(*^ ::[ frontEndVersion = "Microsoft Windows Mathematica Notebook Front End Version 2.2"; microsoftWindowsStandardFontEncoding; fontset = title, "Arial", 14, L0, center, nohscroll, bold; fontset = subtitle, "Arial", 18, L0, center, nohscroll, bold; fontset = subsubtitle, "Arial", 14, L0, center, nohscroll, bold; fontset = section, "Arial", 14, L0, bold, grayBox; fontset = subsection, "Arial", 12, L0, bold, blackBox; fontset = subsubsection, "Arial", 10, L0, bold, whiteBox; fontset = text, "Arial", 12, L0; fontset = smalltext, "Arial", 10, L0; fontset = input, "Arial", 10, L0, nowordwrap, bold, R65280; fontset = output, "Courier New", 12, L0, nowordwrap, bold; fontset = message, "Courier New", 10, L0, nowordwrap, R65280; fontset = print, "Courier New", 10, L0, nowordwrap; fontset = info, "Courier New", 10, L0, nowordwrap; fontset = postscript, "Courier New", 8, L0, nowordwrap; fontset = name, "Arial", 10, L0, nohscroll, italic, R32768, B32768; fontset = header, "Times New Roman", 10, L0, right, nohscroll; fontset = footer, "Times New Roman", 10, L0, right, nohscroll; fontset = help, "Arial", 10, L0, nohscroll; fontset = clipboard, "Arial", 12, L0, nohscroll; fontset = completions, "Arial", 12, L0, nowordwrap, nohscroll; fontset = graphics, "Courier New", 10, L0, nowordwrap, nohscroll; fontset = special1, "Arial", 12, L0, nowordwrap, nohscroll; fontset = special2, "Arial", 12, L0, center, nowordwrap, nohscroll; fontset = special3, "Arial", 12, L0, right, nowordwrap, nohscroll; fontset = special4, "Arial", 12, L0, nowordwrap, nohscroll; fontset = special5, "Arial", 12, L0, nowordwrap, nohscroll; fontset = leftheader, "Arial", 12, L0, nowordwrap, nohscroll; fontset = leftfooter, "Arial", 12, L0, nowordwrap, nohscroll; fontset = reserved1, "Courier New", 10, L0, nowordwrap, nohscroll;] :[font = title; inactive; nohscroll; center; ] Mm2 95 mixmr :[font = input; startGroup; nowordwrap; ] < Cos[theta], Psi ->\ Sin[psi]); :[font = input; startGroup; nowordwrap; ] grcalc[S[bdn,bup]] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] Created a definition for S[bdn, bup] Created a definition for rot[bdn, bup, bdn] For the mix1 metric. Calculated eta[bdn, bdn]( 0.06 sec.) Calculated e[bup, dn]( 0.11 sec.) Calculated g[dn, dn]( 0.28 sec.) Calculated g[up, up]( 2.52 sec.) Calculated e[bdn, up]( 0.77 sec.) Calculated lambda[bdn, bdn, bdn]( 1.42 sec.) Calculated rot[bdn, bdn, bdn]( 0.28 sec.) Calculated rot[bdn, bup, bdn]( 0.55 sec.) Calculated R[bdn, bdn, bdn, bdn]( 1.1 sec.) Calculated R[bdn, bdn]( 0.44 sec.) Calculated Ricciscalar( 0.11 sec.) Calculated S[bdn, bdn]( 0.33 sec.) Calculated S[bdn, bup]( 0.33 sec.) CPU Time = 8.51 sec. :[font = input; startGroup; nowordwrap; ] grmap[Simplify,$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Simplify to S[bdn, bup] CPU Time = 2.36 sec. :[font = input; startGroup; nowordwrap; ] grdisplay[$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. S[bdn, bup] (Theta) 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 c[T] S = (5 E - 3 E - 2 E - 3 E - (Theta) 2 (a[T] + c[T]) 2 (b[T] + c[T]) 2 E + 6 E + 4 a'[T] b'[T] + 4 a'[T] c'[T] + 2 (a[T] + b[T] + c[T]) 4 b'[T] c'[T] + 4 a''[T] - 4 b''[T] - 4 c''[T]) / (8 E ) (Phi) 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 c[T] S = (-3 E + 5 E - 2 E - 3 E + (Phi) 2 (a[T] + c[T]) 2 (b[T] + c[T]) 6 E - 2 E + 4 a'[T] b'[T] + 4 a'[T] c'[T] + 2 (a[T] + b[T] + c[T]) 4 b'[T] c'[T] - 4 a''[T] + 4 b''[T] - 4 c''[T]) / (8 E ) (Psi) 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 c[T] S = (-3 E - 3 E + 6 E + 5 E - (Psi) 2 (a[T] + c[T]) 2 (b[T] + c[T]) 2 E - 2 E + 4 a'[T] b'[T] + 4 a'[T] c'[T] + 2 (a[T] + b[T] + c[T]) 4 b'[T] c'[T] - 4 a''[T] - 4 b''[T] + 4 c''[T]) / (8 E ) (T) 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 c[T] S = (E + E - 2 E + E - (T) 2 (a[T] + c[T]) 2 (b[T] + c[T]) 2 E - 2 E - 12 a'[T] b'[T] - 12 a'[T] c'[T] - 2 (a[T] + b[T] + c[T]) 12 b'[T] c'[T] + 4 a''[T] + 4 b''[T] + 4 c''[T]) / (8 E ) :[font = input; startGroup; nowordwrap; ] grmap[Factor,Ricciscalar] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Factor to Ricciscalar CPU Time = 0.22 sec. :[font = input; startGroup; nowordwrap; ] grdisplay[$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Ricci scalar -2 a[T] - 2 b[T] - 2 c[T] 4 a[T] 4 b[T] 2 a[T] + 2 b[T] R = (E (-E - E + 2 E - 4 c[T] 2 a[T] + 2 c[T] 2 b[T] + 2 c[T] E + 2 E + 2 E - 4 a'[T] b'[T] - 4 a'[T] c'[T] - 4 b'[T] c'[T] + 4 a''[T] + 4 b''[T] + 4 c''[T])) / 2 :[font = input; startGroup; nowordwrap; ] grdefine["SS{(a) ^(b)}",{},"S{(a) ^(c)}*S{(c) ^(b)}"] :[font = message; inactive; formatted; output; endGroup; nowordwrap; ] Can't Format Cell ;[o] grii::create: Created a definition for SS[bdn, bup] :[font = input; startGroup; nowordwrap; ] grcalc[SS[bdn,bup]] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Calculated SS[bdn, bup]( 0.33 sec.) CPU Time = 0.49 sec. :[font = input; startGroup; nowordwrap; ] grmap[Simplify,$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Simplify to SS[bdn, bup] CPU Time = 3.02 sec. :[font = input; startGroup; nowordwrap; ] grdefine["S1",{},"SS{(a) ^(a)}"] :[font = message; inactive; formatted; output; endGroup; nowordwrap; ] Can't Format Cell ;[o] grii::create: Created a definition for S1 :[font = input; startGroup; nowordwrap; ] grdefine["S2",{},"SS{(a) ^(b)}*S{(b) ^(a)}"] :[font = message; inactive; formatted; output; endGroup; nowordwrap; ] Can't Format Cell ;[o] grii::create: Created a definition for S2 :[font = input; startGroup; nowordwrap; ] grdefine["S3",{},"SS{(a) ^(b)}*SS{(b) ^(a)}"] :[font = message; inactive; formatted; output; endGroup; nowordwrap; ] Can't Format Cell ;[o] grii::create: Created a definition for S3 :[font = input; startGroup; nowordwrap; ] grcalc[{S1,S2,S3}] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Calculated S1( 0.33 sec.) Calculated S2( 1.37 sec.) Calculated S3( 6.09 sec.) CPU Time = 8.02 sec. :[font = input; startGroup; nowordwrap; ] grdisplay[$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. S1 S1 = 17616 bytes. Exceeds DisplayLimit S2 S2 = 78824 bytes. Exceeds DisplayLimit S3 S3 = 366420 bytes. Exceeds DisplayLimit :[font = input; startGroup; nowordwrap; ] grmap[Factor,S1] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Factor to S1 CPU Time = 0.6 sec. :[font = input; startGroup; nowordwrap; ] grmap[Simplify,$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Simplify to S1 CPU Time = 3.57 sec. :[font = input; startGroup; nowordwrap; ] grmap[Factor,S2] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Factor to S2 CPU Time = 2.26 sec. :[font = input; startGroup; nowordwrap; ] grmap[Simplify,S2] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Simplify to S2 CPU Time = 2.2 sec. :[font = input; startGroup; nowordwrap; ] grdisplay[S2] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. S2 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 c[T] 2 (a[T] + c[T]) S2 = (3 (3 E - E - 2 E - E - 2 E + 2 (b[T] + c[T]) 2 E - 4 a'[T] b'[T] - 4 a'[T] c'[T] - 4 b'[T] c'[T] + 4 a''[T] 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 c[T] ) (-E + 3 E - 2 E - E + 2 (a[T] + c[T]) 2 (b[T] + c[T]) 2 E - 2 E - 4 a'[T] b'[T] - 4 a'[T] c'[T] - 4 a[T] 4 b[T] 2 (a[T] + b[T]) 4 b'[T] c'[T] + 4 b''[T]) (-E - E + 2 E + 4 c[T] 2 (a[T] + c[T]) 2 (b[T] + c[T]) 3 E - 2 E - 2 E - 4 a'[T] b'[T] - 6 (a[T] + b[T] + c[T]) 4 a'[T] c'[T] - 4 b'[T] c'[T] + 4 c''[T])) / (64 E ) :[font = input; startGroup; nowordwrap; ] grdisplay[S1] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. S1 S1 = 16680 bytes. Exceeds DisplayLimit :[font = input; startGroup; nowordwrap; ] SetOptions[grii,DisplayLimit -> 17000] :[font = output; inactive; formatted; output; endGroup; nowordwrap; ] {DisplayLimit -> 17000, TimeStamp -> True, DefaultSimplification -> Together, Verbose -> True, MetricPath -> "c:/wnmath22/packages/grii/metrics/"} ;[o] {DisplayLimit -> 17000, TimeStamp -> True, DefaultSimplification -> Together, Verbose -> True, MetricPath -> c:/wnmath22/packages/grii/metrics/} :[font = input; nowordwrap; ] grdisplay[$] :[font = input; startGroup; nowordwrap; ] grmap[Factor,S3] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Factor to S3 CPU Time = 12.31 sec. :[font = input; startGroup; nowordwrap; ] grdisplay[S3] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. S3 S3 = 366420 bytes. Exceeds DisplayLimit :[font = input; startGroup; nowordwrap; ] grmap[Simplify,S3] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. Applying Simplify to S3 CPU Time = 107.54 sec. :[font = input; startGroup; nowordwrap; ] grdisplay[$] :[font = print; inactive; formatted; output; endGroup; nowordwrap; ] No Input Form Generated ;[o] For the mix1 metric. S3 S3 = 354468 bytes. Exceeds DisplayLimit :[font = input; startGroup; nowordwrap; ] SetOptions[grii,DisplayLimit -> 360000] :[font = output; inactive; formatted; output; endGroup; nowordwrap; ] {DisplayLimit -> 360000, TimeStamp -> True, DefaultSimplification -> Together, Verbose -> True, MetricPath -> "c:/wnmath22/packages/grii/metrics/"} ;[o] {DisplayLimit -> 360000, TimeStamp -> True, DefaultSimplification -> Together, Verbose -> True, MetricPath -> c:/wnmath22/packages/grii/metrics/} :[font = input; nowordwrap; ] grdisplay[$] :[font = input; startGroup; nowordwrap; ] MaxMemoryUsed[] :[font = output; inactive; formatted; output; endGroup; nowordwrap; ] 3330384 ;[o] 3330384 :[font = input; startGroup; nowordwrap; ] TimeUsed[] :[font = output; inactive; formatted; output; endGroup; nowordwrap; ] 166.29 ;[o] 166.29 ^*)