Essays/Christoffel/Christoffel03

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10 J Session

10.1 Coordinates
NB. ... execute (ijx) ...

   (ypgen-:cyy@cxx@ypgen)''
1

   (xpgen-:cxx@cyy@xpgen)''
1


10.2 Sums
GCH0300C.jpg


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

   +/@:((=@i.@#-:axs@((1;dxdy),0;dydx))"1) xpgen''
8000


GCH0301C.jpg


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

   +/@:((=@i.@#-:axs@((1;dydx),0;dxdy))"1) xpgen''
8000


GCH0302C.jpg


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

   +/@:((=@i.@#-:axs@((1;h20),1;h02))"1) xpgen''
8000


GCH0303C.jpg


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

   +/@:((=@i.@#-:axs@((1;h02),1;h20))"1) xpgen''
8000


GCH0304C.jpg


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

   s0t1p0=:axs@((0;dydx),1;g20@cyy)
   +/@:((h20-:axs@((0;dydx),1;s0t1p0))"1) xpgen''
8000


GCH0305C.jpg


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

   s0t1p0=:axs@((0;dxdy),1;h20)
   +/@:((g20@cyy-:axs@((0;dxdy),1;s0t1p0))"1) xpgen''
8000


GCH0306C.jpg


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

   s0t1p0=:axs@((1;dxdy),1;g02@cyy)
   +/@:((h02-:axs@((1;dxdy),1;s0t1p0))"1) xpgen''
8000


GCH0307C.jpg


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

   s0t1p0=:axs@((1;dydx),1;h02)
   +/@:((g02@cyy-:axs@((1;dydx),1;s0t1p0))"1) xpgen''
8000


GCH0308C.jpg


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

   +/@:((hC2k-:axs@((2;hC1k),1;h02))"1) xpgen''
8000


GCH0309C.jpg


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

   +/@:((hC1k-:axs@((2;hC2k),1;h20))"1) xpgen''
8000


10.3 Equation ISS32.6 (ISS Section 32)
GCH0310C.jpg


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

   s0t1p0=:axs@((0;dydx),1;g20@cyy)
   s0t1  =:axs@((0;dydx),1;s0t1p0)
   +/@:((h20-:s0t1)"1) xpgen''
8000


GCH0311C.jpg


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

   s1t1p0=:axs@((0;dydx),1;g20@cyy)
   s1t1  =:axs@((0;d2ydxdx),1;s1t1p0)
   s1t2p0=:axs@((0;d2ydxdx),0;g20@cyy)
   s1t2  =:axs@((0;dydx),2;s1t2p0)
   s1t3p0=:axs@((0;dydx),2;dg20dy@cyy)
   s1t3p1=:axs@((0;dydx),2;s1t3p0)
   s1t3  =:axs@((0;dydx),2;s1t3p1)
   +/@:((dh20dx-:(1|:s1t1)(+tz)s1t2(+tz)s1t3)"1) xpgen''
8000


GCH0312C.jpg


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

   s1t4  =:s1t1
   s1t5  =:1|:s1t2
   s1t6  =:1|:s1t3
   +/@:(((1|:dh20dx)-:s1t4(+tz)s1t5(+tz)s1t6)"1) xpgen''
8000

   s1t7  =:1|:0|:s1t1
   s1t8  =:0|:0|:s1t2
   s1t9  =:0|:0|:s1t3
   +/@:(((0|:0|:dh20dx)-:s1t7(+tz)s1t8(+tz)s1t9)"1) xpgen''
8000

   s1t10  =:-@(1|:s1t1)
   s1t11  =:-@s1t2
   s1t12  =:-@s1t3
   +/@:((-@dh20dx-:s1t10(+tz)s1t11(+tz)s1t12)"1) xpgen''
8000

   s1j1=:s1t4(+tz)s1t5(+tz)s1t6
   s1j2=:s1t7(+tz)s1t8(+tz)s1t9
   s1j3=:s1t10(+tz)s1t11(+tz)s1t12
   +/@:((hC1k-:0.5*s1j1(+tz)s1j2(+tz)s1j3)"1) xpgen''
8000


GCH0313C.jpg


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

   +/@:(((3 3 3$0:)-:s1t5(+tz)s1t11)"1) xpgen''         NB. terms cancel
8000
   +/@:(((3 3 3$0:)-:s1t8(+tz)s1t10)"1) xpgen''         NB. terms cancel
8000
   +/@:((s1t4-:s1t7)"1) xpgen''                         NB. terms equal
8000


GCH0314C.jpg


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

   +/@:((hC1k-:(0.5*s1t6(+tz)s1t9(+tz)s1t12)(+tz)s1t4)"1) xpgen''
8000


GCH0315C.jpg


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

   s2t1p0=:axs@((0;dydx),2;gC1k@cyy)
   s2t1p1=:axs@((0;dydx),2;s2t1p0)
   s2t1  =:axs@((0;dydx),2;s2t1p1)
   s2t2p0=:axs@((0;dydx),1;g20@cyy)
   s2t2  =:axs@((0;d2ydxdx),1;s2t2p0)
   +/@:((hC1k-:s2t1(+tz)s2t2)"1) xpgen''
8000


GCH0316C.jpg


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

   s3t1p0=:axs@((0;dydx),1;gC2k@cyy)
   s3t1p1=:axs@((0;dydx),1;s3t1p0)
   s3t1  =:0|:axs@((1;dxdy),2;s3t1p1)
   s3t2  =:0|:axs@((1;dxdy),0;d2ydxdx)
   +/@:((hC2k-:s3t1(+tz)s3t2)"1) xpgen''
8000


GCH0317C.jpg


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

   s4t1  =:axs@((1;dydx),2;hC2k)
   s4t2p0=:axs@((0;dydx),1;gC2k@cyy)
   s4t2  =:-@(0|:0|:axs@((0;dydx),1;s4t2p0))
   +/@:((d2ydxdx-:s4t1(+tz)s4t2)"1) xpgen''
8000


10.4 Equation ISS32.5 (ISS Section 32)
GCH0318C.jpg


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

   s0t1p0=:axs@((0;dxdy),1;h20)
   s0t1  =:axs@((0;dxdy),1;s0t1p0)
   +/@:((g20@cyy-:s0t1)"1) xpgen''
8000


GCH0319C.jpg


GCH0320C.jpg


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

   s4t0  =:axs@((2;d2xdydx),0;dxdy)
   s4t1  =:axs@((1;dxdy),2;gC2k@cyy)
   s4t2p0=:axs@((0;dxdy),1;hC2k)
   s4t2  =:-@(0|:0|:axs@((0;dxdy),1;s4t2p0))
   +/@:((s4t0-:s4t1(+tz)s4t2)"1) xpgen''
8000



Download: File:LCH0300C.txt
Download: File:LCH0301C.txt
Download: File:LCH0302C.txt
Download: File:LCH0303C.txt
Download: File:LCH0304C.txt
Download: File:LCH0305C.txt
Download: File:LCH0306C.txt
Download: File:LCH0307C.txt
Download: File:LCH0308C.txt
Download: File:LCH0309C.txt
Download: File:LCH0310C.txt
Download: File:LCH0311C.txt
Download: File:LCH0312C.txt
Download: File:LCH0313C.txt
Download: File:LCH0314C.txt
Download: File:LCH0315C.txt
Download: File:LCH0316C.txt
Download: File:LCH0317C.txt
Download: File:LCH0318C.txt
Download: File:LCH0319C.txt
Download: File:LCH0320C.txt




Download MoinMoin source: File:Christoffel03.ijs




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Contributed by Tom Allen