From: Vadim V. Z. <vv...@us...> - 2007-06-24 16:02:51
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Update of /cvsroot/maxima/maxima/doc/info/ru In directory sc8-pr-cvs16.sourceforge.net:/tmp/cvs-serv8202 Modified Files: Ctensor.texi Log Message: Revision update 1.33 -> 1.34 Index: Ctensor.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/ru/Ctensor.texi,v retrieving revision 1.3 retrieving revision 1.4 diff -u -d -r1.3 -r1.4 --- Ctensor.texi 30 May 2007 13:57:41 -0000 1.3 +++ Ctensor.texi 24 Jun 2007 16:02:40 -0000 1.4 @@ -1,7 +1,7 @@ @c Language=Russian @c Encoding=CP1251 @c File=Ctensor.texi -@c OriginalRevision=1.33 +@c OriginalRevision=1.34 @menu @@ -169,34 +169,47 @@ @example - Ñèìâîë Dim Êîîðäèíàòû Îïèñàíèå/êîììåíòàðèè - -------------------------------------------------------------------------- - cartesian2d 2 [x,y] Äåêàðòîâû 2D êîîðäèíàòû - polar 2 [r,phi] Ïîëÿðíûå êîîðäèíàòû - elliptic 2 [u,v] Ýëëèïòè÷åñêèå êîîðäèíàòû - confocalelliptic 2 [u,v] Êîíôîêàëüíûå ýëëèïòè÷åñêèå - bipolar 2 [u,v] Áèïîëÿðíûå êîîðäèíàòû - parabolic 2 [u,v] Ïàðàáîëè÷åñêèå êîîðäèíàòû - cartesian3d 3 [x,y,z] Äåêàðòîâà 3D ñèñòåìà êîîðäèíàò - polarcylindrical 3 [r,theta,z] Öèëèíäðè÷åñêèå êîîðäèíàòû - ellipticcylindrical 3 [u,v,z] Ýëëèïòè÷åñêèå 2D ñ öèëèíðîì z - confocalellipsoidal 3 [u,v,w] Êîíôîêàëüíûå ýëëèïñîèäàëüíûå - bipolarcylindrical 3 [u,v,z] Áèïîëÿðíûå 2D ñ öèëèíäðîì z - paraboliccylindrical 3 [u,v,z] Ïàðàáîëè÷åñêèå 2D ñ öèëèíäðîì z - paraboloidal 3 [u,v,phi] Ïàðàáîëîèäíûå êîîðäèíàòû - conical 3 [u,v,w] Êîíè÷åñêèå êîîðäèíàòû - toroidal 3 [u,v,phi] Òîðîèäàëüíûå êîîðäèíàòû - spherical 3 [r,theta,phi] Ñôåðè÷åñêèå êîîðäèíàòû - oblatespheroidal 3 [u,v,phi] Ñæàòûå ñôåðîèäàëüíûå - oblatespheroidalsqrt 3 [u,v,phi] - prolatespheroidal 3 [u,v,phi] Âûòÿíóòûå ñôåðîèäàëüíûå - prolatespheroidalsqrt 3 [u,v,phi] - ellipsoidal 3 [r,theta,phi] Ýëëèïñîèäàëüíûå êîîðäèíàòû - cartesian4d 4 [x,y,z,t] Äåêàðòîâû 4D êîîðäèíàòû - spherical4d 4 [r,theta,eta,phi] Ñôåðè÷åñêèå 4D êîîðäèíàòû - exteriorschwarzschild 4 [t,r,theta,phi] Ìåòðèêà Øâàðöøèëüäà - interiorschwarzschild 4 [t,z,u,v] Âíóòðåíÿÿ ìåòðèêà Øðàðöøèëüäà - kerr_newman 4 [t,r,theta,phi] Ìåòðèêà Êåððà-Íüþìàíà + Ñèìâîë Dim Êîîðäèíàòû Îïèñàíèå/êîììåíòàðèè + ------------------------------------------------------------------ + cartesian2d 2 [x,y] Äåêàðòîâû 2D êîîðäèíàòû + polar 2 [r,phi] Ïîëÿðíûå êîîðäèíàòû + elliptic 2 [u,v] Ýëëèïòè÷åñêèå + êîîðäèíàòû + confocalelliptic 2 [u,v] Êîíôîêàëüíûå + ýëëèïòè÷åñêèå + bipolar 2 [u,v] Áèïîëÿðíûå êîîðäèíàòû + parabolic 2 [u,v] Ïàðàáîëè÷åñêèå + êîîðäèíàòû + cartesian3d 3 [x,y,z] Äåêàðòîâà 3D ñèñòåìà + êîîðäèíàò + polarcylindrical 3 [r,theta,z] Öèëèíäðè÷åñêèå + êîîðäèíàòû + ellipticcylindrical 3 [u,v,z] Ýëëèïòè÷åñêèå 2D + ñ öèëèíðîì z + confocalellipsoidal 3 [u,v,w] Êîíôîêàëüíûå + ýëëèïñîèäàëüíûå + bipolarcylindrical 3 [u,v,z] Áèïîëÿðíûå 2D + ñ öèëèíäðîì z + paraboliccylindrical 3 [u,v,z] Ïàðàáîëè÷åñêèå 2D + ñ öèëèíäðîì z + paraboloidal 3 [u,v,phi] Ïàðàáîëîèäíûå + êîîðäèíàòû + conical 3 [u,v,w] Êîíè÷åñêèå êîîðäèíàòû + toroidal 3 [u,v,phi] Òîðîèäàëüíûå êîîðäèíàòû + spherical 3 [r,theta,phi] Ñôåðè÷åñêèå êîîðäèíàòû + oblatespheroidal 3 [u,v,phi] Ñæàòûå ñôåðîèäàëüíûå + oblatespheroidalsqrt 3 [u,v,phi] + prolatespheroidal 3 [u,v,phi] Âûòÿíóòûå ñôåðîèäàëüíûå + prolatespheroidalsqrt 3 [u,v,phi] + ellipsoidal 3 [r,theta,phi] Ýëëèïñîèäàëüíûå + êîîðäèíàòû + cartesian4d 4 [x,y,z,t] Äåêàðòîâû 4D êîîðäèíàòû + spherical4d 4 [r,theta,eta,phi] Ñôåðè÷åñêèå 4D + êîîðäèíàòû + exteriorschwarzschild 4 [t,r,theta,phi] Ìåòðèêà Øâàðöøèëüäà + interiorschwarzschild 4 [t,z,u,v] Âíóòðåíÿÿ ìåòðèêà + Øðàðöøèëüäà + kerr_newman 4 [t,r,theta,phi] Ìåòðèêà Êåððà-Íüþìàíà @end example @@ -239,11 +252,13 @@ r*sin(theta),[r,theta,phi]]); (%o3) done (%i4) fri; - [ cos(phi) cos(theta) - cos(phi) r sin(theta) - sin(phi) r cos(theta) ] - [ ] -(%o4) [ sin(phi) cos(theta) - sin(phi) r sin(theta) cos(phi) r cos(theta) ] - [ ] - [ sin(theta) r cos(theta) 0 ] +(%o4) + [cos(phi)cos(theta) -cos(phi) r sin(theta) -sin(phi) r cos(theta)] + [ ] + [sin(phi)cos(theta) -sin(phi) r sin(theta) cos(phi) r cos(theta)] + [ ] + [ sin(theta) r cos(theta) 0 ] + (%i5) cmetric(); (%o5) false (%i6) lg:trigsimp(lg); @@ -524,7 +539,8 @@ (%o3) true (%i4) ct_coords:[t,r,theta,phi]; (%o4) [t, r, theta, phi] -(%i5) lg:matrix([-1,0,0,0],[0,1,0,0],[0,0,r^2,0],[0,0,0,r^2*sin(theta)^2]); +(%i5) lg:matrix([-1,0,0,0],[0,1,0,0],[0,0,r^2,0], + [0,0,0,r^2*sin(theta)^2]); [ - 1 0 0 0 ] [ ] [ 0 1 0 0 ] @@ -545,15 +561,15 @@ (%i7) depends(l,r); (%o7) [l(r)] (%i8) lg:lg+l*h; - [ h11 l - 1 0 0 0 ] - [ ] - [ 0 h22 l + 1 0 0 ] - [ ] -(%o8) [ 2 ] - [ 0 0 r + h33 l 0 ] - [ ] - [ 2 2 ] - [ 0 0 0 r sin (theta) + h44 l ] + [ h11 l - 1 0 0 0 ] + [ ] + [ 0 h22 l + 1 0 0 ] + [ ] +(%o8) [ 2 ] + [ 0 0 r + h33 l 0 ] + [ ] + [ 2 2 ] + [ 0 0 0 r sin (theta) + h44 l ] (%i9) cmetric(false); (%o9) done (%i10) einstein(false); @@ -621,11 +637,9 @@ (%o22) - (((h11 h22 - h11 ) (l ) r - 2 h33 l r ) sin (theta) r r r - 2 2 4 2 - - 2 h44 l r - h33 h44 (l ) )/(4 r sin (theta)) - r r r - - + 2 2 4 2 + - 2 h44 l r - h33 h44 (l ) )/(4 r sin (theta)) + r r r @end example @@ -732,25 +746,25 @@ (%i6) nptetrad(true); (%t6) np = - [ sqrt(r - 2 m) sqrt(r) ] - [ --------------- --------------------- 0 0 ] - [ sqrt(2) sqrt(r) sqrt(2) sqrt(r - 2 m) ] - [ ] - [ sqrt(r - 2 m) sqrt(r) ] - [ --------------- - --------------------- 0 0 ] - [ sqrt(2) sqrt(r) sqrt(2) sqrt(r - 2 m) ] - [ ] - [ r %i r sin(theta) ] - [ 0 0 ------- --------------- ] - [ sqrt(2) sqrt(2) ] - [ ] - [ r %i r sin(theta) ] - [ 0 0 ------- - --------------- ] - [ sqrt(2) sqrt(2) ] +[ sqrt(r - 2 m) sqrt(r) ] +[--------------- --------------------- 0 0 ] +[sqrt(2) sqrt(r) sqrt(2) sqrt(r - 2 m) ] +[ ] +[ sqrt(r - 2 m) sqrt(r) ] +[--------------- - --------------------- 0 0 ] +[sqrt(2) sqrt(r) sqrt(2) sqrt(r - 2 m) ] +[ ] +[ r %i r sin(theta) ] +[ 0 0 ------- --------------- ] +[ sqrt(2) sqrt(2) ] +[ ] +[ r %i r sin(theta)] +[ 0 0 ------- - ---------------] +[ sqrt(2) sqrt(2) ] - sqrt(r) sqrt(r - 2 m) -(%t7) npi = matrix([- ---------------------, ---------------, 0, 0], - sqrt(2) sqrt(r - 2 m) sqrt(2) sqrt(r) + sqrt(r) sqrt(r - 2 m) +(%t7) npi = matrix([- ---------------------,---------------, 0, 0], + sqrt(2) sqrt(r - 2 m) sqrt(2) sqrt(r) sqrt(r) sqrt(r - 2 m) [- ---------------------, - ---------------, 0, 0], @@ -888,7 +902,8 @@ (%o2) true (%i3) dim:4; (%o3) 4 -(%i4) lg:matrix([a,0,0,0],[0,x^2,0,0],[0,0,x^2*sin(y)^2,0],[0,0,0,-d]); +(%i4) lg:matrix([a, 0, 0, 0], [ 0, x^2, 0, 0], + [0, 0, x^2*sin(y)^2, 0], [0,0,0,-d]); [ a 0 0 0 ] [ ] [ 2 ] @@ -908,12 +923,12 @@ (%o8) done (%i9) findde(ein,2); 2 -(%o9) [d x - a d + d, 2 a d d x - a (d ) x - a d d x + 2 a d d - x x x x x x x +(%o9) [d x - a d + d, 2 a d d x - a (d ) x - a d d x + x x x x x x - 2 2 - - 2 a d , a x + a - a] - x x + 2 2 + + 2 a d d - 2 a d , a x + a - a] + x x x (%i10) deindex; (%o10) [[1, 1], [2, 2], [4, 4]] @@ -1079,23 +1094,23 @@ (%i4) riemann(false); (%o4) done (%i5) cdisplay(riem); - [ 0 0 0 0 ] - [ ] - [ 2 ] - [ 3 m (r - 2 m) m 2 m ] - [ 0 - ------------- + -- - ---- 0 0 ] - [ 4 3 4 ] - [ r r r ] - [ ] - riem = [ m (r - 2 m) ] - 1, 1 [ 0 0 ----------- 0 ] - [ 4 ] - [ r ] - [ ] - [ m (r - 2 m) ] - [ 0 0 0 ----------- ] - [ 4 ] - [ r ] + [ 0 0 0 0 ] + [ ] + [ 2 ] + [ 3 m (r - 2 m) m 2 m ] + [ 0 - ------------- + -- - ---- 0 0 ] + [ 4 3 4 ] + [ r r r ] + [ ] +riem = [ m (r - 2 m) ] + 1, 1 [ 0 0 ----------- 0 ] + [ 4 ] + [ r ] + [ ] + [ m (r - 2 m) ] + [ 0 0 0 ----------- ] + [ 4 ] + [ r ] [ 2 m (r - 2 m) ] [ 0 ------------- 0 0 ] @@ -1141,22 +1156,22 @@ [ ] [ 0 0 0 0 ] - [ 2 m ] - [ ------------ 0 0 0 ] - [ 2 ] - [ r (r - 2 m) ] - [ ] - [ 0 0 0 0 ] - [ ] - riem = [ m ] - 2, 2 [ 0 0 - ------------ 0 ] - [ 2 ] - [ r (r - 2 m) ] - [ ] - [ m ] - [ 0 0 0 - ------------ ] - [ 2 ] - [ r (r - 2 m) ] + [ 2 m ] + [ ------------ 0 0 0 ] + [ 2 ] + [ r (r - 2 m) ] + [ ] + [ 0 0 0 0 ] + [ ] + riem = [ m ] + 2, 2 [ 0 0 - ------------ 0 ] + [ 2 ] + [ r (r - 2 m) ] + [ ] + [ m ] + [ 0 0 0 - ------------ ] + [ 2 ] + [ r (r - 2 m) ] [ 0 0 0 0 ] [ ] @@ -1257,22 +1272,22 @@ [ 0 0 - --------------- 0 ] [ r ] - [ 2 ] - [ m sin (theta) ] - [ - ------------- 0 0 0 ] - [ r ] - [ ] - [ 2 ] - [ m sin (theta) ] - riem = [ 0 - ------------- 0 0 ] - 4, 4 [ r ] - [ ] - [ 2 ] - [ 2 m sin (theta) ] - [ 0 0 --------------- 0 ] - [ r ] - [ ] - [ 0 0 0 0 ] + [ 2 ] + [ m sin (theta) ] + [ - ------------- 0 0 0 ] + [ r ] + [ ] + [ 2 ] + [ m sin (theta) ] +riem = [ 0 - ------------- 0 0 ] + 4, 4 [ r ] + [ ] + [ 2 ] + [ 2 m sin (theta) ] + [ 0 0 --------------- 0 ] + [ r ] + [ ] + [ 0 0 0 0 ] (%o5) done @@ -1559,15 +1574,18 @@ @code{ctensor} (íå ñëåäóåò èõ ïåðåîïðåäåëÿòü): @example - Name Description - --------------------------------------- - _lg() Ïðèñâàèâàåòñÿ ìàññèâó lfg åñëè èñïîëüçóåòñÿ òåòðàäíàÿ - ìåòðèêà; ïî óìîë÷àíèþ ïðèñâàèâàåòñÿ ìàññèâó lg - _ug() Ïðèñâàèâàåòñÿ ìàññèâó ufg åñëè èñïîëüçóåòñÿ òåòðàäíàÿ - ìåòðèêà; ïî óìîë÷àíèþ ïðèñâàèâàåòñÿ ìàññèâó ug + Íàèìåíîâàíèå Îïèñàíèå + ---------------------------------------------------------------- + _lg() Ïðèñâàèâàåòñÿ ìàññèâó lfg åñëè èñïîëüçóåòñÿ + òåòðàäíàÿ ìåòðèêà; ïî óìîë÷àíèþ ïðèñâàèâàåòñÿ + ìàññèâó lg + _ug() Ïðèñâàèâàåòñÿ ìàññèâó ufg åñëè èñïîëüçóåòñÿ + òåòðàäíàÿ ìåòðèêà; ïî óìîë÷àíèþ ïðèñâàèâàåòñÿ + ìàññèâó ug cleanup() Óäàëÿåò ýëåìåíòû drom ñïèñêà deindex contract4() èñïîëüçóåòñÿ ôóíêöèåé psi() - filemet() èñïîëüçóåòñÿ ôóíêöèåé csetup() ïðè ÷òåíèè ìåòðèêè èç ôàéëà + filemet() èñïîëüçóåòñÿ ôóíêöèåé csetup() ïðè ÷òåíèè ìåòðèêè + èç ôàéëà findde1() èñïîëüçóåòñÿ ôóíêöèåé findde() findde2() èñïîëüçóåòñÿ ôóíêöèåé findde() findde3() èñïîëüçóåòñÿ ôóíêöèåé findde() @@ -1577,13 +1595,17 @@ setflags() èñïîëüçóåòñÿ ôóíêöèåé init_ctensor() readvalue() resimp() - sermet() èñïîëüçóåòñÿ ôóíêöèåé csetup() äëÿ ââîäà ìåòðèêè â âèäå - Òýéëîðîâñêîãî ðàçëîæåíèÿ + sermet() èñïîëüçóåòñÿ ôóíêöèåé csetup() äëÿ ââîäà ìåòðèêè + â âèäå ðàçëîæåíèÿ â ðÿä Òýéëîðà txyzsum() - tmetric() Ìåòðèêà òåòðàäû, èñïîëüçóåòñÿ ôóíêöèåé cmetric(), åñëè cframe_flag:true - triemann() Òåíçîð Ðèìàíà â òåòðàäíîì ïðåäñòàâëåíèè, èñïîëüçóåòñÿ åñëè cframe_flag:true - tricci() Òåíçîð Ðè÷÷è â òåòðàäíîì ïðåäñòàâëåíèè, èñïîëüçóåòñÿ åñëè cframe_flag:true - trrc() Êîýôôèöèåíòû âðàùåíèÿ Ðè÷÷è, èñïîëüçóåòñÿ ôóíêöèåé christof() + tmetric() Ìåòðèêà òåòðàäû, èñïîëüçóåòñÿ ôóíêöèåé cmetric(), + åñëè cframe_flag:true + triemann() Òåíçîð Ðèìàíà â òåòðàäíîì ïðåäñòàâëåíèè, + èñïîëüçóåòñÿ åñëè cframe_flag:true + tricci() Òåíçîð Ðè÷÷è â òåòðàäíîì ïðåäñòàâëåíèè, + èñïîëüçóåòñÿ åñëè cframe_flag:true + trrc() Êîýôôèöèåíòû âðàùåíèÿ Ðè÷÷è, èñïîëüçóåòñÿ + ôóíêöèåé christof() yesp() @end example @@ -1596,9 +1618,10 @@ @example - New Name Old Name Description - -------------------------------------------------------------------------- - ctaylor() DLGTAYLOR() Òýéëîðîâñêîå ðàçëîæåíèå âûðàæåíèÿ + Íîâîå èìÿ Ñòàòîå èìÿ Îïèñàíèå + ----------------------------------------------------------------- + ctaylor() DLGTAYLOR() Ðàçëîæåíèå âûðàæåíèÿ â ðÿä + Òýéëîðà lgeod[] EM Óðàâíåíèÿ ãåîäåçè÷åñêèõ ein[] G[] Ñìåøàííûé òåíçîð Ýéíøòåéíà ric[] LR[] Ñìåøàííûé òåíçîð Ðè÷÷è @@ -1608,17 +1631,22 @@ ct_coords OMEGA ìåòðè÷åñêèå êîîðäèíàòû ctayvar PARAM Ïåðåìåííàÿ ðÿäà Òýéëîðà lriem[] R[] - uriemann() RAISERIEMANN() Âû÷èñëÿåò êîíòðàâàðèàíòíûé òåíçîð Ðèìàíà - ratriemann RATRIEMAN Ðàöèîíàëüíîå óïðîùåíèå òåíçîðà Ðèìàíà + uriemann() RAISERIEMANN() Âû÷èñëÿåò êîíòðàâàðèàíòíûé òåíçîð + Ðèìàíà + ratriemann RATRIEMAN Ðàöèîíàëüíîå óïðîùåíèå òåíçîðà + Ðèìàíà uric[] RICCI[] Êîíòðàâàðèàíòíûé òåíçîð Ðè÷÷è - uricci() RICCICOM() Âû÷èñëÿåò êîíòðàâàðèàíòíûé òåíçîð Ðè÷÷è + uricci() RICCICOM() Âû÷èñëÿåò êîíòðàâàðèàíòíûé òåíçîð + Ðè÷÷è cmetric() SETMETRIC() Îïðåäåëÿåò ìåòðèêó - ctaypt TAYPT Öåíòðàëüíàÿ òî÷êà îêðåñòíîñòè ðÿäà Òýéëîðà - ctayswitch TAYSWITCH êëþ÷ óñòàíàâëèâàþùèé èñïîëüçîâàòü ëè - ðÿäû Òýéëîðà â ìåòðèêå - csetup() TSETUP() Âûçûâàåò íà÷àëî èíòåðàêòèâíîãî ðåæèìà - çàäàíèÿ ìåòðèêè è ïð. - ctransform() TTRANSFORM() Èíòåðàêòèâíîå ïðåîáðàçîâàíèå êîîðäèíàò + ctaypt TAYPT Öåíòðàëüíàÿ òî÷êà îêðåñòíîñòè ðÿäà + Òýéëîðà + ctayswitch TAYSWITCH Êëþ÷, óñòàíàâëèâàþùèé èñïîëüçîâàòü + ëè ðÿäû Òýéëîðà â ìåòðèêå + csetup() TSETUP() Âûçûâàåò íà÷àëî èíòåðàêòèâíîãî + ðåæèìà çàäàíèÿ ìåòðèêè è ïð. + ctransform() TTRANSFORM() Èíòåðàêòèâíîå ïðåîáðàçîâàíèå + êîîðäèíàò uriem[] UR[] Êîíòðàâàðèàíòíûé òåíçîð Ðèìàíà weyl[] W[] Òåíçîð Âåéëÿ ðàíãà (3,1) |