From: Viktor T. <vt...@us...> - 2004-12-22 22:22:15
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Update of /cvsroot/maxima/maxima/doc/info In directory sc8-pr-cvs1.sourceforge.net:/tmp/cvs-serv25129 Modified Files: Itensor.texi Log Message: Correcting the frame base implementation documentation Index: Itensor.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/Itensor.texi,v retrieving revision 1.14 retrieving revision 1.15 diff -u -d -r1.14 -r1.15 --- Itensor.texi 19 Dec 2004 15:21:36 -0000 1.14 +++ Itensor.texi 22 Dec 2004 22:22:06 -0000 1.15 @@ -176,6 +176,8 @@ (%i9) ishow(extdiff(v([i],[]),j))$ (%t9) v - v j,i i,j + ----------- + 2 (%i10) ishow(liediff(v,w([i],[])))$ %3 %3 (%t10) v w + v w @@ -198,17 +200,17 @@ (%t14) v - v icc2 i,j %6 i j (%i15) ishow(ev(%,icc2))$ - %6 %6 -(%t15) v - v (ifc2 + ichr2 ) - i,j %6 i j i j -(%i16) ishow(radcan(ev(%,ifc2)))$ - %1 %1 %3 %2 %1 -(%t16) (v ifb - 2 v ichr2 + g ifb v g + 2 v - %1 i j %1 i j %2 j %3 i %1 i,j + %6 +(%t15) v - v ifc2 + i,j %6 i j +(%i16) ishow(radcan(ev(%,ifc2,ifc1)))$ + %6 %8 %6 %8 +(%t16) - (ifg v ifb + ifg v ifb - 2 v + %6 j %8 i %6 i j %8 i,j - %3 %1 %2 - - g ifb g v )/2 - %1 i %2 j %3 + %6 %8 + - ifg v ifb )/2 + %6 %8 i j (%i17) ishow(canform(s([i,j],[])-s([j,i])))$ (%t17) s - s i j j i @@ -1335,19 +1337,15 @@ (%t4) v (ifc2 + ichr2 ) + v %1 j %1 j ,j (%i5) ishow(ev(%,ifc2))$ - i %3 %2 %2 i - ifg (ifb ifg - ifg ifb ) - ifb - %1 %1 %3 %2 j %1 %2 %3 j %1 j -(%t5) v (------------------------------------------------------- - 2 - - i i - + ichr2 ) + v - %1 j ,j -(%i6) ishow(ifb([a,b],[c]))$ - c c %4 %5 -(%t6) (ifri - ifri ) ifr ifr - %4,%5 %5,%4 a b + %1 i %2 + v ifg (ifb - ifb + ifb ) + j %2 %1 %2 %1 j %1 j %2 i +(%t5) -------------------------------------------------- + v + 2 ,j +(%i6) ishow(ifb([a,b,c]))$ + %5 %4 +(%t6) ifr ifr (ifri - ifri ) + a b c %4,%5 c %5,%4 @end example @@ -1356,10 +1354,10 @@ @example -(%i8) block([iframe_bracket_form:false],ishow(ifb([a,b],[c])))$ - c %7 %6 %6 %7 -(%t8) ifri (ifr ifr - ifr ifr ) - %6 a b,%7 a,%7 b +(%i8) block([iframe_bracket_form:false],ishow(ifb([a,b,c])))$ + %7 %6 %6 %7 +(%t8) (ifr ifr - ifr ifr ) ifri + a b,%7 a,%7 b c %6 @end example @@ -1383,9 +1381,10 @@ @example - c cd e cd e c -ifc2 = ifg ifg ifb - ifg ifg ifb - ifb - ab be ad ae db ab + - ifb + ifb + ifb + c a b b c a a b c +ifc1 = -------------------------------- + abc 2 @end example @@ -1395,9 +1394,10 @@ @example - c c c d e -ifb = ( ifri - ifri ) ifr ifr - ab d,e e,d a b + e d +ifb = ifr ifr (ifri - ifri ) + abc a b c d,e c e,d + @end example @@ -1405,9 +1405,9 @@ @example - c c e d d e -ifb = ifri (ifr ifr - ifr ifr ) - ab d i j,e i,e j + e d d e +ifb = (ifr ifr - ifr ifr ) ifri + abc a b,e a,e b c d @end example @@ -1418,17 +1418,18 @@ @c @unnumberedsec phony @defvar icc1 -Connection coefficients of the first kind (also known as Ricci rotation -coefficients.) In ITENSOR, defined as +Connection coefficients of the first kind. In ITENSOR, defined as @example -icc1 = ichr1 + ifc1 + ikt1 - inmc1 - abc abc abc abc abc +icc1 = ichr1 - ikt1 - inmc1 + abc abc abc abc @end example -In this expression, if @code{itorsion_flag} is @code{false}, @code{ikt1} +In this expression, if @code{iframe_flag} is true, the Christoffel-symbol +@code{ichr1} is replaced with the frame connection coefficient @code{ifc1}. +If @code{itorsion_flag} is @code{false}, @code{ikt1} will be omitted. Similarly, of @code{inonmet_flag} is @code{false}, @code{inmc1} will not be present. @@ -1439,18 +1440,19 @@ @c @unnumberedsec phony @defvar icc2 -Connection coefficients of the first kind (also known as Ricci rotation -coefficients.) In ITENSOR, defined as +Connection coefficients of the second kind. In ITENSOR, defined as @example - c c c c c -icc2 = ichr2 + ifc2 - ikt2 - inmc2 - ab ab ab ab ab + c c c c +icc2 = ichr2 - ikt2 - inmc2 + ab ab ab ab @end example -In this expression, if @code{itorsion_flag} is @code{false}, @code{ikt2} +In this expression, if @code{iframe_flag} is true, the Christoffel-symbol +@code{ichr2} is replaced with the frame connection coefficient @code{ifc2}. +If @code{itorsion_flag} is @code{false}, @code{ikt2} will be omitted. Similarly, of @code{inonmet_flag} is @code{false}, @code{inmc2} will not be present. @@ -1460,15 +1462,18 @@ @c @unnumberedsec phony @defvar ifc1 -Frame coefficient of the first kind. This tensor represents the contribution +Frame coefficient of the first kind (also known as Ricci-rotation +coefficients.) This tensor represents the contribution of the frame metric to the connection coefficient of the first kind. Defined as: @example - d -ifc1 = ifg ifc2 - abc cd ab + - ifb + ifb + ifb + c a b b c a a b c +ifc1 = -------------------------------- + abc 2 + @end example @@ -1485,9 +1490,9 @@ @example - c cd e cd e c -ifc2 = ifg ifg ifb - ifg ifg ifb - ifb - ab be ad ae db ab + c cd +ifc2 = ifg ifc1 + ab abd @end example @@ -1848,10 +1853,10 @@ (%i1) load(itensor); (%o1) /share/tensor/itensor.lisp (%i2) ishow(extdiff(v([i]),j))$ - v - v - j,i i,j -(%t2) - ----------- - 2 + v - v + j,i i,j +(%t2) ----------- + 2 (%i3) decsym(a,2,0,[anti(all)],[]); (%o3) done (%i4) ishow(extdiff(a([i,j]),k))$ @@ -1862,8 +1867,8 @@ (%i5) igeowedge_flag:true; (%o5) true (%i6) ishow(extdiff(v([i]),j))$ -(%t6) - (v - v ) - j,i i,j +(%t6) v - v + j,i i,j (%i7) ishow(extdiff(a([i,j]),k))$ (%t7) a - a + a j k,i i k,j i j,k |