Essays/SpaceTime2D/SpaceTime2D04

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3 Derivatives (continued)

GST0400C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

qcdv=:(([qcdy ycC)([gXsmx 0|:])"2 2 xcdv)"1


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

   p4aUd1=.0.25;0.25;2;11.62;1
   p4aUd2=.0 0.646447 30,:0 2p1 100

   p4a1d1=.p4aUd1 qcdv vGen(p4aUd2)
   p4a1d2=.p4aUd1(0|:[:(p4aUd1([qc ycC)])D.1])"1 vGen(p4aUd2)
   p4a1d1((2^_13)gXteq[;])p4a1d2
1
   (p4a1d1=.0),p4a1d2=.0
0 0


GST0401C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

qcdvdvt1  =:(([qcdy   ycC)([     gXsmx 0|:])"2 3 xcdvdv)"1
qcdvdvt2p0=:(([qcdydy ycC)([     gXsmx 0|:])"3 2 xcdv  )"1
qcdvdvt2  =:(qcdvdvt2p0   ((1|:[)gXsmx 0|:])"3 2 xcdv  )"1

qcdvdv    =:(qcdvdvt1+qcdvdvt2)"1


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

   p4aVd1=.0.25;0.25;2;11.62;1
   p4aVd2=.0 0.646447 30,:0 2p1 100

   p4a2d1=.p4aVd1 qcdvdv vGen(p4aVd2)
   p4a2d2=.p4aVd1(0|:[:(p4aVd1 qcdv])D.1])"1 vGen(p4aVd2)
   p4a2d1((2^_11)gXteq[;])p4a2d2
1
   (p4a2d1=.0),p4a2d2=.0
0 0


GST0402C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

qcdvdvdvt1  =:(([qcdy   ycC)                      ([     gXsmx 0|:])"2 4 xcdvdvdv)"1
qcdvdvdvt2p0=:(([qcdydy ycC)                      ([     gXsmx 0|:])"3 2 xcdv)"1
qcdvdvdvt2  =:(qcdvdvdvt2p0   ((1|:])+(1 3|:])+])@((1|:[)gXsmx 0|:])"3 3 xcdvdv)"1
qcdvdvdvt3p0=:(([qcdydydy ycC)                    ([     gXsmx 0|:])"4 2 xcdv)"1
qcdvdvdvt3p1=:(qcdvdvdvt3p0                       ((1|:[)gXsmx 0|:])"4 2 xcdv)"1
qcdvdvdvt3  =:(qcdvdvdvt3p1                       ((1|:[)gXsmx 0|:])"4 2 xcdv)"1

qcdvdvdv    =:(qcdvdvdvt1+qcdvdvdvt2+qcdvdvdvt3)"1


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

   p4aWd1=.0.25;0.25;2;11.62;1
   p4aWd2=.0 0.646447 30,:0 2p1 100

   p4a3d1=.p4aWd1 qcdvdvdv vGen(p4aWd2)
   p4a3d2=.p4aWd1(0|:[:(p4aWd1 qcdvdv])D.1])"1 vGen(p4aWd2)
   ((2^_16)&gXtsz p4a3d1)((2^_7)gXteq[;])((2^_16)&gXtsz p4a3d2)
1
   (p4a3d1=.0),p4a3d2=.0
0 0


GST0403C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

tRqcdvdvdvdvt2=:(1|:])+(1 4|:])+(1 3 4|:])+]
tRqcdvdvdvdvt3=:]+(2 4|:])+2|:]
tRqcdvdvdvdvt4=:(2 1|:])+(2 4 1|:])+(2|:])+(2 1 4|:])+(2 4|:])+]

qcdvdvdvdvt1  =:(([qcdy ycC)                      ([     gXsmx 0|:])"2 5 xcdvdvdvdv)"1
qcdvdvdvdvt2p0=:(([qcdydy ycC)                    ([     gXsmx 0|:])"3 2 xcdv)"1
qcdvdvdvdvt2  =:(qcdvdvdvdvt2p0    tRqcdvdvdvdvt2@((1|:[)gXsmx 0|:])"3 4 xcdvdvdv)"1
qcdvdvdvdvt3p0=:(([qcdydy ycC)                    ([     gXsmx 0|:])"3 3 xcdvdv)"1
qcdvdvdvdvt3  =:(qcdvdvdvdvt3p0    tRqcdvdvdvdvt3@((1|:[)gXsmx 0|:])"4 3 xcdvdv)"1
qcdvdvdvdvt4p0=:(([qcdydydy ycC)                  ([     gXsmx 0|:])"4 2 xcdv)"1
qcdvdvdvdvt4p1=:(qcdvdvdvdvt4p0                   ((1|:[)gXsmx 0|:])"4 2 xcdv)"1
qcdvdvdvdvt4  =:(qcdvdvdvdvt4p1    tRqcdvdvdvdvt4@((1|:[)gXsmx 0|:])"4 3 xcdvdv)"1
qcdvdvdvdvt5p0=:(([qcdydydydy ycC)                ([     gXsmx 0|:])"5 2 xcdv)"1
qcdvdvdvdvt5p1=:(qcdvdvdvdvt5p0                   ((1|:[)gXsmx 0|:])"5 2 xcdv)"1
qcdvdvdvdvt5p2=:(qcdvdvdvdvt5p1                   ((1|:[)gXsmx 0|:])"5 2 xcdv)"1
qcdvdvdvdvt5  =:(qcdvdvdvdvt5p2                   ((1|:[)gXsmx 0|:])"5 2 xcdv)"1

qcdvdvdvdv    =:(qcdvdvdvdvt1+qcdvdvdvdvt2+qcdvdvdvdvt3+qcdvdvdvdvt4+qcdvdvdvdvt5)"1


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

   p4aXd1=.0.25;0.25;2;11.62;1
   p4aXd2=.0 0.646447 30,:0 2p1 100

   p4a4d1=.p4aXd1 qcdvdvdvdv vGen(p4aXd2)
   p4a4d2=.p4aXd1(0|:[:(p4aXd1 qcdvdvdv])D.1])"1 vGen(p4aXd2)
   ((2^_12)&gXtsz p4a4d1)((2^_7)gXteq[;])((2^_12)&gXtsz p4a4d2)
1
   (p4a4d1=.0),p4a4d2=.0
0 0


GST0404C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

tR1=:   ((gXa0*(gXb0^1:)*bSj2D1@(gXb0*cq1))*(2^0:)*+@cos@(2*cq2))"1
tR2=:   ((gXa0*(gXb0^0:)*bSj2D0@(gXb0*cq1))*(2^1:)*-@sin@(2*cq2))"1

tR11=:  ((gXa0*(gXb0^2:)*bSj2D2@(gXb0*cq1))*(2^0:)*+@cos@(2*cq2))"1
tR12=:  ((gXa0*(gXb0^1:)*bSj2D1@(gXb0*cq1))*(2^1:)*-@sin@(2*cq2))"1
tR22=:  ((gXa0*(gXb0^0:)*bSj2D0@(gXb0*cq1))*(2^2:)*-@cos@(2*cq2))"1

tR111=: ((gXa0*(gXb0^3:)*bSj2D3@(gXb0*cq1))*(2^0:)*+@cos@(2*cq2))"1
tR112=: ((gXa0*(gXb0^2:)*bSj2D2@(gXb0*cq1))*(2^1:)*-@sin@(2*cq2))"1
tR122=: ((gXa0*(gXb0^1:)*bSj2D1@(gXb0*cq1))*(2^2:)*-@cos@(2*cq2))"1
tR222=: ((gXa0*(gXb0^0:)*bSj2D0@(gXb0*cq1))*(2^3:)*+@sin@(2*cq2))"1

tR1111=:((gXa0*(gXb0^4:)*bSj2D4@(gXb0*cq1))*(2^0:)*+@cos@(2*cq2))"1
tR1112=:((gXa0*(gXb0^3:)*bSj2D3@(gXb0*cq1))*(2^1:)*-@sin@(2*cq2))"1
tR1122=:((gXa0*(gXb0^2:)*bSj2D2@(gXb0*cq1))*(2^2:)*-@cos@(2*cq2))"1
tR1222=:((gXa0*(gXb0^1:)*bSj2D1@(gXb0*cq1))*(2^3:)*+@sin@(2*cq2))"1
tR2222=:((gXa0*(gXb0^0:)*bSj2D0@(gXb0*cq1))*(2^4:)*+@cos@(2*cq2))"1

NB. ...

tq1=:tR1
tq2=:tR2

tdq=:(tq1,tq2)"1

NB. ...

tq1q1=:tR11
tq1q2=:tR12
tq2q1=:tR12
tq2q2=:tR22

tdqdq=:((tq1q1,tq1q2),:tq2q1,tq2q2)"1

NB. ...

tq1q1q1=:tR111
tq1q1q2=:tR112
tq1q2q1=:tR112
tq1q2q2=:tR122

tq2q1q1=:tR112
tq2q1q2=:tR122
tq2q2q1=:tR122
tq2q2q2=:tR222

tdqdqdqp1=:(tq1q1q1,tq1q1q2),:tq1q2q1,tq1q2q2
tdqdqdqp2=:(tq2q1q1,tq2q1q2),:tq2q2q1,tq2q2q2
tdqdqdq  =:(tdqdqdqp1,:tdqdqdqp2)"1

NB. ...

tq1q1q1q1=:tR1111
tq1q1q1q2=:tR1112
tq1q1q2q1=:tR1112
tq1q1q2q2=:tR1122

tq1q2q1q1=:tR1112
tq1q2q1q2=:tR1122
tq1q2q2q1=:tR1122
tq1q2q2q2=:tR1222


tq2q1q1q1=:tR1112
tq2q1q1q2=:tR1122
tq2q1q2q1=:tR1122
tq2q1q2q2=:tR1222

tq2q2q1q1=:tR1122
tq2q2q1q2=:tR1222
tq2q2q2q1=:tR1222
tq2q2q2q2=:tR2222

tdqdqdqdqp1=:(tq1q1q1q1,tq1q1q1q2),:tq1q1q2q1,tq1q1q2q2
tdqdqdqdqp2=:(tq1q2q1q1,tq1q2q1q2),:tq1q2q2q1,tq1q2q2q2
tdqdqdqdqp3=:(tq2q1q1q1,tq2q1q1q2),:tq2q1q2q1,tq2q1q2q2
tdqdqdqdqp4=:(tq2q2q1q1,tq2q2q1q2),:tq2q2q2q1,tq2q2q2q2
tdqdqdqdq  =:((tdqdqdqdqp1,:tdqdqdqdqp2),:tdqdqdqdqp3,:tdqdqdqdqp4)"1


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

   p4bUd1=.0.25;0.25;2;11.62;1
   p4bUd2=.0 0.646447 30,:0 2p1 100

   p4b1d1=.p4bUd1([tdq qcC)vGen(p4bUd2)
   p4b1d2=.p4bUd1([:(p4bUd1 t])D.1 qcC)"1 vGen(p4bUd2)
   p4b1d1((2^_10)gXteq[;])p4b1d2
1
   (p4b1d1=.0),p4b1d2=.0
0 0

   p4b2d1=.p4bUd1([tdqdq qcC)vGen(p4bUd2)
   p4b2d2=.p4bUd1(0|:[:(p4bUd1 tdq])D.1 qcC)"1 vGen(p4bUd2)
   ((2^_19)&gXtsz p4b2d1)((2^_10)gXteq[;])((2^_19)&gXtsz p4b2d2)
1
   (p4b2d1=.0),p4b2d2=.0
0 0

   p4b3d1=.p4bUd1([tdqdqdq qcC)vGen(p4bUd2)
   p4b3d2=.p4bUd1(0|:[:(p4bUd1 tdqdq])D.1 qcC)"1 vGen(p4bUd2)
   ((2^_15)&gXtsz p4b3d1)((2^_10)gXteq[;])((2^_15)&gXtsz p4b3d2)
1
   (p4b3d1=.0),p4b3d2=.0
0 0

   p4b4d1=.p4bUd1([tdqdqdqdq qcC)vGen(p4bUd2)
   p4b4d2=.p4bUd1(0|:[:(p4bUd1 tdqdqdq])D.1 qcC)"1 vGen(p4bUd2)
   ((2^_12)&gXtsz p4b4d1)((2^_5)gXteq[;])((2^_12)&gXtsz p4b4d2)
1
   (p4b4d1=.0),p4b4d2=.0
0 0


GST0405C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

tdv=:(([tdq qcC)([gXsmx 0|:])"1 2 qcdv)"1


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

   p4cUd1=.0.25;0.25;2;11.62;1
   p4cUd2=.0 0.646447 30,:0 2p1 100

   p4c1d1=.p4cUd1 tdv vGen(p4cUd2)
   p4c1d2=.p4cUd1([:(p4cUd1([t qcC)])D.1])"1 vGen(p4cUd2)
   p4c1d1((2^_9)gXteq[;])p4c1d2
1
   (p4c1d1=.0),p4c1d2=.0
0 0


GST0406C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

tdvdvt1  =:(([tdq qcC)   ([     gXsmx 0|:])"1 3 qcdvdv)"1
tdvdvt2p0=:(([tdqdq qcC) ([     gXsmx 0|:])"2 2 qcdv)"1
tdvdvt2  =:(tdvdvt2p0    ((0|:[)gXsmx 0|:])"2 2 qcdv)"1

tdvdv    =:(tdvdvt1+tdvdvt2)"1


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

   p4cVd1=.0.25;0.25;2;11.62;1
   p4cVd2=.0 0.646447 30,:0 2p1 100

   p4c2d1=.p4cVd1 tdvdv vGen(p4cVd2)
   p4c2d2=.p4cVd1(0|:[:(p4cVd1 tdv])D.1])"1 vGen(p4cVd2)
   p4c2d1((2^_8)gXteq[;])p4c2d2
1
   (p4c2d1=.0),p4c2d2=.0
0 0


GST0407C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

tdvdvdvt1  =:(([tdq qcC)                         ([     gXsmx 0|:])"1 4 qcdvdvdv)"1
tdvdvdvt2p0=:(([tdqdq qcC)                       ([     gXsmx 0|:])"2 2 qcdv)"1
tdvdvdvt2  =:(tdvdvdvt2p0    ((0|:])+(0 2|:])+])@((0|:[)gXsmx 0|:])"2 3 qcdvdv)"1
tdvdvdvt3p0=:(([tdqdqdq qcC)                     ([     gXsmx 0|:])"3 2 qcdv)"1
tdvdvdvt3p1=:(tdvdvdvt3p0                        ((0|:[)gXsmx 0|:])"3 2 qcdv)"1
tdvdvdvt3  =:(tdvdvdvt3p1                        ((0|:[)gXsmx 0|:])"3 2 qcdv)"1

tdvdvdv    =:(tdvdvdvt1+tdvdvdvt2+tdvdvdvt3)"1


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

   p4cWd1=.0.25;0.25;2;11.62;1
   p4cWd2=.0 0.646447 30,:0 2p1 100

   p4c3d1=.p4cWd1 tdvdvdv vGen(p4cWd2)
   p4c3d2=.p4cWd1(0|:[:(p4cWd1 tdvdv])D.1])"1 vGen(p4cWd2)
   ((2^_11)&gXtsz p4c3d1)((2^_8)gXteq[;])((2^_11)&gXtsz p4c3d2)
1
   (p4c3d1=.0),p4c3d2=.0
0 0


GST0408C.jpg


NB. ... script SpaceTime2D.ijs (continued) ...

tRtdvdvdvdvt2=:(0|:])+(0 3|:])+(0 2 3|:])+]
tRtdvdvdvdvt3=:]+(1 3|:])+1|:]
tRtdvdvdvdvt4=:(1 0|:])+(1 3 0|:])+(1|:])+(1 0 3|:])+(1 3|:])+]

tdvdvdvdvt1  =:(([tdq qcC)                     ([     gXsmx 0|:])"1 5 qcdvdvdvdv)"1
tdvdvdvdvt2p0=:(([tdqdq qcC)                   ([     gXsmx 0|:])"2 2 qcdv)"1
tdvdvdvdvt2  =:(tdvdvdvdvt2p0    tRtdvdvdvdvt2@((0|:[)gXsmx 0|:])"2 4 qcdvdvdv)"1
tdvdvdvdvt3p0=:(([tdqdq qcC)                   ([     gXsmx 0|:])"2 3 qcdvdv)"1
tdvdvdvdvt3  =:(tdvdvdvdvt3p0    tRtdvdvdvdvt3@((0|:[)gXsmx 0|:])"3 3 qcdvdv)"1
tdvdvdvdvt4p0=:(([tdqdqdq qcC)                 ([     gXsmx 0|:])"3 2 qcdv)"1
tdvdvdvdvt4p1=:(tdvdvdvdvt4p0                  ((0|:[)gXsmx 0|:])"3 2 qcdv)"1
tdvdvdvdvt4  =:(tdvdvdvdvt4p1    tRtdvdvdvdvt4@((0|:[)gXsmx 0|:])"3 3 qcdvdv)"1
tdvdvdvdvt5p0=:(([tdqdqdqdq qcC)               ([     gXsmx 0|:])"4 2 qcdv)"1
tdvdvdvdvt5p1=:(tdvdvdvdvt5p0                  ((0|:[)gXsmx 0|:])"4 2 qcdv)"1
tdvdvdvdvt5p2=:(tdvdvdvdvt5p1                  ((0|:[)gXsmx 0|:])"4 2 qcdv)"1
tdvdvdvdvt5  =:(tdvdvdvdvt5p2                  ((0|:[)gXsmx 0|:])"4 2 qcdv)"1

tdvdvdvdv    =:(tdvdvdvdvt1+tdvdvdvdvt2+tdvdvdvdvt3+tdvdvdvdvt4+tdvdvdvdvt5)"1


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

   p4cXd1=.0.25;0.25;2;11.62;1
   p4cXd2=.0 0.646447 30,:0 2p1 100

   p4c4d1=.p4cXd1 tdvdvdvdv vGen(p4cXd2)
   p4c4d2=.p4cXd1(0|:[:(p4cXd1 tdvdvdv])D.1])"1 vGen(p4cXd2)
   p4c4d1((2^_6)gXteq[;])p4c4d2
1
   (p4c4d1=.0),p4c4d2=.0
0 0



Download: File:LST0400C.txt
Download: File:LST0401C.txt
Download: File:LST0402C.txt
Download: File:LST0403C.txt
Download: File:LST0404C.txt
Download: File:LST0405C.txt
Download: File:LST0406C.txt
Download: File:LST0407C.txt
Download: File:LST0408C.txt




Download MoinMoin source: File:SpaceTime2D04.ijs




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Contributed by Tom Allen