sage: x = SR.symbol('x')
: x_0 = SR.symbol('x_0')
: logr = SR.symbol('L_x/x_0')
: logr_ex = logr == log(x/x_0)
: latex(logr_ex)
: latex(logr_ex.solve(x)[0])
L_{\mathit{x/x}_{0}} = \log\left(\frac{x}{x_{0}}\right)
x = x_{0} e^{\frac{L_{x}}{x_{0}}}
The above attempt at using a
I agree with Samuel that the numbers involved are huge.
After
sage: xtn,xtd=xt.numerator_denominator()
sage: ytn,ytd=yt.numerator_denominator()
one can see that
xtn ~ - e^(2*t)
xtd ~ e^(2*t)
ytn ~ e^(8*t)
ytd ~ 2*e^(8*t)
However, SageMath has no problems evaluating it:
sage: *for* i in
The expressions for the coordinates involve exp(8*t) and t^24.
sage: exp(8*88.)
5.53751938928459e305
sage: 88.^24
4.65140474534598e46
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Also the following:
> parametric_plot(C, (t,89.0,95.0))
.
verbose 0 (2200: graphics.py, get_minmax_data) ymin was NaN (setting to 0)
verbose 0 (2200: graphics.py, get_minmax_data) ymax was NaN (setting to 0)
> parametric_plot(C, (t,89,95))
.
verbose 0 (2200: graphics.py, get_minmax_data)
Some thing happened after t=89. Is it because of the following two cases:
for T in srange(1,100,1.0):
print(T, float(C(T)[0]), float(C(T)[1]))
.
87.0 -0. 0.5001
88.0 -0. 0.5
89.0 -1.0 0.5
Sorry, my message was incomplete.
So yes, there is a problem.
On Mon, 4 Jul 2022 at 16:14, G. M.-S. wrote:
>
> Hi Gema.
>
> Doing
>
> sage: xt,yt=C[*0*],C[*1*]
>
> sage: xt.taylor(t,oo,*3*)
>
> -6*t^4*e^(-3*t)*log(t)^2 - 3*t*e^(-2*t)*log(t)^2 - 1
>
> sage: yt.taylor(t,oo,*3*)
>
>
Hi Gema.
Doing
sage: xt,yt=C[*0*],C[*1*]
sage: xt.taylor(t,oo,*3*)
-6*t^4*e^(-3*t)*log(t)^2 - 3*t*e^(-2*t)*log(t)^2 - 1
sage: yt.taylor(t,oo,*3*)
1/2*t*e^(-2*t)*log(t)^2 + 1/2*(2*t^4*log(t)^2 + t*log(t)^3)*e^(-3*t) + 1/2
sage:
you see that it converges towards (-1, 1/2) exponentially
Hello,
I've the following curve,
t=var('t')
C=[(-exp(2*t) + (-t^2 - 2*t)*ln(t)^2 - t^6 + 2*exp(t)*t^3)/(exp(2*t) + (t^2
- t)*ln(t)^2 + t^6 - 2*exp(t)*t^3), ((28*t^18 + 60*ln(t)^2*t^14 +
36*ln(t)^4*t^10 - 10*ln(t)^3*t^10 + 4*t^6*ln(t)^6 - 6*ln(t)^5*t^6)*exp(2*t)
+ (-56*t^15 - 80*ln(t)^2*t^11 -
