ASKSAGE: Sage Q&A Forum - Latest question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sat, 19 Oct 2019 05:55:20 -0500False perpendicular bisectorhttps://ask.sagemath.org/question/48426/false-perpendicular-bisector/ Hello, I use the Poincare Disc Model in SAGE and I try to get the perpendicular bisector of a geodesic joining to points in the PD. It gives me a perpendicular geodesic, but it does not pass through the midpoint of my geodesic. I can not upload a screenshot of my situation so it is all I can say. Please help meeecreyesm1992Sat, 19 Oct 2019 05:55:20 -0500https://ask.sagemath.org/question/48426/Convert exponential form to hyperbolic functionshttps://ask.sagemath.org/question/39602/convert-exponential-form-to-hyperbolic-functions/Is there a method to convert expression containing exponentials like (e^a + e^-a) / 2 to hyperbolic functions?
I tried to even call maxima functions directly, but thinks like
`
cosh(a)._maxima_().exponentialize().demoivre()
`
still don't give me `cosh(a)` back but instead return the form in exponentials.TobiasDThu, 16 Nov 2017 06:49:23 -0600https://ask.sagemath.org/question/39602/Solution of ODE expressed with hyperbolic trigonometric functionhttps://ask.sagemath.org/question/34665/solution-of-ode-expressed-with-hyperbolic-trigonometric-function/ With Sage 7.3, consider
t=var('t')
v=function('v')(t)
m, g, h = var('m g h')
assume(m > 0)
assume(g > 0)
assume(h > 0)
sol = desolve(m*diff(v,t) == m*g - h*v**2, v, ivar=t)
show(sol)
sol.solve(v)
The outcomes are
$$\newcommand{\Bold}[1]{\mathbf{#1}}-\frac{m \log\left(\frac{h v\left(t\right) - \sqrt{g h m}}{h v\left(t\right) + \sqrt{g h m}}\right)}{2 \, \sqrt{g h m}} = C + t$$
$$\newcommand{\Bold}[1]{\mathbf{#1}}\left[v\left(t\right) = \frac{\sqrt{g h m} {\left(e^{\left(\frac{2 \, \sqrt{g h m} C}{m} + \frac{2 \, \sqrt{g h m} t}{m}\right)} + 1\right)}}{h {\left(e^{\left(\frac{2 \, \sqrt{g h m} C}{m} + \frac{2 \, \sqrt{g h m} t}{m}\right)} - 1\right)}}\right]$$
Nevermind `desolve` came with an implicit solution I had to further solve by hand but then `solve` missed that the last expression for v(t) is a mere hyperbolic tangent. How would I get the solution in its simpler form?
$$v(t) = \sqrt{\frac{gm}{h}}\ \text{tanh}\left(\sqrt{\frac{gh}{m}}(t + m C)\right)$$
Thanks for any hint!ljboWed, 31 Aug 2016 06:48:17 -0500https://ask.sagemath.org/question/34665/Can Sage verify (some) hyperbolic identities?https://ask.sagemath.org/question/28694/can-sage-verify-some-hyperbolic-identities/ If I enter `bool( cosh(x) == (exp(x)+exp(-x))/2 )`, the output is `False`. This happens with other hyperbolic identities. Is it possible to verify them in Sage? If so, what is the correct way?f9qMRIktzYLGFri, 24 Jul 2015 07:35:00 -0500https://ask.sagemath.org/question/28694/expand hyperbolic trig functionshttps://ask.sagemath.org/question/23546/expand-hyperbolic-trig-functions/ Part of a symbolic expression is
ex = 2*e^(1/2*x)*sinh(1/2*x)
How to substitute sinh(x) with its expansion (e^x-e^(-x))/2 and simplify ex to e^x-1? I have tried all expand and simplify functions.rwsWed, 23 Jul 2014 08:48:08 -0500https://ask.sagemath.org/question/23546/