Essays/Schwarzschild/Schwarzschild01
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NB. ... script Schwarzschild.ijs (continued) ...
gcv =:>@(0{])
gcvdx =:>@(1{])
gcvdxdx =:>@(2{])
gcvdxdxdx =:>@(3{])
gcvdxdxdxdx =:>@(4{])
gcvdxdxdxdxdx=:>@(5{])
mXsign =:*/~@({.@$$1,_1:)
mXdet =:-/ . * NB. see Vocabulary 'Determinant'
mXminors=:1&(|:\.)"2^:2 NB. see Vocabulary 'Outfix'
mXsign1=:(0 |:])@:((mXsign*])"2)@(0 1|:])"3
mXsign2=:(0 1 |:])@:((mXsign*])"2)@(0 1|:])"4
mXsign3=:(0 1 2 |:])@:((mXsign*])"2)@(0 1|:])"5
mXsign4=:(0 1 2 3|:])@:((mXsign*])"2)@(0 1|:])"6
L2G=:(mXsign*])"2@:mXdet@(mXminors^:3)"2@gcv
L3G=:(mXsign*])"2@:mXdet@(mXminors^:2)"2@gcv
L4G=:(mXsign*])"2@:mXdet@(mXminors^:1)"2@gcv
g4 =: mXdet@(mXminors^:0)"2@gcv
L2gdx =:(0 |:])@(mXminors^:2)@(0 1|:])"3@gcvdx
L2gdxdx =:(0 1 |:])@(mXminors^:2)@(0 1|:])"4@gcvdxdx
L2gdxdxdx =:(0 1 2 |:])@(mXminors^:2)@(0 1|:])"5@gcvdxdxdx
L2gdxdxdxdx=:(0 1 2 3|:])@(mXminors^:2)@(0 1|:])"6@gcvdxdxdxdx
L2Gdx =:(0 |:])@:((mXsign*])@:(|."1)@|."2)@(mXminors^:2)@(0 1|:])"3@gcvdx
L2Gdxdx =:(0 1 |:])@:((mXsign*])@:(|."1)@|."2)@(mXminors^:2)@(0 1|:])"4@gcvdxdx
L2Gdxdxdx =:(0 1 2 |:])@:((mXsign*])@:(|."1)@|."2)@(mXminors^:2)@(0 1|:])"5@gcvdxdxdx
L2Gdxdxdxdx=:(0 1 2 3|:])@:((mXsign*])@:(|."1)@|."2)@(mXminors^:2)@(0 1|:])"6@gcvdxdxdxdx
L3gdx =:(0 |:])@(mXminors^:1)@(0 1|:])"3@gcvdx
L3gdxdx =:(0 1 |:])@(mXminors^:1)@(0 1|:])"4@gcvdxdx
L3gdxdxdx =:(0 1 2 |:])@(mXminors^:1)@(0 1|:])"5@gcvdxdxdx
L3gdxdxdxdx=:(0 1 2 3|:])@(mXminors^:1)@(0 1|:])"6@gcvdxdxdxdx
L3Gdx =:L2gdx (mXsign1@:(+/"1@((<0 2)|:])@((1|:[)smx ])"3 2)"5 4)L2G
L3Gdxdxt1 =:L2gdx (mXsign2@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 3)"5 5)L2Gdx
L3Gdxdxt2 =:L2gdxdx (mXsign2@:(+/"1@((<0 3)|:])@((1|:[)smx ])"4 2)"6 4)L2G
L3Gdxdx =:L3Gdxdxt1+L3Gdxdxt2
L3Gdxdxdxt1 =:L2gdx (mXsign3@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 4)"5 6)L2Gdxdx
L3Gdxdxdxt2 =:L2gdxdx (mXsign3@:(+/"1@((<0 3)|:])@((1|:[)smx 1|:])"4 3)"6 5)L2Gdx
L3Gdxdxdxt3 =:L2gdxdxdx (mXsign3@:(+/"1@((<0 4)|:])@((1|:[)smx ])"5 2)"7 4)L2G
L3Gdxdxdx =:L3Gdxdxdxt1+((1|:])+])"3@L3Gdxdxdxt2+L3Gdxdxdxt3
L3Gdxdxdxdxt1=:L2gdx (mXsign4@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 5)"5 7)L2Gdxdxdx
L3Gdxdxdxdxt2=:L2gdxdx (mXsign4@:(+/"1@((<0 3)|:])@((1|:[)smx 1|:])"4 4)"6 6)L2Gdxdx
L3Gdxdxdxdxt3=:L2gdxdxdx (mXsign4@:(+/"1@((<0 4)|:])@((1|:[)smx 1|:])"5 3)"7 5)L2Gdx
L3Gdxdxdxdxt4=:L2gdxdxdxdx(mXsign4@:(+/"1@((<0 5)|:])@((1|:[)smx ])"6 2)"8 4)L2G
L3Gdxdxdxdx =:L3Gdxdxdxdxt1+((1|:])+(1 3|:])+])"4@L3Gdxdxdxdxt2+((1 2|:])+(2|:])+])"4@L3Gdxdxdxdxt3+L3Gdxdxdxdxt4
L4Gdx =:L3gdx mXsign1@:(+/"1@((<0 2)|:])@((1|:[)smx ])"3 2)L3G
L4Gdxdxt1 =:L3gdx mXsign2@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 3)L3Gdx
L4Gdxdxt2 =:L3gdxdx mXsign2@:(+/"1@((<0 3)|:])@((1|:[)smx ])"4 2)L3G
L4Gdxdx =:L4Gdxdxt1+L4Gdxdxt2
L4Gdxdxdxt1 =:L3gdx mXsign3@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 4)L3Gdxdx
L4Gdxdxdxt2 =:L3gdxdx mXsign3@:(+/"1@((<0 3)|:])@((1|:[)smx 1|:])"4 3)L3Gdx
L4Gdxdxdxt3 =:L3gdxdxdx mXsign3@:(+/"1@((<0 4)|:])@((1|:[)smx ])"5 2)L3G
L4Gdxdxdx =:L4Gdxdxdxt1+((1|:])+])"3@L4Gdxdxdxt2+L4Gdxdxdxt3
L4Gdxdxdxdxt1=:L3gdx mXsign4@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 5)L3Gdxdxdx
L4Gdxdxdxdxt2=:L3gdxdx mXsign4@:(+/"1@((<0 3)|:])@((1|:[)smx 1|:])"4 4)L3Gdxdx
L4Gdxdxdxdxt3=:L3gdxdxdx mXsign4@:(+/"1@((<0 4)|:])@((1|:[)smx 1|:])"5 3)L3Gdx
L4Gdxdxdxdxt4=:L3gdxdxdxdx mXsign4@:(+/"1@((<0 5)|:])@((1|:[)smx ])"6 2)L3G
L4Gdxdxdxdx =:L4Gdxdxdxdxt1+((1|:])+(1 3|:])+])"4@L4Gdxdxdxdxt2+((1 2|:])+(2|:])+])"4@L4Gdxdxdxdxt3+L4Gdxdxdxdxt4
g4dx =:gcvdx +/"1@((<0 2)|:])@((1|:[)smx ])"3 2 L4G
g4dxdxt1 =:gcvdx +/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 3 L4Gdx
g4dxdxt2 =:gcvdxdx +/"1@((<0 3)|:])@((1|:[)smx ])"4 2 L4G
g4dxdx =:g4dxdxt1+g4dxdxt2
g4dxdxdxt1 =:gcvdx +/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 4 L4Gdxdx
g4dxdxdxt2 =:gcvdxdx +/"1@((<0 3)|:])@((1|:[)smx 1|:])"4 3 L4Gdx
g4dxdxdxt3 =:gcvdxdxdx +/"1@((<0 4)|:])@((1|:[)smx ])"5 2 L4G
g4dxdxdx =:g4dxdxdxt1+((1|:])+])"3@g4dxdxdxt2+g4dxdxdxt3
g4dxdxdxdxt1=:gcvdx +/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 5 L4Gdxdxdx
g4dxdxdxdxt2=:gcvdxdx +/"1@((<0 3)|:])@((1|:[)smx 1|:])"4 4 L4Gdxdx
g4dxdxdxdxt3=:gcvdxdxdx +/"1@((<0 4)|:])@((1|:[)smx 1|:])"5 3 L4Gdx
g4dxdxdxdxt4=:gcvdxdxdxdx +/"1@((<0 5)|:])@((1|:[)smx ])"6 2 L4G
g4dxdxdxdx =:g4dxdxdxdxt1+((1|:])+(1 3|:])+])"4@g4dxdxdxdxt2+((1 2|:])+(2|:])+])"4@g4dxdxdxdxt3+g4dxdxdxdxt4
NB. ... execute (ijx) ... bTaC=:1.5,1.5,1.2,1.2,1.5,0"_ bTaP=:25 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTa0=:[L2Gdx gs bTa1=:(0|:[:(bTaC([L2G gs)])D.1])"1 (5 5$]) *./@(*./)"2^:3 (bTaC(bTa0(((2^_44);2^_15)tcm[;])"1 bTa1)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa2=:[L2Gdxdx gs bTa3=:(0|:[:(bTaC([L2Gdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:3 (bTaC(bTa2(((2^_44);2^_18)tcm[;])"2 bTa3)bTaP)'' 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 bTa4=:[L2Gdxdxdx gs bTa5=:(0|:[:(bTaC([L2Gdxdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:3 (bTaC(bTa4(((2^_44);2^_18)tcm[;])"3 bTa5)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa6=:[L2Gdxdxdxdx gs bTa7=:(0|:[:(bTaC([L2Gdxdxdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:3 (bTaC(bTa6(((2^_44);2^_18)tcm[;])"4 bTa7)bTaP)'' 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 bTa8=:[L3Gdx gs bTa9=:(0|:[:(bTaC([L3G gs)])D.1])"1 (5 5$]) *./@(*./)"2^:2 (bTaC(bTa8(((2^_44);2^_18)tcm[;])"1 bTa9)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa10=:[L3Gdxdx gs bTa11=:(0|:[:(bTaC([L3Gdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:2 (bTaC(bTa10(((2^_44);2^_18)tcm[;])"2 bTa11)bTaP)'' 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 bTa12=:[L3Gdxdxdx gs bTa13=:(0|:[:(bTaC([L3Gdxdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:2 (bTaC(bTa12(((2^_44);2^_18)tcm[;])"3 bTa13)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa14=:[L3Gdxdxdxdx gs bTa15=:(0|:[:(bTaC([L3Gdxdxdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:2 (bTaC(bTa14(((2^_44);2^_18)tcm[;])"4 bTa15)bTaP)'' 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 bTa16=:[L4Gdx gs bTa17=:(0|:[:(bTaC([L4G gs)])D.1])"1 (5 5$]) *./@(*./)"2^:1 (bTaC(bTa16(((2^_44);2^_18)tcm[;])"1 bTa17)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa18=:[L4Gdxdx gs bTa19=:(0|:[:(bTaC([L4Gdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:1 (bTaC(bTa18(((2^_44);2^_18)tcm[;])"2 bTa19)bTaP)'' 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 bTa20=:[L4Gdxdxdx gs bTa21=:(0|:[:(bTaC([L4Gdxdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:1 (bTaC(bTa20(((2^_40);2^_18)tcm[;])"3 bTa21)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa22=:[L4Gdxdxdxdx gs bTa23=:(0|:[:(bTaC([L4Gdxdxdx gs)])D.1])"1 (5 5$]) *./@(*./)"2^:1 (bTaC(bTa22(((2^_38);2^_17)tcm[;])"4 bTa23)bTaP)'' 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 bTa24=:[g4dx gs bTa25=:(0|:[:(bTaC([g4 gs)])D.1])"1 (5 5$]) (bTaC(bTa24(((2^_44);2^_18)tcm[;])"1 bTa25)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa26=:[g4dxdx gs bTa27=:(0|:[:(bTaC([g4dx gs)])D.1])"1 (5 5$]) (bTaC(bTa26(((2^_44);2^_18)tcm[;])"2 bTa27)bTaP)'' 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 bTa28=:[g4dxdxdx gs bTa29=:(0|:[:(bTaC([g4dxdx gs)])D.1])"1 (5 5$]) (bTaC(bTa28(((2^_44);2^_18)tcm[;])"3 bTa29)bTaP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTa30=:[g4dxdxdxdx gs bTa31=:(0|:[:(bTaC([g4dxdxdx gs)])D.1])"1 (5 5$]) (bTaC(bTa30(((2^_42);2^_17)tcm[;])"4 bTa31)bTaP)'' 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
NB. ... script Schwarzschild.ijs (continued) ... g1m=:(g4^_1:) g1mdx=:_1*(g4^_2:)*"0 1 g4dx g1mdxdxt1=:_1*(g4^_2:)*"0 2 g4dxdx g1mdxdxt2=: 2*(g4^_3:)*"0 2 g4dx*/"1 g4dx g1mdxdx =:g1mdxdxt1+g1mdxdxt2 g1mdxdxdxt1=:_1*(g4^_2:)*"0 3 g4dxdxdx g1mdxdxdxt2=: 2*(g4^_3:)*"0 3 g4dx*/"1 2 g4dxdx g1mdxdxdxt3=:_6*(g4^_4:)*"0 3 g4dx*/"1 2 g4dx*/"1 g4dx g1mdxdxdx =:g1mdxdxdxt1+((0|:])+(0 2|:])+])"3@g1mdxdxdxt2+g1mdxdxdxt3 g1mdxdxdxdxt1=:_1*(g4^_2:)*"0 4 g4dxdxdxdx g1mdxdxdxdxt2=: 2*(g4^_3:)*"0 4 g4dx*/"1 3 g4dxdxdx g1mdxdxdxdxt3=: 2*(g4^_3:)*"0 4 g4dxdx*/"2 g4dxdx g1mdxdxdxdxt4=:_6*(g4^_4:)*"0 4 g4dx*/"1 3 g4dx*/"1 2 g4dxdx g1mdxdxdxdxt5=:24*(g4^_5:)*"0 4 g4dx*/"1 3 g4dx*/"1 2 g4dx*/"1 g4dx g1mdxdxdxdxt2Sum=:((0|:])+(0 3|:])+(0 2 3|:])+])"4@g1mdxdxdxdxt2 g1mdxdxdxdxt3Sum=:(]+(0 3 1|:])+1|:])"4@g1mdxdxdxdxt3 g1mdxdxdxdxt4Sum=:((1 0|:])+(1 3 0|:])+(1|:])+(1 0 3|:])+(2 1 3|:])+])"4@g1mdxdxdxdxt4 g1mdxdxdxdx=:g1mdxdxdxdxt1+g1mdxdxdxdxt2Sum+g1mdxdxdxdxt3Sum+g1mdxdxdxdxt4Sum+g1mdxdxdxdxt5
NB. ... execute (ijx) ... bTbC=:1.5,1.5,1.2,1.2,1.5,0"_ bTbP=:25 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTb0=:[g1mdx gs bTb1=:([:(bTbC([g1m gs)])D.1])"1 (5 5$]) (bTbC(bTb0(((2^_44);2^_18)tcm[;])"1 bTb1)bTbP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTb2=:[g1mdxdx gs bTb3=:(0|:[:(bTbC([g1mdx gs)])D.1])"1 (5 5$]) (bTbC(bTb2(((2^_44);2^_18)tcm[;])"2 bTb3)bTbP)'' 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 bTb4=:[g1mdxdxdx gs bTb5=:(0|:[:(bTbC([g1mdxdx gs)])D.1])"1 (5 5$]) (bTbC(bTb4(((2^_44);2^_18)tcm[;])"3 bTb5)bTbP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTb6=:[g1mdxdxdxdx gs bTb7=:(0|:[:(bTbC([g1mdxdxdx gs)])D.1])"1 (5 5$]) (bTbC(bTb6(((2^_44);2^_17)tcm[;])"4 bTb7)bTbP)'' 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
NB. ... script Schwarzschild.ijs (continued) ... gcn=:g1m*"0 2 L4G gcndxt1=:g1m * "0 3 L4Gdx gcndxt2=:g1mdx*/"1 2 L4G gcndx =:gcndxt1+(0|:])"3@gcndxt2 gcndxdxt1=:g1m * "0 4 L4Gdxdx gcndxdxt2=:g1mdx */"1 3 L4Gdx gcndxdxt3=:g1mdxdx*/"2 2 L4G gcndxdx =:gcndxdxt1+((0|:])+0 3|:])"4@gcndxdxt2+(0 1|:])"4@gcndxdxt3 gcndxdxdxt1=:g1m * "0 5 L4Gdxdxdx gcndxdxdxt2=:g1mdx */"1 4 L4Gdxdx gcndxdxdxt3=:g1mdxdx */"2 3 L4Gdx gcndxdxdxt4=:g1mdxdxdx*/"3 2 L4G gcndxdxdxt2Sum=:((0|:])+(0 4|:])+0 3 4|:])"5@gcndxdxdxt2 gcndxdxdxt3Sum=:((0 1|:])+(0 4 1|:])+0 1 4|:])"5@gcndxdxdxt3 gcndxdxdxt4Sum=:(0 1 2|:])"5@gcndxdxdxt4 gcndxdxdx=:gcndxdxdxt1+gcndxdxdxt2Sum+gcndxdxdxt3Sum+gcndxdxdxt4Sum gcndxdxdxdxt1=:g1m * "0 6 L4Gdxdxdxdx gcndxdxdxdxt2=:g1mdx */"1 5 L4Gdxdxdx gcndxdxdxdxt3=:g1mdxdx */"2 4 L4Gdxdx gcndxdxdxdxt4=:g1mdxdxdx */"3 3 L4Gdx gcndxdxdxdxt5=:g1mdxdxdxdx*/"4 2 L4G gcndxdxdxdxt2Sum=:((0|:])+(0 5|:])+(0 4 5|:])+0 3 4 5|:])"6@gcndxdxdxdxt2 gcndxdxdxdxt3Sum=:((0 1|:])+(0 5 1|:])+(0 1 5|:])+(0 4 5 1|:])+(0 4 1 5|:])+0 1 4 5|:])"6@gcndxdxdxdxt3 gcndxdxdxdxt4Sum=:((0 1 2|:])+(0 5 1 2|:])+(0 1 5 2|:])+0 1 2 5|:])"6@gcndxdxdxdxt4 gcndxdxdxdxt5Sum=:(0 1 2 3|:])"6@gcndxdxdxdxt5 gcndxdxdxdx=:gcndxdxdxdxt1+gcndxdxdxdxt2Sum+gcndxdxdxdxt3Sum+gcndxdxdxdxt4Sum+gcndxdxdxdxt5Sum
NB. ... execute (ijx) ... bTcC=:1.5,1.5,1.2,1.2,1.5,0"_ bTcP=:25 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTc0=:[gcndx gs bTc1=:(0|:[:(bTcC([gcn gs)])D.1])"1 (5 5$]) (bTcC(bTc0(((2^_43);2^_13)tcm[;])"3 bTc1)bTcP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTc2=:[gcndxdx gs bTc3=:(0|:[:(bTcC([gcndx gs)])D.1])"1 (5 5$]) (bTcC(bTc2(((2^_40);2^_12)tcm[;])"4 bTc3)bTcP)'' 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 bTc4=:[gcndxdxdx gs bTc5=:(0|:[:(bTcC([gcndxdx gs)])D.1])"1 (5 5$]) (bTcC(bTc4(((2^_36);2^_11)tcm[;])"5 bTc5)bTcP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTc6=:[gcndxdxdxdx gs bTc7=:(0|:[:(bTcC([gcndxdxdx gs)])D.1])"1 (5 5$]) (bTcC(bTc6(((2^_29);2^_9)tcm[;])"6 bTc7)bTcP)'' 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
NB. ... script Schwarzschild.ijs (continued) ... ch1k =:0.5*((1 |:])+(0 1 |:])-])"3@gcvdx ch1kdx =:0.5*((1 3 |:])+(0 1 3 |:])-])"4@gcvdxdx ch1kdxdx =:0.5*((1 3 4 |:])+(0 1 3 4 |:])-])"5@gcvdxdxdx ch1kdxdxdx =:0.5*((1 3 4 5 |:])+(0 1 3 4 5 |:])-])"6@gcvdxdxdxdx ch1kdxdxdxdx=:0.5*((1 3 4 5 6|:])+(0 1 3 4 5 6|:])-])"7@gcvdxdxdxdxdx
NB. ... execute (ijx) ... bTdC=:1.5,1.5,1.2,1.2,1.5,0"_ bTdP=:25 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTd0=:[ch1kdx gs bTd1=:(0|:[:(bTdC([ch1k gs)])D.1])"1 (5 5$]) (bTdC(bTd0(((2^_44);2^_18)tcm[;])"4 bTd1)bTdP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTd2=:[ch1kdxdx gs bTd3=:(0|:[:(bTdC([ch1kdx gs)])D.1])"1 (5 5$]) (bTdC(bTd2(((2^_44);2^_18)tcm[;])"5 bTd3)bTdP)'' 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 bTd4=:[ch1kdxdxdx gs bTd5=:(0|:[:(bTdC([ch1kdxdx gs)])D.1])"1 (5 5$]) (bTdC(bTd4(((2^_44);2^_18)tcm[;])"6 bTd5)bTdP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTd6=:[ch1kdxdxdxdx gs bTd7=:(0|:[:(bTdC([ch1kdxdxdx gs)])D.1])"1 (5 5$]) (bTdC(bTd6(((2^_44);2^_18)tcm[;])"7 bTd7)bTdP)'' 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
NB. ... script Schwarzschild.ijs (continued) ... ch2k=:gcn(0|:])@:smx"2 3 ch1k ch2kdxt1=:gcn (( [)smx 2|:])"2 4 ch1kdx ch2kdxt2=:gcndx((1|:[)smx ])"3 3 ch1k ch2kdx =:(0 3|:])"4@ch2kdxt1+(0 1|:])"4@ch2kdxt2 ch2kdxdxt1=:gcn (( [)smx 2|:])"2 5 ch1kdxdx ch2kdxdxt2=:gcndx ((1|:[)smx 2|:])"3 4 ch1kdx ch2kdxdxt3=:gcndxdx((1|:[)smx ])"4 3 ch1k ch2kdxdx =:(0 3 4|:])"5@ch2kdxdxt1+((0 4 1|:])+0 1 4|:])"5@ch2kdxdxt2+(0 1 2|:])"5@ch2kdxdxt3 ch2kdxdxdxt1=:gcn (( [)smx 2|:])"2 6 ch1kdxdxdx ch2kdxdxdxt2=:gcndx ((1|:[)smx 2|:])"3 5 ch1kdxdx ch2kdxdxdxt3=:gcndxdx ((1|:[)smx 2|:])"4 4 ch1kdx ch2kdxdxdxt4=:gcndxdxdx((1|:[)smx ])"5 3 ch1k ch2kdxdxdxt1Sum=:(0 3 4 5|:])"6@ch2kdxdxdxt1 ch2kdxdxdxt2Sum=:((0 4 5 1|:])+(0 4 1 5|:])+0 1 4 5|:])"6@ch2kdxdxdxt2 ch2kdxdxdxt3Sum=:((0 5 1 2|:])+(0 1 5 2|:])+0 1 2 5|:])"6@ch2kdxdxdxt3 ch2kdxdxdxt4Sum=:(0 1 2 3|:])"6@ch2kdxdxdxt4 ch2kdxdxdx=:ch2kdxdxdxt1Sum+ch2kdxdxdxt2Sum+ch2kdxdxdxt3Sum+ch2kdxdxdxt4Sum ch2kdxdxdxdxt1=:gcn (( [)smx 2|:])"2 7 ch1kdxdxdxdx ch2kdxdxdxdxt2=:gcndx ((1|:[)smx 2|:])"3 6 ch1kdxdxdx ch2kdxdxdxdxt3=:gcndxdx ((1|:[)smx 2|:])"4 5 ch1kdxdx ch2kdxdxdxdxt4=:gcndxdxdx ((1|:[)smx 2|:])"5 4 ch1kdx ch2kdxdxdxdxt5=:gcndxdxdxdx((1|:[)smx ])"6 3 ch1k ch2kdxdxdxdxt1Sum=:(0 3 4 5 6|:])"7@ch2kdxdxdxdxt1 ch2kdxdxdxdxt2Sum=:((0 4 5 6 1|:])+(0 4 5 1 6|:])+(0 4 1 5 6|:])+0 1 4 5 6|:])"7@ch2kdxdxdxdxt2 ch2kdxdxdxdxt3Sum=:((0 5 6 1 2|:])+(0 5 1 6 2|:])+(0 5 1 2 6|:])+(0 1 5 6 2|:])+(0 1 5 2 6|:])+0 1 2 5 6|:])"7@ch2kdxdxdxdxt3 ch2kdxdxdxdxt4Sum=:((0 6 1 2 3|:])+(0 1 6 2 3|:])+(0 1 2 6 3|:])+0 1 2 3 6|:])"7@ch2kdxdxdxdxt4 ch2kdxdxdxdxt5Sum=:(0 1 2 3 4|:])"7@ch2kdxdxdxdxt5 ch2kdxdxdxdx=:ch2kdxdxdxdxt1Sum+ch2kdxdxdxdxt2Sum+ch2kdxdxdxdxt3Sum+ch2kdxdxdxdxt4Sum+ch2kdxdxdxdxt5Sum
NB. ... execute (ijx) ... bTeC=:1.5,1.5,1.2,1.2,1.5,0"_ bTeP=:25 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTe0=:[ch2kdx gs bTe1=:(0|:[:(bTeC([ch2k gs)])D.1])"1 (5 5$]) (bTeC(bTe0(((2^_41);2^_16)tcm[;])"4 bTe1)bTeP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTe2=:[ch2kdxdx gs bTe3=:(0|:[:(bTeC([ch2kdx gs)])D.1])"1 (5 5$]) (bTeC(bTe2(((2^_37);2^_12)tcm[;])"5 bTe3)bTeP)'' 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 bTe4=:[ch2kdxdxdx gs bTe5=:(0|:[:(bTeC([ch2kdxdx gs)])D.1])"1 (5 5$]) (bTeC(bTe4(((2^_33);2^_11)tcm[;])"6 bTe5)bTeP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTe6=:[ch2kdxdxdxdx gs bTe7=:(0|:[:(bTeC([ch2kdxdxdx gs)])D.1])"1 (5 5$]) (bTeC(bTe6(((2^_27);2^_8)tcm[;])"7 bTe7)bTeP)'' 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
NB. ... script Schwarzschild.ijs (continued) ... B2kt1=: ch2kdx B2kt2=:ch2k([smx 0|:])"3 3 ch2k B2kt1Sum=:((1 2|:])+-@(2|:]))"4@B2kt1 B2kt2Sum=: ((1 3|:])+-@(]))"4@B2kt2 B2k=:B2kt1Sum+B2kt2Sum B2kdxt1=: ch2kdxdx B2kdxt2=:ch2k (( [)smx 0|:])"3 4 ch2kdx B2kdxt3=:ch2kdx((2|:[)smx 0|:])"4 3 ch2k B2kdxt1Sum=:((1 2 4|:])+-@(2 4|:]))"5@B2kdxt1 B2kdxt2Sum=: ((1 3 4|:])+-@(]))"5@B2kdxt2 B2kdxt3Sum=: ((1 4 2|:])+-@(2|:]))"5@B2kdxt3 B2kdx=:B2kdxt1Sum+B2kdxt2Sum+B2kdxt3Sum B2kdxdxt1=: ch2kdxdxdx B2kdxdxt2=:ch2k (( [)smx 0|:])"3 5 ch2kdxdx B2kdxdxt3=:ch2kdx ((2|:[)smx 0|:])"4 4 ch2kdx B2kdxdxt4=:ch2kdxdx((2|:[)smx 0|:])"5 3 ch2k B2kdxdxt1Sum=: ((1 2 4 5|:])+-@(2 4 5|:]))"6@B2kdxdxt1 B2kdxdxt2Sum=: ((1 3 4 5|:])+-@(]))"6@B2kdxdxt2 B2kdxdxt3Sum=:((1 4 5 2|:])+(1 4 2 5|:])+-@(2|:])+-@(2 5|:]))"6@B2kdxdxt3 B2kdxdxt4Sum=: ((1 5 2 3|:])+-@(2 3|:]))"6@B2kdxdxt4 B2kdxdx=:B2kdxdxt1Sum+B2kdxdxt2Sum+B2kdxdxt3Sum+B2kdxdxt4Sum B2kdxdxdxt1=: ch2kdxdxdxdx B2kdxdxdxt2=:ch2k (( [)smx 0|:])"3 6 ch2kdxdxdx B2kdxdxdxt3=:ch2kdx ((2|:[)smx 0|:])"4 5 ch2kdxdx B2kdxdxdxt4=:ch2kdxdx ((2|:[)smx 0|:])"5 4 ch2kdx B2kdxdxdxt5=:ch2kdxdxdx((2|:[)smx 0|:])"6 3 ch2k B2kdxdxdxt1Sum=: ((1 2 4 5 6|:])+-@(2 4 5 6|:]))"7@B2kdxdxdxt1 B2kdxdxdxt2Sum=: ((1 3 4 5 6|:])+-@(]))"7@B2kdxdxdxt2 B2kdxdxdxt3Sum=: ((1 4 5 6 2|:])+(1 4 5 2 6|:])+(1 4 2 5 6|:])+-@(2|:])+-@(2 6|:])+-@(2 5 6|:]))"7@B2kdxdxdxt3 B2kdxdxdxt4Sum=:((1 5 6 2 3|:])+(1 5 2 6 3|:])+(1 5 2 3 6|:])+-@(2 3|:])+-@(2 6 3|:])+-@(2 3 6|:]))"7@B2kdxdxdxt4 B2kdxdxdxt5Sum=: ((1 6 2 3 4|:])+-@(2 3 4|:]))"7@B2kdxdxdxt5 B2kdxdxdx=:B2kdxdxdxt1Sum+B2kdxdxdxt2Sum+B2kdxdxdxt3Sum+B2kdxdxdxt4Sum+B2kdxdxdxt5Sum
NB. ... execute (ijx) ... bTfC=:1.5,1.5,1.2,1.2,1.5,0"_ bTfP=:16 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTf0=:[B2kdx gs bTf1=:(0|:[:(bTfC([B2k gs)])D.1])"1 (4 4$]) (bTfC(bTf0(((2^_38);2^_15)tcm[;])"5 bTf1)bTfP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTf2=:[B2kdxdx gs bTf3=:(0|:[:(bTfC([B2kdx gs)])D.1])"1 (4 4$]) (bTfC(bTf2(((2^_32);2^_14)tcm[;])"6 bTf3)bTfP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTf4=:[B2kdxdxdx gs bTf5=:(0|:[:(bTfC([B2kdxdx gs)])D.1])"1 (4 4$]) (bTfC(bTf4(((2^_25);2^_11)tcm[;])"7 bTf5)bTfP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... script Schwarzschild.ijs (continued) ... R20i =:+/"1@((<2 3)|:])"4@B2k R20idx =:+/"1@((<2 3)|:])"5@B2kdx R20idxdx =:+/"1@((<2 3)|:])"6@B2kdxdx R20idxdxdx=:+/"1@((<2 3)|:])"7@B2kdxdxdx
NB. ... execute (ijx) ... bTgC=:1.5,1.5,1.2,1.2,1.5,0"_ bTgP=:16 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ bTg0=:[R20idx gs bTg1=:(0|:[:(bTgC([R20i gs)])D.1])"1 (4 4$]) (bTgC(bTg0(((2^_39);2^_13)tcm[;])"3 bTg1)bTgP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTg2=:[R20idxdx gs bTg3=:(0|:[:(bTgC([R20idx gs)])D.1])"1 (4 4$]) (bTgC(bTg2(((2^_33);2^_12)tcm[;])"4 bTg3)bTgP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 bTg4=:[R20idxdxdx gs bTg5=:(0|:[:(bTgC([R20idxdx gs)])D.1])"1 (4 4$]) (bTgC(bTg4(((2^_28);2^_9)tcm[;])"5 bTg5)bTgP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... execute (ijx) ... NB. ... when e is not equal to 0 the Ricci tensor is not 0 ... bThC=:1.5,1.5,1.2,1.2,1.5,0"_ bThP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ (nzcount,nzmin,nzmax) ((2^_44)tsz]) (bThC([R20i gs)bThP)'' 600 8.84329e_5 0.137292
NB. ... execute (ijx) ... NB. ... when e is equal to 0 the Ricci tensor is 0 ... NB. ... this is the Schwarzschild metric ... bTiC=:1.5,1.5,1.2,0,1.5,0"_ bTiP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ (10 10$]) *./^:2"2 (0=]) ((2^_42)tsz]) (bTiC([R20i gs)bTiP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... script Schwarzschild.ijs (continued) ... R=:gcn+/@((<0 1)|:])@:smx"2 R20i
NB. ... execute (ijx) ... NB. ... for this metric R=0 ... bTjC=:1.5,1.5,1.2,1.2,1.5,0"_ bTjP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ (10 10$]) (0=]) ((2^_44)tsz]) (bTjC([R gs)bTjP)'' 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 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
NB. ... script Schwarzschild.ijs (continued) ... B2kcvt1=:-@((1|:])@([smx 0|:])) B2kcvt2=:-@((0 3 4 1|:])@([smx 1|:])) B2kcvt3=:-@((0 4 1|:])@([smx 2|:])) B2kcvt4=:(1 0|:])@((0|:[)smx]) B2kcv =:B2kdx+ch2k(B2kcvt1+B2kcvt2+B2kcvt3+B2kcvt4)"3 4 B2k
NB. ... script Schwarzschild.ijs (continued) ... Bianchi=:(]+(1 3 2|:])+3 1|:])"5@B2kcv
NB. ... execute (ijx) ... NB. ... Bianchi identity ... bTkC=:1.5,1.5,1.2,1.2,1.5,0"_ bTkP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ (10 10$]) *./^:6"5 (0=]) ((2^_41)tsz]) (bTkC([Bianchi gs)bTkP)'' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
NB. ... script Schwarzschild.ijs (continued) ... Edivt1=:+/"1@((<1 2)|:])"3 Edivt2=:(0.5*+/"1@((<0 1)|:]))"3 Ediv =:(Edivt1-Edivt2)@(gcn(0 2|:])@([smx 1|:])"2 3+/"1@((<2 3)|:])"5@B2kcv)
NB. ... execute (ijx) ... NB. ... divergence of Einstein's tensor is zero ... bTlC=:1.5,1.5,1.2,1.2,1.5,0"_ bTlP=:100 c4Gen 3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 2p1 20"_ (10 10$]) *./"1 (0=]) ((2^_42)tsz]) (bTlC([Ediv gs)bTlP)'' 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 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
Download: File:LSC0100C.txt
Download: File:LSC0101C.txt
Download: File:LSC0102C.txt
Download: File:LSC0103C.txt
Download: File:LSC0104C.txt
Download: File:LSC0105C.txt
Download: File:LSC0106C.txt
Download: File:LSC0107C.txt
Download: File:LSC0108C.txt
Download: File:LSC0109C.txt
Download: File:LSC0110C.txt
Download MoinMoin source: File:Schwarzschild01.ijs
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Contributed by Tom Allen