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13h
comment Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$
@JunhoLee I also just verified it with Rubi, it also gives -Pi/2 or 3 Pi/2 : !Mathematica graphics so I think the symbolic result is correct. May be there is problem with numerical integration.
13h
comment Different results of a definite integral $\int_0^{\cosh ^{-1}(a)} \frac{1}{\sqrt{a^2 \text{sech}^2(x)-1}}\, dx$
@JunhoLee Well, may be, but looking at: r = Integrate[1/Sqrt[-1 + 2^2*Sech[x]^2], x]; Limit[r, x -> ArcCosh[2]] - Limit[r, x -> 0]; N[%] gives -Pi/2 and -Pi/2 is actually the same as 3 Pi/2 However, NIntegrate[1/Sqrt[-1 + 2^2*Sech[x]^2], {x, 0, ArcCosh[2]}] gives Pi/2. So I am not sure. May be someone knows.
15h
comment Can I define an axiomatic (Boolean algebra) system and prove theorems using Mathematica?
Wolfram is working on adding pure math to Mathematica, here is his blog on this computational-knowledge-and-the-future-of-pure-mathematics/ the idea is that one should be able to proof things and do more pure math using Mathematica. Proofs can be generated or checked. But this is for future versions.
20h
comment Buying a new computer (specifically for Mathematica)
get a mac for Mathematica. many at WRI use mac's not PC's. I think due to origin of how Mathematica was created, it is apple first, windows second, and then Linux 5th.
21h
accepted How to check if Integrate solved the integral?
1d
comment How to check if Integrate solved the integral?
@Jens sure. This sounds like a smart way to go about it. I did not think about it.
1d
asked How to check if Integrate solved the integral?
Dec
13
comment about the design of Part related to Association
I found more documentation on part with association. it is all here reference.wolfram.com/language/ref/Part.html about half way down the page. many examples.
Dec
13
comment about the design of Part related to Association
I think I figured it. To obtain the whole part, i.e. (key->value), one must use [[n;;n]] syntax or [[n;;]]. But if you use [[n]] this will only give the value at part n. The reason why [[n;;m]] work for both key,values at both n through m parts, is because of the ;; usage. So to pull both key+value, use ;;, else it will default to only the value at that part.
Dec
13
comment about the design of Part related to Association
I agree. It is not consistent. May be it is a bug?
Dec
13
comment Plot with Mathematica
nice. but no control buttons :)
Dec
12
revised Plot with Mathematica
made axes pi ticks
Dec
12
answered Plot with Mathematica
Dec
12
comment Order of operations
a/bc is always parsed as (a/b)*c, if you know a computer language that parses it as a/(bc) that would be very interesting to know.
Dec
12
comment AbsoluteOptions prints error messages in V10
@gwr I see. I was only using the example provided. For the example given, it did not give an error. There is a new post today on AbsoluteOptions problems also. mathematica.stackexchange.com/questions/68937/… so it seems there is more issue still with this. May be you can post your example as separate question? This will make it easier to track it on its own?
Dec
12
comment Fourier and InverseFourier precision
Chop[x1 - Abs[x1]] gives {0, 0, 0, -1.5136, -1.91785, -0.558831, 0, 0, 0, -1.08804, -1.99998, -1.07315, 0, 0, 0, -0.575807, -1.92279, -1.50197, 0, 0}
Dec
12
comment Solve a differential equation with an integral inside?
@NimblePawn added Laplace method. Not sure why -Sin[t] shows up in the ODE method vs. +Sin[t] in the Laplace now. But these are two methods I know about. The correct answer with zero IC should be the ODE based one. with -sin.
Dec
12
revised Solve a differential equation with an integral inside?
added 276 characters in body
Dec
12
answered Solve a differential equation with an integral inside?
Dec
11
awarded  Revival