Mathematica -- Solving a system of equations over a domain

evene · 2016-12-28 16:12:55

How would you solve a system of equations over a specific domain, such as the reals, integers, rationals, etc.

Specifically, I mean this:

Over the integers (i.e integer solutions). I tried this code:

Solve[{f, f^2 g, f g^2 + f^2 h, g^3 + 6 f g h, g^2 h + f h^2, g h^2, h^3} == {c, a + c^2 d, a^2 + b + c d^2 + c^2 e, a^3 + 6 a b + d^3 + 6 c d e, a^2 b + b^2 + d^2 e + c e^2, a b^2 + d e^2, b^3 + e^3}, Integer]

But that didn't work. Mathematica didn't respond. What went wrong?

Last edited by evene (2016-12-28 16:15:07)

bobbym · 2016-12-28 17:13:21

Hi;

For one thing you have more variables than equations and there are non-linear terms.

Still using FindInstance I found this one pretty quick.

{a -> 3, b -> -1, c -> 1, d -> 0, e -> 0, g -> 3, h -> -1}

evene · 2016-12-29 07:59:07

Oh... I was kind of hoping that

.

So replace Solve[] with FindInstance[]? Is that what was wrong with my code?

bobbym · 2016-12-29 08:27:36

That is what I was looking for too but I could not find a solution like that quickly.

There is not much wrong with your code and using FindInstance is just another try at getting an answer. There are other commands too.

When Hercules was instructed to get a bunch of magical apples he was told that only Atlas ( I am using the Roman names here ) could fetch them for him. So Hercules took the journey to go see Atlas. When he got there he could see that Atlas was really busy. I mean, the guy was literally holding up the entire world on his shoulders. He also noticed how hard Atlas was working to hold that weight but still Hercules took the world from Atlas' mighty shoulders and sent him to get those delicious apples. Even Hercules strained under the task of holding up the world. Some historians believe that the strain was so great that Hercules' spleen exploded.

The point: Mathematica is like Hercules. If you ask it to do an extremely difficult problem it will have to work very hard. You saw how hard it was working and for how long. The moral of the story: Hard tasks are hard to do even if you are Hercules.

This is where you come in to the story. You could have told Hercules to put a back supporter on or maybe given him a protein shake ( mixed in a blender of course ) to strengthen him. Or, you could have lightened the load by eliminating all the humans and their skyscrapers from the face of the earth. Math is like the earth, a big heavy ball of grass, water and air. You have to make the problem a bit easier when Mathematica struggles, else it too will suffer from an exploding spleen.

evene · 2016-12-29 08:56:05

But Mathematica doesn't have a spleen!

Hm... okay, then this is a bit problematic.

So using an alternative method, I got (I think) a smaller system, but with the same number of variables. Is that considered an improvement?

bobbym · 2016-12-29 08:56:52

Does it run any faster?

evene · 2016-12-29 08:57:48

I haven't written/tested the program code yet...

bobbym · 2016-12-29 09:02:40

That is the best test. Are there any other equations?

evene · 2016-12-30 04:03:43

No, I think that's it...

Then what would be the code? I tried

Solve[{c^2 f, c f^2, 6 c e f + f^3, e f^2, e^2 f} == {a + c^2 d, a^2 + c d^2, a^3 + 6 a b + d^3 + 6 c d e, a^2 b + d^2 e, a b^2 + d e^2}, Integer]

But the output was just .

Last edited by evene (2016-12-30 04:04:02)

bobbym · 2016-12-30 04:06:43

You have a syntax error!

evene · 2017-01-05 13:03:58

Thanks, I got it!

Another question: Is there a way to solve

For and such that the formula for does not include and vice versa.

I'm trying to find a substitution for and such that when they are substituted into , it produces an identity such as .

bobbym · 2017-01-05 13:55:02

Hi;

I do not understand what you want.

Math Is Fun Forum

#1 2016-12-28 16:12:55

Mathematica -- Solving a system of equations over a domain

#2 2016-12-28 17:13:21

Re: Mathematica -- Solving a system of equations over a domain

#3 2016-12-29 07:59:07

Re: Mathematica -- Solving a system of equations over a domain

#4 2016-12-29 08:27:36

Re: Mathematica -- Solving a system of equations over a domain

#5 2016-12-29 08:56:05

Re: Mathematica -- Solving a system of equations over a domain

#6 2016-12-29 08:56:52

Re: Mathematica -- Solving a system of equations over a domain

#7 2016-12-29 08:57:48

Re: Mathematica -- Solving a system of equations over a domain

#8 2016-12-29 09:02:40

Re: Mathematica -- Solving a system of equations over a domain

#9 2016-12-30 04:03:43

Re: Mathematica -- Solving a system of equations over a domain

#10 2016-12-30 04:06:43

Re: Mathematica -- Solving a system of equations over a domain

#11 2017-01-05 13:03:58

Re: Mathematica -- Solving a system of equations over a domain

#12 2017-01-05 13:55:02

Re: Mathematica -- Solving a system of equations over a domain

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