# [R] computer algebra in R

Leo Mada |eo@m@d@ @end|ng |rom @yon|c@eu
Wed Nov 29 12:53:42 CET 2023

```Dear Konrad,

I presume that the system can be written as follows, where h0, d0, ga0, kga and kd are given:

err1 = h + hd + hga - h0;
err2 = d + hd - d0;
err3 = ga + hga - ga0;
err4 = hga - kga*h*ga;
err5 = hd - kd*h*d;

All error terms should be zero.

Do you need (a) the symbolic solution or (b) is a numeric solution fine?

I do not have any experience with yacas or caracas. But see below.

### Case (a)
I did write a (very rudimentary) symbolic solver for systems of polynomial equations in pure R. It should be able to solve this one. Please let me know if this is of interest and I will provide further details.

### Case (b)
Again, it should be possible to solve, see some examples:
https://github.com/discoleo/R/blob/master/Math/Systems.NLE.Tutorial.md
https://github.com/discoleo/R/blob/master/Math/Systems.Lambert.R
I did solve much more complex ones, for a monster see:
https://github.com/discoleo/R/blob/master/Math/Poly.System.S5.Ht.Formulas.Derivation.HS0.R
[and the remaining Poly.System.S5.Ht... scripts]

I presume that only the real roots are required (it's possible to solve systems with complex roots as well). I can provide further details as well.

Sincerely,

Leonard

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```

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