# Tagged Questions

Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).

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### Deciding whether a semi-algebraic set is empty. Which command is best?

[Update] I was able to prove that the "larger" set $1\ge x \ge y,w \ge 0$ and $p(x,y,w)>0$ is empty with another computer algebra system in my slow laptop in few minutes but in Mathematica even ...
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### FindRoot gives a wrong solution which obviously should not be there

I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here. I try to find roots of a particular function, which in the ...
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### RSolve not returning known solution

I have the following recurrence relationship for which I know the solution is given by a binomial distribution: ...
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### Solving a system of nonlinear equations self-consistently

I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
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### How to define amazing Goodstein's sequence?

There is an amazing and counterintuitive theorem: For all $n$, there exists a $k$ such that the $k$-th term of the Goodstein sequence $G_k(n)=0$. In other words, every Goodstein sequence ...
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### Solving an equation entered by the user via the Input function

I am new to Mathematica. I am trying to create a program that takes in an equation from user input and then gives the answer. I started with a manipulate function as I created a similar program for ...
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### Unusual error message from Solve when called by DSolve

Question 111150 presents an equation nonlinear in its leading derivative ...
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### Can equation solving be done in parallel?

I'm solving a set of equations that look like: ...
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### Solving this system of nonlinear equations

Edit Interestingly, I realized solving my problem with $2n$ equations appeared to be more efficient than using mathematical results on the solutions to reduce the problem to $n$ equations (the $n$ ...
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### Solving a non-linear equation in Mathematica with many variables

I have a beautiful equation, where I am trying to compute for R2. I am using Mathematica. So far every single time that I have tried to use Solve[] or Reduce [] the computation takes forever. I hope ...
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### NIntegrate over statistical variables with parameter

Essentially, what I am trying to do is the following: Integrate a function which contains the parameter k ...
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### speeding up Solve(ing) the Diophantine equation

Trying to solve the Diophantine equation (or variation?) using Solve in order to generate some chemical formulas. I need to generate all possible solutions. The ...
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### How to handle solution returned by ParametricNDSolveValue in FindRoot

i was trying to solve a problem relative to root finding in a system of differential equations; here's a simpler case. With two distinct set of parametric differential equations, i'm able to find the ...
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### Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
218 views

### NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
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### Proving large inequality in 6 variables

I have arrived at a very large inequality in 6 variables that I would like to prove is true. The command I have tried is the following: ...
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### Apart for complex roots?

Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x]. ...
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### What are the steps using boolean algebra for transforming one equation into another?

I have a special case where I have two equations, which I have solved in a better and quicker way, but I need to solve with Boolean algebra. Using the laws of Boolean algebra, I have to prove that ...
493 views