Super newbie question re: solving systems of equations

[Natalie Ulrich]

I'm using SageMathCell to solve chemical equilibrium problems, so at least one set of my solutions has to be real and positive. 

Here's my code: 

var('x, y, z')

xi=0

yi=0.150/2.0

zi=0.150/2.0

K=8.3e-4

eq1=K == y*z/ x

eq2=xi+yi==x+y

eq3=2*xi+2*zi==2*x+2*z

solve([eq1, eq2, eq3],[x, y, z])

 

And here are my solutions:

[[x == -1/200000*sqrt(2496889) + 15083/200000, y == 1/200000*sqrt(2496889) - 83/200000, z == 1/200000*sqrt(2496889) - 83/200000], [x == 1/200000*sqrt(2496889) + 15083/200000, y == -1/200000*sqrt(2496889) - 83/200000, z == -1/200000*sqrt(2496889) - 83/200000]]

---

Any thoughts? Thanks in advance.

[Emmanuel Charpentier]

what's wrong with :

map(lambda S:map(lambda s:s.lhs()==s.rhs().n(), S), solve([eq1, eq2, eq3], [x, y, z]))

[[x == 0.0675142263037092, y == 0.00748577369629076, z == 0.00748577369629076],
 [x == 0.0833157736962908,  y == -0.00831577369629076,  z == -0.00831577369629076]]

Which shows that the first solution fulfills your constraints ?

HTH,

--
Emmanuel Charpentier

[Natalie Ulrich]

So.. is all of that just converting all the crazy square roots into rational numbers? Thanks for your help!

[Emmanuel Charpentier]

Some may find my first answer a bit Lispish. More Pythonish :

[[s.lhs()==s.rhs().n() for s in S] for S in solve([eq1, eq2, eq3],[x, y, z])]

[[x == 0.0675142263037092, y == 0.00748577369629076, z == 0.00748577369629076],
 [x == 0.0833157736962908, y == -0.00831577369629076, z == -0.00831577369629076]]

HTH,

--
Emmanuel Charpentier

[Emmanuel Charpentier]

Even more Pythonish, and more direct (no conversions, Sage will take care of the (hairy !) exact arithmetics)...) :

[s for s in solve([eq1, eq2, eq3],[x, y, z], solution_dict=True) if all(map(lambda t:bool(t>0), s.values()))]

[{z: 1/200000*sqrt(2496889) - 83/200000,
  y: 1/200000*sqrt(2496889) - 83/200000,
  x: -1/200000*sqrt(2496889) + 15083/200000}]

HTH,

--
Emmanuel Charpentier

[Natalie Ulrich]

That is extremely helpful. Many thanks, and have a beautiful day!

[Emmanuel Charpentier]

Le vendredi 22 septembre 2017 15:42:40 UTC+2, Natalie Ulrich a écrit :

That is extremely helpful. Many thanks, and have a beautiful day!

Thanks !

Two notes :

1. This kind of question, which is more oriented at learning how to use Sage than at reporting a problem with it or suggesting a new development, is probably more useful when asked on ask.sagemath.org
2. Most potential answerers, being scholars/teachers/etc.., are wary of "homework" questions, and won't answer them (maybe providing helpful hints). Giving the context of the question and showing what parts of the work you did yourself may help them choosing the right answer...

HTH,

--
Emmanuel Charpentier

[Dima Pasechnik]

On Friday, September 22, 2017 at 12:44:50 PM UTC+1, Natalie Ulrich wrote:

So.. is all of that just converting all the crazy square roots into rational numbers? Thanks for your help!

more precisely, it provided approximations of the crazy roots by floating point numbers.

(most square roots cannot be exactly represented by rational numbers, e.g. sqrt(2) already cannot...)

[Natalie Ulrich]

Got it. I'm a college chemistry professor, just terrible at math solvers :) I've found where I can find answers to those types of questions now. Thanks again!

[Natalie Ulrich]

Ah, I see. Thank you.