Output of TraditionalForm for Exp
in [Mathematica]
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From: fizzy on 13 Sep 2009 08:01 Diff Eqn: 1/a^2 D[T[t],t] + b D[T[t],t] + c^2 T[t] == 0 Solution to this gives the following in TraditionalForm = output:....V7.01.... C1 Exp[1/2 t (a^2 (-b) - a Sqrt[a^2 b^2 -4 c^2])] + C2 e^(1/2 t (Sqrt[a^2 b^2 -4 c^2] - a^2 b)]) ..... where the second part, i.e. e^( )...the exponent part, ( ) , is actuallly on the same line as the ^ as it would be if I used the power exponent from the Basic Math pallette..... Q:....why this difference in output??....why arent both 'e' raised to the power of, etc??... I realize I can fix this with a rule and HoldForm but why doesnt TradForm use only one of the output forms especially in the same output? thanks....jerry blimbaum
From: Bob Hanlon on 14 Sep 2009 07:10 I get a different (simpler) result. $Version 7.0 for Mac OS X x86 (64-bit) (February 19, 2009) eqn = 1/a^2 D[T[t], t] + b D[T[t], t] + c^2 T[t] == 0; soln = T[t] /. DSolve[eqn, T[t], t][[1]] C[1]/E^((a^2*c^2*t)/(a^2*b + 1)) eqn /. NestList[D[#, t] &, T[t] -> soln, 1] // Simplify True Recommend that you start with a clean kernel. Bob Hanlon ---- fizzy <fizzycist(a)knology.net> wrote: ============= Diff Eqn: 1/a^2 D[T[t],t] + b D[T[t],t] + c^2 T[t] == 0 Solution to this gives the following in TraditionalForm = output:....V7.01.... C1 Exp[1/2 t (a^2 (-b) - a Sqrt[a^2 b^2 -4 c^2])] + C2 e^(1/2 t (Sqrt[a^2 b^2 -4 c^2] - a^2 b)]) ..... where the second part, i.e. e^( )...the exponent part, ( ) , is actuallly on the same line as the ^ as it would be if I used the power exponent from the Basic Math pallette..... Q:....why this difference in output??....why arent both 'e' raised to the power of, etc??... I realize I can fix this with a rule and HoldForm but why doesnt TradForm use only one of the output forms especially in the same output? thanks....jerry blimbaum
From: Murray Eisenberg on 14 Sep 2009 07:11 I don't get that with Mathematica 7.0.1: InputForm[ T[t] /. First @ DSolve[1/a^2 D[T[t], t] + b D[T[t], t] + c^2 T[t] == 0, T[t], t] ] C[1]/E^((a^2*c^2*t)/(1 + a^2*b)) I have to show InputForm since the standard OutputForm, obviously, uses the usual 2D layout. And TraditionalForm shows essentially the same thing (with the stylized e instead of E, and of course all letters in Italic). fizzy wrote: > Diff Eqn: 1/a^2 D[T[t],t] + b D[T[t],t] + c^2 T[t] == 0 > > Solution to this gives the following in TraditionalForm = > output:....V7.01.... > > C1 Exp[1/2 t (a^2 (-b) - a Sqrt[a^2 b^2 -4 c^2])] + C2 e^(1/2 t (Sqrt[a^2 b^2 -4 c^2] - a^2 b)]) ..... > > where the second part, i.e. e^( )...the exponent part, ( ) , is actuallly on the same line as the ^ as it would be if I used the power exponent from the Basic Math pallette..... > > > Q:....why this difference in output??....why arent both 'e' raised to the power of, etc??... > > I realize I can fix this with a rule and HoldForm but why doesnt TradForm use only one of the output forms especially in the same output? > > thanks....jerry blimbaum > -- Murray Eisenberg murray(a)math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305
From: fizzy on 14 Sep 2009 07:12 oops...I goofed...I meant 1/a^2 D[T[t],{t,2}] with the rest the same.... I tried it again with a fresh kernel and, for TraditionalForm, I still get the same form of output of Exp and e^.......however, when I asked for the form of the output in StandardForm then I get the form e^ for the outputs.... jerry blimbaum ----- Original Message ----- From: Bob Hanlon To: fizzy ; mathgroup(a)smc.vnet.net Sent: Sunday, September 13, 2009 8:14 AM Subject: Re: Output of TraditionalForm for Exp I get a different (simpler) result. $Version 7.0 for Mac OS X x86 (64-bit) (February 19, 2009) eqn = 1/a^2 D[T[t], t] + b D[T[t], t] + c^2 T[t] == 0; soln = T[t] /. DSolve[eqn, T[t], t][[1]] C[1]/E^((a^2*c^2*t)/(a^2*b + 1)) eqn /. NestList[D[#, t] &, T[t] -> soln, 1] // Simplify True Recommend that you start with a clean kernel. Bob Hanlon ---- fizzy <fizzycist(a)knology.net> wrote: ============= Diff Eqn: 1/a^2 D[T[t],t] + b D[T[t],t] + c^2 T[t] == 0 Solution to this gives the following in TraditionalForm = output:....V7.01.... C1 Exp[1/2 t (a^2 (-b) - a Sqrt[a^2 b^2 -4 c^2])] + C2 e^(1/2 t = (Sqrt[a^2 b^2 -4 c^2] - a^2 b)]) ..... where the second part, i.e. e^( )...the exponent part, ( ) , is = actuallly on the same line as the ^ as it would be if I used the power = exponent from the Basic Math pallette..... Q:....why this difference in output??....why arent both 'e' raised to = the power of, etc??... I realize I can fix this with a rule and HoldForm but why doesnt = TradForm use only one of the output forms especially in the same output? thanks....jerry blimbaum
From: DrMajorBob on 15 Sep 2009 04:24 Or... T[t] /. First@ DSolve[1/a^2 D[T[t], t] + b D[T[t], t] + c^2 T[t] == 0, T[t], t] E^(-((a^2 c^2 t)/(1 + a^2 b))) C[1] Bobby On Mon, 14 Sep 2009 06:11:56 -0500, Murray Eisenberg <murray(a)math.umass.edu> wrote: > I don't get that with Mathematica 7.0.1: > > InputForm[ T[t] /. First @ > DSolve[1/a^2 D[T[t], t] + b D[T[t], t] + c^2 T[t] == 0, T[t], t] > ] > > C[1]/E^((a^2*c^2*t)/(1 + a^2*b)) > > I have to show InputForm since the standard OutputForm, obviously, uses > the usual 2D layout. And TraditionalForm shows essentially the same > thing (with the stylized e instead of E, and of course all letters in > Italic). > > > fizzy wrote: >> Diff Eqn: 1/a^2 D[T[t],t] + b D[T[t],t] + c^2 T[t] == 0 >> >> Solution to this gives the following in TraditionalForm = >> output:....V7.01.... >> >> C1 Exp[1/2 t (a^2 (-b) - a Sqrt[a^2 b^2 -4 c^2])] + C2 e^(1/2 t >> (Sqrt[a^2 b^2 -4 c^2] - a^2 b)]) ..... >> >> where the second part, i.e. e^( )...the exponent part, ( ) , is >> actuallly on the same line as the ^ as it would be if I used the power >> exponent from the Basic Math pallette..... >> >> >> Q:....why this difference in output??....why arent both 'e' raised to >> the power of, etc??... >> >> I realize I can fix this with a rule and HoldForm but why doesnt >> TradForm use only one of the output forms especially in the same output? >> >> thanks....jerry blimbaum >> > -- DrMajorBob(a)yahoo.com
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