... common verbs ...

```NB. ... script experimentalV00.ijs ...

zfaV17XX=:[cfFN4(sin@cx1;  cos@cx1;-@sin@cx1;-@cos@cx1;sin@cx1;_"_),:cx1XX
zfaV18XX=:[cfFN4(cos@cx1;-@sin@cx1;-@cos@cx1;  sin@cx1;cos@cx1;_"_),:cx1XX
zfaV19XX=:[cfFN4(sin@cx2;  cos@cx2;-@sin@cx2;-@cos@cx2;sin@cx2;_"_),:cx2XX
zfaV20XX=:[cfFN4(cos@cx2;-@sin@cx2;-@cos@cx2;  sin@cx2;cos@cx2;_"_),:cx2XX
```

... functions of the x coordinates ...

```NB. ... script experimentalV00.ijs ...

zfy0=:cx0*sin@cx1*cos@cx2
zfy1=:cx0*sin@cx1*sin@cx2
zfy2=:cx0*cos@cx1
zfy3=:cx3

zfyc=:zfy0,zfy1,zfy2,zfy3
```

... 4th partial derivatives of functions of the x coordinates (for 4 dimensional spacetime) ...

```NB. ... script experimentalV00.ijs ...

zfy0x0=:                   [cfMP4 zfaV17XX,:zfaV20XX
zfy0x1=:[cfMP4      cx0XX,:[cfMP4 zfaV18XX,:zfaV20XX
zfy0x2=:[cfMP4 -&.>@cx0XX,:[cfMP4 zfaV17XX,:zfaV19XX
zfy0x3=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfy0XX=:<@:>"1@(0|:])@(zfy0x0,zfy0x1,zfy0x2,:zfy0x3)
```

```NB. ... script experimentalV00.ijs ...

zfy1x0=:              [cfMP4 zfaV17XX,:zfaV19XX
zfy1x1=:[cfMP4 cx0XX,:[cfMP4 zfaV18XX,:zfaV19XX
zfy1x2=:[cfMP4 cx0XX,:[cfMP4 zfaV17XX,:zfaV20XX
zfy1x3=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfy1XX=:<@:>"1@(0|:])@(zfy1x0,zfy1x1,zfy1x2,:zfy1x3)
```

```NB. ... script experimentalV00.ijs ...

zfy2x0=:                   zfaV18XX
zfy2x1=:[cfMP4 -&.>@cx0XX,:zfaV17XX
zfy2x2=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfy2x3=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfy2XX=:<@:>"1@(0|:])@(zfy2x0,zfy2x1,zfy2x2,:zfy2x3)
```

```NB. ... script experimentalV00.ijs ...

zfy3x0=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfy3x1=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfy3x2=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfy3x3=:1;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfy3XX=:<@:>"1@(0|:])@(zfy3x0,zfy3x1,zfy3x2,:zfy3x3)
```

... prefix the y coordinates (make them available) ...

```NB. ... script experimentalV00.ijs ...

zfyXXS=:zfyc;}:@:(<@:>"1)@(0|:])@(zfy0XX,zfy1XX,zfy2XX,:zfy3XX)
```

... common verbs ...

```NB. ... script experimentalV00.ijs ...

zfaV06=:cy0^2:
zfaV07=:cy1^2:
zfaV08=:cy2^2:

zfaV06XX=:(cy0^2:);((2*cy0),0,0,0:);(         2 0 0 0,3 4\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfaV07XX=:(cy1^2:);(0,(2*cy1),0,0:);((1 4\$0:),0 2 0 0,2 4\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfaV08XX=:(cy2^2:);(0,0,(2*cy2),0:);((2 4\$0:),0 0 2 0,1 4\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
```

```NB. ... script experimentalV00.ijs ...

zfaV09=:(cy0^2:)+(cy1^2:)+cy2^2:

zfaV09XX=:zfaV06XX+&.>zfaV07XX+&.>zfaV08XX
```

```NB. ... script experimentalV00.ijs ...

zfaV10=:zfaV09^0.5"_

zfaV09U0=:                                  zfaV09^0.5"_
zfaV09U1=:                              0.5*zfaV09^0.5+_1:
zfaV09U2=:                    (0.5+_1:)*0.5*zfaV09^0.5+_2:
zfaV09U3=:          (0.5+_2:)*(0.5+_1:)*0.5*zfaV09^0.5+_3:
zfaV09U4=:(0.5+_3:)*(0.5+_2:)*(0.5+_1:)*0.5*zfaV09^0.5+_4:

zfaV10XX=:[cfFN4(zfaV09U0;zfaV09U1;zfaV09U2;zfaV09U3;zfaV09U4;_"_),:zfaV09XX
```

```NB. ... script experimentalV00.ijs ...

zfaV11=:zfaV10^_1:

zfaV10U0=:            zfaV10^_1:
zfaV10U1=:         _1*zfaV10^_2:
zfaV10U2=:      _2*_1*zfaV10^_3:
zfaV10U3=:   _3*_2*_1*zfaV10^_4:
zfaV10U4=:_4*_3*_2*_1*zfaV10^_5:

zfaV11XX=:[cfFN4(zfaV10U0;zfaV10U1;zfaV10U2;zfaV10U3;zfaV10U4;_"_),:zfaV10XX
```

```NB. ... script experimentalV00.ijs ...

zfaV12=:zfaV09^_1:

zfaV09xU0=:            zfaV09^_1:
zfaV09xU1=:         _1*zfaV09^_2:
zfaV09xU2=:      _2*_1*zfaV09^_3:
zfaV09xU3=:   _3*_2*_1*zfaV09^_4:
zfaV09xU4=:_4*_3*_2*_1*zfaV09^_5:

zfaV12XX=:[cfFN4(zfaV09xU0;zfaV09xU1;zfaV09xU2;zfaV09xU3;zfaV09xU4;_"_),:zfaV09XX
```

```NB. ... script experimentalV00.ijs ...

zfaV13=:(cy0^2:)+cy1^2:

zfaV13XX=:zfaV06XX+&.>zfaV07XX
```

```NB. ... script experimentalV00.ijs ...

zfaV14=:zfaV13^0.5"_

zfaV13U0=:                                  zfaV13^0.5"_
zfaV13U1=:                              0.5*zfaV13^0.5+_1:
zfaV13U2=:                    (0.5+_1:)*0.5*zfaV13^0.5+_2:
zfaV13U3=:          (0.5+_2:)*(0.5+_1:)*0.5*zfaV13^0.5+_3:
zfaV13U4=:(0.5+_3:)*(0.5+_2:)*(0.5+_1:)*0.5*zfaV13^0.5+_4:

zfaV14XX=:[cfFN4(zfaV13U0;zfaV13U1;zfaV13U2;zfaV13U3;zfaV13U4;_"_),:zfaV13XX
```

```NB. ... script experimentalV00.ijs ...

zfaV15=:zfaV14^_1:

zfaV14U0=:            zfaV14^_1:
zfaV14U1=:         _1*zfaV14^_2:
zfaV14U2=:      _2*_1*zfaV14^_3:
zfaV14U3=:   _3*_2*_1*zfaV14^_4:
zfaV14U4=:_4*_3*_2*_1*zfaV14^_5:

zfaV15XX=:[cfFN4(zfaV14U0;zfaV14U1;zfaV14U2;zfaV14U3;zfaV14U4;_"_),:zfaV14XX
```

```NB. ... script experimentalV00.ijs ...

zfaV16=:zfaV13^_1:

zfaV13xU0=:            zfaV13^_1:
zfaV13xU1=:         _1*zfaV13^_2:
zfaV13xU2=:      _2*_1*zfaV13^_3:
zfaV13xU3=:   _3*_2*_1*zfaV13^_4:
zfaV13xU4=:_4*_3*_2*_1*zfaV13^_5:

zfaV16XX=:[cfFN4(zfaV13xU0;zfaV13xU1;zfaV13xU2;zfaV13xU3;zfaV13xU4;_"_),:zfaV13XX
```

... functions of the y coordinates ...

```NB. ... script experimentalV00.ijs ...

zfx0=:((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_
zfx1=:arctan@(cy2,((cy0^2:)+cy1^2:)^0.5"_)
zfx2=:arctan@(cy0,cy1)
zfx3=:cy3

zfxc=:zfx0,zfx1,zfx2,zfx3
```

... 4th partial derivatives of functions of the y coordinates (for 4 dimensional spacetime) ...

```NB. ... script experimentalV00.ijs ...

zfx0y0=:[cfMP4 cy0XX,:zfaV11XX
zfx0y1=:[cfMP4 cy1XX,:zfaV11XX
zfx0y2=:[cfMP4 cy2XX,:zfaV11XX
zfx0y3=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfx0XX=:<@:>"1@(0|:])@(zfx0y0,zfx0y1,zfx0y2,:zfx0y3)
```

```NB. ... script experimentalV00.ijs ...

zfx1y0=:[cfMP4 cy2XX,:[cfMP4 zfaV12XX,:[cfMP4 cy0XX,:zfaV15XX
zfx1y1=:[cfMP4 cy2XX,:[cfMP4 zfaV12XX,:[cfMP4 cy1XX,:zfaV15XX
zfx1y2=:[cfMP4 -&.>@zfaV12XX,:zfaV14XX
zfx1y3=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfx1XX=:<@:>"1@(0|:])@(zfx1y0,zfx1y1,zfx1y2,:zfx1y3)
```

```NB. ... script experimentalV00.ijs ...

zfx2y0=:[cfMP4 -&.>@cy1XX,:zfaV16XX
zfx2y1=:[cfMP4      cy0XX,:zfaV16XX
zfx2y2=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfx2y3=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfx2XX=:<@:>"1@(0|:])@(zfx2y0,zfx2y1,zfx2y2,:zfx2y3)
```

```NB. ... script experimentalV00.ijs ...

zfx3y0=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfx3y1=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfx3y2=:0;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_
zfx3y3=:1;((1\$4:)\$0:);((2\$4:)\$0:);((3\$4:)\$0:);((4\$4:)\$0:);_"_

zfx3XX=:<@:>"1@(0|:])@(zfx3y0,zfx3y1,zfx3y2,:zfx3y3)
```

... prefix the x coordinates (make them available) ...

```NB. ... script experimentalV00.ijs ...

zfxXXS=:zfxc;}:@:(<@:>"1)@(0|:])@(zfx0XX,zfx1XX,zfx2XX,:zfx3XX)
```

```NB. ... script experimentalV00.ijs ...

zfyXX=:<@:>"1@(0|:])@:(zfyXXS"_ 1)
zfxXX=:<@:>"1@(0|:])@:(zfxXXS"_ 1)
```