HP Prime can't solve some nonlinear system of equations

[rombva]

The HP Prime G2 with last SW version can't solve these systems, but xCas solves it properly excluding example 2):

1) solve([x^2+y^2=a,1/x^2+1/y^2=b],[x,y])

G2 doesn't response while solving it.

2) solve([z^x=x,z^y=y,y^y=x],[x,y,z])

G2 returns a "Bad Argument Value" error.

3) solve([x^2-(y-z)^2=a,y^2-(z-x)^2=b,z^2-(x-y)^2=c],[x,y,z])

G2 returns an empty list []. The last beta emu unexpectedly closes after a few seconds.

4) solve([x^2+y^2=a*x*y*z,y^2+z^2=b*x*y*z,z^2+x^2=c*x*y*z],[x,y,z])

G2 returns only a [0 0 0]. The last beta emu unexpectedly closes after a few seconds.

5) solve([2*(x^2+y^2)=x*y*z,10*(y^2+z^2)=29*x*y*z,5*(z^2+x^2)=13*x*y*z],[x,y,z])

G2 returns an answer with variables x, y and z.

6) solve([4*x*y+x^2+y^2=1,8*x*z+x^2+4*z^2=-2,8*y*z+y^2+4*z^2=1],[x,y,z])

G2 returns an answer with variables x, y and z.

I discovered that while running some tasks the HP Prime's busy icon doesn't appears on the upper right corner of the screen.

[Simone Cerica]

try using fsolve --> https://en.hpprime.club/docs/reference/fsolve

and take a look at this wonderful app:

SolveSys - Equation Library and Multiple Equations Solver
https://www.hpcalc.org/details/7777
https://www.hpmuseum.org/forum/thread-7725.html

[Albert Chan]

(11-03-2019 03:45 PM)rombva Wrote:  2) solve([z^x=x,z^y=y,y^y=x],[x,y,z])

Is the answer (x,y,z) = (1,1,1), (-1,-1,-1), (4,2,√2), (4,2,-√2) ?

[rombva]

(11-04-2019 12:40 PM)Albert Chan Wrote:  

(11-03-2019 03:45 PM)rombva Wrote:  2) solve([z^x=x,z^y=y,y^y=x],[x,y,z])

Is the answer (x,y,z) = (1,1,1), (-1,-1,-1), (4,2,√2), (4,2,-√2) ?

Yes, it is.

[rombva]

Will any improvements of Prime's CAS appear in the future update that pertain to the equalization of the possibilities of Prime's CAS with the possibilities of Xcas?

[parisse]

Polynomial system solving like in Xcas require advanced algorithms, like rational univariate representation, and these algorithms require a lot of ressources (e.g. Go of RAM, faster CPU), that is the reason why they are not ported on the Prime.

[compsystems]

What is the minimum requirement RAM-CPU_Hz to run Xcas completely?

[rombva]

(11-05-2019 04:15 PM)parisse Wrote:  Polynomial system solving like in Xcas require advanced algorithms, like rational univariate representation, and these algorithms require a lot of ressources (e.g. Go of RAM, faster CPU), that is the reason why they are not ported on the Prime.

How many Xcas's functions availible on the Prime lose full functionality after their porting to the Prime?

[parisse]

Some fast algorithms for large computations were not ported. Some Xcas commands are not available (3d geometry for example) or disabled (like algebraic extensions of Q: rootof). LGPL or GPL-only code is not available, like GMP+MPFR+MPFI, or PARI/NTL/GSL, or optimization/signalprocessing/graphtheory code by Luka Marohnic.

[rombva]

(11-06-2019 08:37 PM)parisse Wrote:  Some fast algorithms for large computations were not ported. Some Xcas commands are not available (3d geometry for example) or disabled (like algebraic extensions of Q: rootof). LGPL or GPL-only code is not available, like GMP+MPFR+MPFI, or PARI/NTL/GSL, or optimization/signalprocessing/graphtheory code by Luka Marohnic.

Thanks.