Fireworks while trying to solve system of equations
07-02-2021, 05:22 PM
Post: #1
 dah145 Junior Member Posts: 37 Joined: Aug 2020
Fireworks while trying to solve system of equations
Trying to solve this system of non linear equations makes my HP Prime display some nice fireworks:

solve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z])

It also crashes the virtual calculator on PC.
07-03-2021, 12:35 AM
Post: #2
 Albert Chan Senior Member Posts: 2,231 Joined: Jul 2018
RE: Fireworks while trying to solve system of equations
Quote:solve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z])

This crash on XCas as well.

We can simplify system of equations into 1 equation.
For real solutions, equating y:

CAS> z := sqrt(exp(sqrt(x))/3)
CAS> fsolve(sqrt(z^3/x) = (5*z*x)^(1/x), x)

[0.281669416538, 11.005909666]
07-03-2021, 07:20 PM
Post: #3
 dah145 Junior Member Posts: 37 Joined: Aug 2020
RE: Fireworks while trying to solve system of equations
(07-03-2021 12:35 AM)Albert Chan Wrote:
Quote:solve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z])

This crash on XCas as well.

We can simplify system of equations into 1 equation.
For real solutions, equating y:

CAS> z := sqrt(exp(sqrt(x))/3)
CAS> fsolve(sqrt(z^3/x) = (5*z*x)^(1/x), x)

[0.281669416538, 11.005909666]

I was testing out some equations I found in different places, I got that particular system from here: https://www.youtube.com/watch?v=OUO1P5ZgH2s

07-03-2021, 08:25 PM
Post: #4
 Albert Chan Senior Member Posts: 2,231 Joined: Jul 2018
RE: Fireworks while trying to solve system of equations
(07-03-2021 07:20 PM)dah145 Wrote:  I was testing out some equations I found in different places, I got that particular system from here: https://www.youtube.com/watch?v=OUO1P5ZgH2s

The video assumed log() is really log10().
log(x) vs ln(x) — The curse of scientific computing

HP Prime home mode, both log and LOG meant log10.
CAS mode have different meanings (log = ln, LOG = log10, same as XCAS)

CAS> fsolve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])

[0.281669416538, 1.23071511956, 0.75280920719]

CAS> fsolve([z^3=y^2*x,sqrt(x)=LOG(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])

[0.235667688071, 2.0897828558, 1.00964210847]
07-04-2021, 01:51 AM
Post: #5
 dah145 Junior Member Posts: 37 Joined: Aug 2020
RE: Fireworks while trying to solve system of equations
(07-03-2021 08:25 PM)Albert Chan Wrote:
(07-03-2021 07:20 PM)dah145 Wrote:  I was testing out some equations I found in different places, I got that particular system from here: https://www.youtube.com/watch?v=OUO1P5ZgH2s

The video assumed log() is really log10().
log(x) vs ln(x) — The curse of scientific computing

HP Prime home mode, both log and LOG meant log10.
CAS mode have different meanings (log = ln, LOG = log10, same as XCAS)

CAS> fsolve([z^3=y^2*x,sqrt(x)=log(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])

[0.281669416538, 1.23071511956, 0.75280920719]

CAS> fsolve([z^3=y^2*x,sqrt(x)=LOG(3*z^2),5*z*x=y^x],[x,y,z]=[1,1,1])

[0.235667688071, 2.0897828558, 1.00964210847]

Duly noted, thanks.
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