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 sxrange(*10000.*,*10010.*,*1*):
....: print(xt(t=i),yt(t=i))
....:
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
-1.00000000000000 0.500000000000000
sage:
On Mon, 4 Jul 2022 at 17:27, Samuel Lelievre <samuel.lelie...@gmail.com>
wrote:
> The expressions for the coordinates involve exp(8*t) and t^24.
>
> sage: exp(8*88.)
> 5.53751938928459e305
>
> sage: 88.^24
> 4.65140474534598e46
>
>
On Mon, 4 Jul 2022 at 17:25, Niranjana K M <niranjan...@gmail.com> wrote:
> 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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