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) ymin was NaN (setting to 0)
verbose 0 (2200: graphics.py, get_minmax_data) ymax was NaN (setting to 0)
Regards
Niranjana
On Monday, July 4, 2022 at 8:42:58 PM UTC+5:30 Niranjana K M wrote:
> 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]))
> .....
> 87.0000000000000 -0.9999999999999999 0.5000000000000001
> 88.0000000000000 -0.9999999999999999 0.5
> 89.0000000000000 -1.0 0.5
> 90.0000000000000 -1.0 0.5
> 91.0000000000000 -1.0 0.5
> 92.0000000000000 -0.9999999999999999 0.5
> 93.0000000000000 -1.0 0.5
> 94.0000000000000 -1.0 0.5
> 95.0000000000000 -1.0 0.49999999999999994
> 96.0000000000000 -1.0 0.5000000000000001
> 97.0000000000000 -1.0 0.5
> 98.0000000000000 -0.9999999999999999 0.49999999999999994
> 99.0000000000000 -1.0 0.49999999999999994
>
>
>
> for T in srange(1,100,1):
> print(T, float(C(T)[0]), float(C(T)[1]))
> .....
> 87 -0.9999999999999999 0.5
> 88 -0.9999999999999999 0.49999999999999994
> 89 -1.0 inf
> 90 -1.0 inf
> 91 -1.0 inf
> 92 -0.9999999999999999 inf
> 93 -1.0 inf
> 94 -1.0 nan
> 95 -1.0 nan
> 96 -1.0 nan
> 97 -1.0 nan
> 98 -0.9999999999999999 nan
> 99 -1.0 nan
>
> On Monday, July 4, 2022 at 7:51:58 PM UTC+5:30 GMS wrote:
>
>>
>> Sorry, my message was incomplete.
>>
>> So yes, there is a problem.
>>
>> On Mon, 4 Jul 2022 at 16:14, G. M.-S. <list...@gmail.com> 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*)
>>>
>>> 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 quickly.
>>>
>>> HTH,
>>>
>>> Guillermo
>>>
>>> On Mon, 4 Jul 2022 at 13:56, Gema María Diaz <gemama...@gmail.com>
>>> wrote:
>>>
>>>> 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 - 24*ln(t)^4*t^7 + 10*ln(t)^3*t^7 +
>>>> 2*ln(t)^5*t^3)*exp(3*t) + (70*t^12 + 60*ln(t)^2*t^8 + 6*ln(t)^4*t^4 -
>>>> 5*ln(t)^3*t^4)*exp(4*t) + (-56*t^9 - 24*ln(t)^2*t^5 + ln(t)^3*t)*exp(5*t)
>>>> +
>>>> (28*t^6 + 4*t^2*ln(t)^2)*exp(6*t) - 8*exp(7*t)*t^3 + exp(8*t) + (t^8 +
>>>> t^4)*ln(t)^8 + ((t^5 + 2*t^3)*exp(t) - t^8 - 2*t^6)*ln(t)^7 + (4*t^12 -
>>>> 8*t^9*exp(t))*ln(t)^6 + (-2*t^12 + 6*t^9*exp(t))*ln(t)^5 + (6*t^16 -
>>>> 24*t^13*exp(t))*ln(t)^4 + (-t^16 + 5*t^13*exp(t))*ln(t)^3 + (4*t^20 -
>>>> 24*t^17*exp(t))*ln(t)^2 + t^24 - 8*exp(t)*t^21)/(2*(((3*t^4 -
>>>> 2*t^3)*ln(t)^4 + (18*t^8 - 6*t^7)*ln(t)^2 + 15*t^12)*exp(2*t) + ((-12*t^5
>>>> +
>>>> 4*t^4)*ln(t)^2 - 20*t^9)*exp(3*t) + ((3*t^2 - t)*ln(t)^2 +
>>>> 15*t^6)*exp(4*t)
>>>> - 6*exp(5*t)*t^3 + exp(6*t) + (t^6 - t^5)*ln(t)^6 + (t^5/2 -
>>>> exp(t)*t^2/2)*ln(t)^5 + ((-6*t^7 + 4*t^6)*exp(t) + 3*t^10 - 2*t^9)*ln(t)^4
>>>> + ((-12*t^11 + 4*t^10)*exp(t) + 3*t^14 - t^13)*ln(t)^2 + t^18 -
>>>> 6*exp(t)*t^15)*(exp(2*t) + t^2*ln(t)^2 + t^3*(t^3 - 2*exp(t))))]
>>>>
>>>> and I'd like to see how it is like. Just with:
>>>>
>>>> parametric_plot(C, (t,0,80), plot_points=5500)
>>>>
>>>> one sees what's going on. However, with
>>>>
>>>> parametric_plot(C, (t,0,90), plot_points=5500)
>>>>
>>>> suddenly a vertical lines appears. I think it is a bug, am I right ?
>>>>
>>>> thanks
>>>> Gema M.
>>>>
>>>
>>>
>>
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