1+JBt2


NB. ... execute (ijx) ...

   gXcw  =:  1.2  0    _  _    _    _"_
   gXbAll=: _0.6  3.5  3  1.3  1.2  0"_

   xCpts=:_ 1 3 27,_ 0 1p1 27,_ 0 2p1 27,:_ 0 2 27"_

NB. ... skew symmetry ...

   *./^:2"2 (0=]) ((2^_44)qtsz]) (]+0|:])"2 (gXZ([F xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''
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. ... derivative of F ...

   A=:(gXZ([Fdc xRef@hkxM)])                             ((0.1;50"_)pTRandom xCpts)''
   B=:(gXZ(0|:[:(gXZ([(0{])@F xRef@hkxM),:@])D.1])"_ 1]) ((0.1;50"_)pTRandom xCpts)''

   A (((2^_16);2^_16)qteq[;])"3 B
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. ... JB ...

   (gXZ([(JB(((2^_44);2^_44)qteq[;])"3+/"1@((<0 1)|:])"5@B2kcv)xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''
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


GTEZ0602C.jpg


NB. ... script experimentalZ.ijs ...

JSB=:+/"1@((<0 1)|:])"5@:((0 1 4|:])"5)@(S smx"3 4 B2k)


NB. ... execute (ijx) ...

   gXcw  =:  1.2  0    _  _    _    _"_
   gXbAll=: _0.6  3.5  3  1.3  1.2  0"_

   xCpts=:_ 1 3 27,_ 0 1p1 27,_ 0 2p1 27,:_ 0 2 27"_

NB. ... skew symmetry ...

   *./^:3"3 (0=]) (]+0|:])"2 (0 1|:])"3 (gXZ([JSB xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''
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. ... J=JB+JSB ...

   (gXZ([(J3(((2^_44);2^_44)qteq[;])"3 JB+JSB)xRef@hkxM)]) ((0.1;50"_)pTRandom xCpts)''
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


GTEZ0603C.jpg



Download: File:LTEZ0600C.txt
Download: File:LTEZ0601C.txt
Download: File:LTEZ0602C.txt
Download: File:LTEZ0603C.txt




Download MoinMoin source: File:TensorExperimentsZ06.ijs