Essays/Torsion Tensor/TorsionTensor01
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NB. ... script torsiontensor.ijs ... mXsign =:*/~@({.@$$1,_1:) mXdet =:-/ . * mXminors=:1&(|:\.)"2^:2 mXsign1=:( 0|:])@:((mXsign*])"2)@(0 1|:])"3 mXsign2=:(0 1|:])@:((mXsign*])"2)@(0 1|:])"4 L2hdx =:( 0|:])@(mXminors^:2)@(0 1|:])"3@hcvdx L3hdx =:( 0|:])@(mXminors^:1)@(0 1|:])"3@hcvdx L3hdxdx=:(0 1|:])@(mXminors^:1)@(0 1|:])"4@hcvdxdx L2H=:(mXsign*])"2@:mXdet@(mXminors^:3)@hcv L3H=:(mXsign*])"2@:mXdet@(mXminors^:2)@hcv L4H=:(mXsign*])"2@:mXdet@(mXminors^:1)@hcv hdet=: mXdet@(mXminors^:0)@hcv L3Hdx =:L2hdx mXsign1@:(+/"1@((<0 2)|:])@((1|:[)smx ])"3 2)L2H L4Hdx =:L3hdx mXsign1@:(+/"1@((<0 2)|:])@((1|:[)smx ])"3 2)L3H hdetdx =:hcvdx +/"1@((<0 2)|:])@((1|:[)smx ])"3 2 L4H L4Hdxdxt1=:L3hdx mXsign2@:(+/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 3)L3Hdx hdetdxdxt1=:hcvdx +/"1@((<0 2)|:])@((1|:[)smx 1|:])"3 3 L4Hdx L4Hdxdxt2=:L3hdxdx mXsign2@:(+/"1@((<0 3)|:])@((1|:[)smx ])"4 2)L3H hdetdxdxt2=:hcvdxdx +/"1@((<0 3)|:])@((1|:[)smx ])"4 2 L4H L4Hdxdx=: L4Hdxdxt1+ L4Hdxdxt2 hdetdxdx=:hdetdxdxt1+hdetdxdxt2
NB. ... execute (ijx) ... gXcme =:( 1.50 1.45 1.51 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( 0 0 0 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 6 20"_ *./^:4"4 (gXT(([L3Hdx hkAy)(((2^_14);2^_18)qteq[;])"1(0|:[:(gXT([L3H hkAy)])D.1])"_ 1)]) (50 yCrandom 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 *./^:2"2 (gXT(([L4Hdx hkAy)(((2^_12);2^_19)qteq[;])"1(0|:[:(gXT([L4H hkAy)])D.1])"_ 1)]) (50 yCrandom 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 *./^:2"2 (gXT(([L4Hdxdx hkAy)(((2^_13);2^_18)qteq[;])"2(0|:[:(gXT([L4Hdx hkAy)])D.1])"_ 1)]) (50 yCrandom 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 *./^:0"0 (gXT(([hdetdx hkAy)(((2^_12);2^_19)qteq[;])"1(0|:[:(gXT([hdet hkAy)])D.1])"_ 1)]) (50 yCrandom 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 *./^:0"0 (gXT(([hdetdxdx hkAy)(((2^_12);2^_18)qteq[;])"2(0|:[:(gXT([hdetdx hkAy)])D.1])"_ 1)]) (50 yCrandom 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
NB. ... script torsiontensor.ijs ... hdetm1=:hdet^_1: hdetm1dx=:-@(hdet^_2:)*"0 1 hdetdx hdetm1dxdxt1=:-@(hdet^_2:)*"0 2 hdetdxdx hdetm1dxdxt2=:2*(hdet^_3:)*"0 2 hdetdx*/"1 hdetdx hdetm1dxdx =:hdetm1dxdxt1+hdetm1dxdxt2
NB. ... execute (ijx) ... gXcme =:( 1.50 1.45 1.51 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( 0 0 0 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 6 20"_ (gXT(([hdetm1dx hkAy)(((2^_32);2^_17)qteq[;])"1(0|:[:(gXT([hdetm1 hkAy)])D.1])"_ 1)]) (50 yCrandom 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(([hdetm1dxdx hkAy)(((2^_32);2^_17)qteq[;])"2(0|:[:(gXT([hdetm1dx hkAy)])D.1])"_ 1)]) (50 yCrandom 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
NB. ... script torsiontensor.ijs ... hcn=:hdetm1*"0 2 L4H hcndxt1=:hdetm1 (* )"0 3 L4Hdx hcndxt2=:hdetm1dx(0|:])@(*/)"1 2 L4H hcndx =:hcndxt1+hcndxt2 hcndxdxt1=:hdetm1 (* )"0 4 L4Hdxdx hcndxdxt2=:hdetm1dx ( 0|:])@(*/)"1 3 L4Hdx hcndxdxt3=:hdetm1dx (0 3|:])@(*/)"1 3 L4Hdx hcndxdxt4=:hdetm1dxdx(0 1|:])@(*/)"2 2 L4H hcndxdx =:hcndxdxt1+hcndxdxt2+hcndxdxt3+hcndxdxt4
NB. ... execute (ijx) ... gXcme =:( 1.50 1.45 1.51 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( 0 0 0 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 6 20"_ (gXT(([hcndx hkAy)(((2^_25);2^_17)qteq[;])"3(0|:[:(gXT([hcn hkAy)])D.1])"_ 1)]) (50 yCrandom 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(([hcndxdx hkAy)(((2^_20);2^_17)qteq[;])"4(0|:[:(gXT([hcndx hkAy)])D.1])"_ 1)]) (50 yCrandom 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
NB. ... script torsiontensor.ijs ... ch1k =:0.5*(( 1|:])+( 0 1|:])-])"3@hcvdx ch1kdx =:0.5*(( 1 3|:])+( 0 1 3|:])-])"4@hcvdxdx ch1kdxdx=:0.5*((1 3 4|:])+(0 1 3 4|:])-])"5@hcvdxdxdx
NB. ... execute (ijx) ... gXcme =:( 1.50 1.45 1.51 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( 0 0 0 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 6 20"_ (gXT(([ch1kdx hkAy)(((2^_20);2^_18)qteq[;])"4(0|:[:(gXT([ch1k hkAy)])D.1])"_ 1)]) (50 yCrandom 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(([ch1kdxdx hkAy)(((2^_17);2^_18)qteq[;])"5(0|:[:(gXT([ch1kdx hkAy)])D.1])"_ 1)]) (50 yCrandom 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
NB. ... script torsiontensor.ijs ... ch2k=:hcn(0|:])@smx"2 3 ch1k ch2kdxt1=:hcn (0 3|:])@(( [)smx 2|:])"2 4 ch1kdx ch2kdxt2=:hcndx(0 1|:])@((1|:[)smx ])"3 3 ch1k ch2kdx =:ch2kdxt1+ch2kdxt2 ch2kdxdxt1=:hcn (0 3 4|:])@(( [)smx 2|:])"2 5 ch1kdxdx ch2kdxdxt2=:hcndx (0 4 1|:])@((1|:[)smx 2|:])"3 4 ch1kdx ch2kdxdxt3=:hcndx (0 1 4|:])@((1|:[)smx 2|:])"3 4 ch1kdx ch2kdxdxt4=:hcndxdx(0 1 2|:])@((1|:[)smx ])"4 3 ch1k ch2kdxdx =:ch2kdxdxt1+ch2kdxdxt2+ch2kdxdxt3+ch2kdxdxt4
NB. ... execute (ijx) ... gXcme =:( 1.50 1.45 1.51 )"_ gXpAll=:( 0 0 0 )"_ gXqAll=:( 0 0 0 )"_ gXwAll=:( 0 _ _ )"_ yCpts=:3.5 10 28,(0.1,(1p1-0.1),28),0 2p1 44,:0 6 20"_ (gXT(([ch2kdx hkAy)(((2^_21);2^_16)qteq[;])"4(0|:[:(gXT([ch2k hkAy)])D.1])"_ 1)]) (50 yCrandom 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(([ch2kdxdx hkAy)(((2^_17);2^_17)qteq[;])"5(0|:[:(gXT([ch2kdx hkAy)])D.1])"_ 1)]) (50 yCrandom 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
Download: File:LTT0100C.txt
Download: File:LTT0101C.txt
Download: File:LTT0102C.txt
Download: File:LTT0103C.txt
Download: File:LTT0104C.txt
Download MoinMoin source: File:TorsionTensor01.ijs
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Contributed by Tom Allen