cannot solve simple equation

[Peter C]

I just got an HP Prime and was trying out its CAS function. I came across a question on special relativity and wanted to try it out.
Please help me out!

Peter

[Peter C]

in case the pictures in the first post didn't work:        

[Albert Chan]

Error screen already gives all the information you need.

v = tan(t) , t=-1.57 .. 1.57
tan(1.57) ≈ 1256., v guess (unit m/s) too low to have measurable relativistic effect

Let x = v/c, where c = 3e8

> solve(4.1 = 2.6/sqrt(1-x*x), x)      → {−0.773213048007, 0.773213048007}

Iterative solve: 4.1/2.6 about sqrt(2) → x about 0.75

> solve(4.1 = 2.6/sqrt(1-x*x), x=0.75)      → 0.773213048007

Bisection solve:

> solve(4.1 = 2.6/sqrt(1-x*x), x=0.6 .. 0.9)      → [0.773213048007]

[C.Ret]

(11-23-2023 03:22 AM)Peter C Wrote:  I just got an HP Prime and was trying out its CAS function. I came across a question on special relativity and wanted to try it out.

Hi Peter !

Apparently, you didn't get your Hp Prime from Officer Montgomery "Scotty" Scott (retired chief engineer responsible for the propulsion of the starship Enterprise).
With your new calculator, you have to give from her all she's got, Peter!. You cannot change the laws of the CAS's physics!.

You made no mistake, only the HP Prime is sometime quite a true obscure and unpredictable Klingon:
   

[Peter C]

(11-23-2023 05:30 PM)C.Ret Wrote:  

(11-23-2023 03:22 AM)Peter C Wrote:  I just got an HP Prime and was trying out its CAS function. I came across a question on special relativity and wanted to try it out.

Hi Peter !

Apparently, you didn't get your Hp Prime from Officer Montgomery "Scotty" Scott (retired chief engineer responsible for the propulsion of the starship Enterprise).
With your new calculator, you have to give from her all she's got, Peter!. You cannot change the laws of the CAS's physics!.

You made no mistake, only the HP Prime is sometime quite a true obscure and unpredictable Klingon:

I tried yours and it worked! Does it mean that I cannot use decimals in CAS?
Appreciate the help!

[nickapos]

Does anyone know why this is happening?
Why it does not work with 4.1 and it does work with 41/10?

I would be curious to see the reason behind this.

[Albert Chan]

(11-24-2023 07:20 PM)nickapos Wrote:  Why it does not work with 4.1 and it does work with 41/10?

With exact number, solve does it symbolically.
It is equivalent to solve with symbols, then substitute for answer.

Cas> solve(a = b/sqrt(1-(v/c)^2), v) (a=4.1, b=2.6, c=3e8)

{231963914.402, −231963914.402}

With float, solver use Newton's method, but guess (v=tan(t), t = ±1.57) is too low.
There is no measurable relativistic effect, the region examined is just a flatline.

Cas> f(v) := 4.1 - 2.6 / sqrt(1-(v/3e8)^2)
Cas> f(tan(−1.57))      → 1.49999999998
Cas> f(0)                    →   1.5
Cas> f(tan(+1.57))      → 1.49999999998

We have to provide a better guess for v

Cas> solve(f(v), v=2e8)      → 231963914.402

[nickapos]

(11-24-2023 08:34 PM)Albert Chan Wrote:  

(11-24-2023 07:20 PM)nickapos Wrote:  Why it does not work with 4.1 and it does work with 41/10?

With exact number, solve does it symbolically.
It is equivalent to solve with symbols, then substitute for answer.

Cas> solve(a = b/sqrt(1-(v/c)^2), v) (a=4.1, b=2.6, c=3e8)

{231963914.402, −231963914.402}

With float, solver use Newton's method, but guess (v=tan(t), t = ±1.57) is too low.
There is no measurable relativistic effect, the region examined is just a flatline.

Cas> f(v) := 4.1 - 2.6 / sqrt(1-(v/3e8)^2)
Cas> f(tan(−1.57))      → 1.49999999998
Cas> f(0)                    →   1.5
Cas> f(tan(+1.57))      → 1.49999999998

We have to provide a better guess for v

Cas> solve(f(v), v=2e8)      → 231963914.402

Thank you very much Albert that makes sense