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
NB. ... execute (ijx) ... +/@:((=@i.@#-:axs@((1;dxdy),0;dydx))"1) xpgen'' 8000
NB. ... execute (ijx) ... +/@:((=@i.@#-:axs@((1;dydx),0;dxdy))"1) xpgen'' 8000
NB. ... execute (ijx) ... +/@:((=@i.@#-:axs@((1;h20),1;h02))"1) xpgen'' 8000
NB. ... execute (ijx) ... +/@:((=@i.@#-:axs@((1;h02),1;h20))"1) xpgen'' 8000
NB. ... execute (ijx) ... s0t1p0=:axs@((0;dydx),1;g20@cyy) +/@:((h20-:axs@((0;dydx),1;s0t1p0))"1) xpgen'' 8000
NB. ... execute (ijx) ... s0t1p0=:axs@((0;dxdy),1;h20) +/@:((g20@cyy-:axs@((0;dxdy),1;s0t1p0))"1) xpgen'' 8000
NB. ... execute (ijx) ... s0t1p0=:axs@((1;dxdy),1;g02@cyy) +/@:((h02-:axs@((1;dxdy),1;s0t1p0))"1) xpgen'' 8000
NB. ... execute (ijx) ... s0t1p0=:axs@((1;dydx),1;h02) +/@:((g02@cyy-:axs@((1;dydx),1;s0t1p0))"1) xpgen'' 8000
NB. ... execute (ijx) ... +/@:((hC2k-:axs@((2;hC1k),1;h02))"1) xpgen'' 8000
NB. ... execute (ijx) ... +/@:((hC1k-:axs@((2;hC2k),1;h20))"1) xpgen'' 8000
10.3 Equation ISS32.6 (ISS Section 32)
NB. ... execute (ijx) ... s0t1p0=:axs@((0;dydx),1;g20@cyy) s0t1 =:axs@((0;dydx),1;s0t1p0) +/@:((h20-:s0t1)"1) xpgen'' 8000
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
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
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
NB. ... execute (ijx) ... +/@:((hC1k-:(0.5*s1t6(+tz)s1t9(+tz)s1t12)(+tz)s1t4)"1) xpgen'' 8000
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
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
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)
NB. ... execute (ijx) ... s0t1p0=:axs@((0;dxdy),1;h20) s0t1 =:axs@((0;dxdy),1;s0t1p0) +/@:((g20@cyy-:s0t1)"1) xpgen'' 8000
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
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Download: File:LCH0320C.txt
Download MoinMoin source: File:Christoffel03.ijs
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Contributed by Tom Allen