# Essays/Tensor Experiments/TensorExperiments04

```NB. ... script experimental.ijs ...

y0=:cx0*sin@cx1*cos@(cx2+gXw*cx3)
y1=:cx0*sin@cx1*sin@(cx2+gXw*cx3)
y2=:cx0*cos@cx1
y3=:cx3

yc=:(y0,y1,y2,y3)"_ 1
```

```NB. ... script experimental.ijs ...

fq3VXX=:cx3;(0,0,0,1:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);(5\$4:)\$0:
```

```NB. ... script experimental.ijs ...

fq2VXX=:cx2;(0,0,1,0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);(5\$4:)\$0:

fq2WXX=:(gXw*cx3);(0,0,0,gXw );((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);(5\$4:)\$0:
fq2PXX=:<@(+/)@:>"1@(0|:])@(fq2VXX,:fq2WXX)
```

```NB. ... script experimental.ijs ...

fq2VOO=:cx2+gXw*cx3
fq2SXX=:[cfFN5(sin@fq2VOO;  cos@fq2VOO;-@sin@fq2VOO;-@cos@fq2VOO;sin@fq2VOO;  cos@fq2VOO),:fq2PXX
fq2CXX=:[cfFN5(cos@fq2VOO;-@sin@fq2VOO;-@cos@fq2VOO;  sin@fq2VOO;cos@fq2VOO;-@sin@fq2VOO),:fq2PXX
```

```NB. ... script experimental.ijs ...

fq1VXX=:cx1;(0,1,0,0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);(5\$4:)\$0:

fq1SXX=:[cfFN5(sin@cx1;  cos@cx1;-@sin@cx1;-@cos@cx1;sin@cx1;  cos@cx1),:fq1VXX
fq1CXX=:[cfFN5(cos@cx1;-@sin@cx1;-@cos@cx1;  sin@cx1;cos@cx1;-@sin@cx1),:fq1VXX
```

```NB. ... script experimental.ijs ...

fq1S2SXX=:[cfMP5 fq1SXX,:fq2SXX
fq1S2CXX=:[cfMP5 fq1SXX,:fq2CXX
```

```NB. ... script experimental.ijs ...

fq0VXX=:cx0;(1,0,0,0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);(5\$4:)\$0:
```

```NB. ... script experimental.ijs ...

y0XX=:[cfMP5 fq0VXX,:fq1S2CXX
y1XX=:[cfMP5 fq0VXX,:fq1S2SXX
y2XX=:[cfMP5 fq0VXX,:fq1CXX
y3XX=:fq3VXX

yXXS=:<@:>"1@(0|:])@(y0XX,y1XX,y2XX,:y3XX)

yXX=:<@:>"1@(0|:])@:(yXXS"_ 1)
```

```NB. ... script experimental.ijs ...

x0=:((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_
x1=:arctan@(cy2,((cy0^2:)+cy1^2:)^0.5"_)
x2=:arctan@(cy0,cy1)+-@(gXw*cy3)
x3=:cy3

xc=:(x0,x1,x2,x3)"_ 1
```

```NB. ... script experimental.ijs ...

fsqA=:(cy0^2:)+(cy1^2:)+cy2^2:

fsqAy0=:2*cy0
fsqAy1=:2*cy1
fsqAy2=:2*cy2
fsqAy3=:0:

fsqAy0y0=:2:
fsqAy1y1=:2:
fsqAy2y2=:2:

fsqA00=:>@(0{]);([fsqAy0y0>@(0{]))`(<"1@aVn2@(0 0"_))`(>@(1{]))}
fsqA11=:>@(0{]);([fsqAy1y1>@(0{]))`(<"1@aVn2@(1 1"_))`(>@(1{]))}
fsqA22=:>@(0{]);([fsqAy2y2>@(0{]))`(<"1@aVn2@(2 2"_))`(>@(1{]))}

```

```NB. ... script experimental.ijs ...

fsqApow=:0.5"_

fsqAU0=:                                                                fsqA^fsqApow
fsqAU1=:                                                        fsqApow*fsqA^fsqApow+_1:
fsqAU2=:                                          (fsqApow+_1:)*fsqApow*fsqA^fsqApow+_2:
fsqAU3=:                            (fsqApow+_2:)*(fsqApow+_1:)*fsqApow*fsqA^fsqApow+_3:
fsqAU4=:              (fsqApow+_3:)*(fsqApow+_2:)*(fsqApow+_1:)*fsqApow*fsqA^fsqApow+_4:
fsqAU5=:(fsqApow+_4:)*(fsqApow+_3:)*(fsqApow+_2:)*(fsqApow+_1:)*fsqApow*fsqA^fsqApow+_5:

x0XX=:[cfFN5(fsqAU0;fsqAU1;fsqAU2;fsqAU3;fsqAU4;fsqAU5),:fsqAXX
```

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

gXcw  =: 0  0  _  _  _"_
gXpAll=: 0  0  0  0  0"_

yCpts=:__ 0.5 5 8,__ 0.5 5 8,__ 0.5 5 8,:_ 0 20 8"_

x0dy        =:cfXX1@x0XX
x0dydy      =:cfXX2@x0XX
x0dydydy    =:cfXX3@x0XX
x0dydydydy  =:cfXX4@x0XX
x0dydydydydy=:cfXX5@x0XX

(gXT(x0dy"_ 1        (((2^_44);2^_22)qteq[;])"1(0|:[:(gXT x0        ])D.1])"_ 1)]) ((0;50"_)pTRandom 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

(gXT(x0dydy"_ 1      (((2^_44);2^_21)qteq[;])"2(0|:[:(gXT x0dy      ])D.1])"_ 1)]) ((0;50"_)pTRandom 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

(gXT(x0dydydy"_ 1    (((2^_44);2^_16)qteq[;])"3(0|:[:(gXT x0dydy    ])D.1])"_ 1)]) ((0;50"_)pTRandom 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

(gXT(x0dydydydy"_ 1  (((2^_44);2^_16)qteq[;])"4(0|:[:(gXT x0dydydy  ])D.1])"_ 1)]) ((0;50"_)pTRandom 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

(gXT(x0dydydydydy"_ 1(((2^_44);2^_13)qteq[;])"5(0|:[:(gXT x0dydydydy])D.1])"_ 1)]) ((0;50"_)pTRandom 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
```