# Questions tagged [findinstance]

The tag has no usage guidance.

47 questions
Filter by
Sorted by
Tagged with
47 views

### Conditional Statement and Loop in Mathematica to find bound

I have a question regarding loop and conditional statements. I have an equation where I would like to find the bound for n and m based on the value of h. Here is what I have so far; ...
29 views

### Tips to help FindInstance with a lot of complicated inequalities

I'm trying to find a numerical instance (I don't need arbitrarily high precision) of solution to 7 relatively complicated inequalities (plus the region specification) involving 8 variables. The ...
45 views

### Defining new Domain for variables

I am trying to define a new Domain for variables to use with functions like FindInstance or Solve. For example, If I wanted to solve x+y+z=1 over the Reals, I'd get a large solution space. But If I ...
59 views

### How to calculate multiple solutions from big to small with FindInstance funtion

I want to find the nearest 50(or 80, even 100)solutions under 1.4628 from big to small, I tried FindInstance function in MMA, but still cannot get the desired results I need.Here is my code: ...
122 views

### Finding all solutions to coupled algebraic equations without exhaustive enumeration

A Cambridge University mathematics interview question states: Find all $a,b,c,d,e,f \in \mathbb{N}$ such that $$a + b + c = d \cdot e \cdot f$$ and $$d + e + f = a \cdot b \cdot c$$ (There are a ...
121 views

### Elementary number theory problem and FindInstance

Find $\{ m,n \} \in \mathbb{Z}$ such that $m \neq n$ and $m^n = n^m$. This has (unordered) solutions $\{ 2, 4 \}$ and $\{ -2, -4 \}$, as can be easily checked. I'm of course hoping for an analytic ...
145 views

### Solve equation with summation and factorial over Integers

Find all $\{ m, n \} \in \mathbb{Z}^+$ such that $$\sum\limits_{k=1}^m k! = n^2 .$$ The two solutions are $\{ m,n \} = \{ 1,1 \}$ and $\{ 3,3 \}$, as can be confirmed. Here is how to solve this ...
64 views

### Find smallest instance satisfying certain inequalities

I need a "clean" way to find the smallest solution to some (in)equalities given by Reduce and containing only one variable ...
58 views

### Control evaluation for functional constraints

I'm trying to understand how to use Mathematica to find a solution subject to constraints, where one of the constraints is specified as a predicate function. But I don't know how to control evaluation ...
45 views

### Restrict FindInstance to exact value

I would like to restrict the FindInstance function to exact values (ex. 2Pi/3) The following doesn't work ...
51 views

### Why does FindInstance refuse to find a second instance, in a number theory problem?

Hi I am looking for reversible Markov generating matrices of order three, whose upper (2,2) block has integer eigenvalues. There are 5 free parameters; I specified 2 ...
66 views

### Does FindInstance traverse the entire domain?

If the result of FindInstance[expr<=0,vars,dom] is empty set, can it mean that expr is always greater than ...
73 views

86 views

93 views

### What are the 'special or interesting points in the set' returned by FindInstance?

The documentation for FindInstance[] says: The instances returned by FindInstance typically correspond to special or ...
70 views

### Why is FindInstance unable to find multiple pythagorean triples?

If I input the code FindInstance[x^2 + y^2 == z^2 && 0 < x && 0 < y && 0 < z, {x, y, z}, Integers, 2] Mathematica outputs "...
81 views

### Reducing system of 10 inequalities

I have the following system of inequalities of real variables ...
148 views

### Improving FindInstance efficiency

I am relatively new to Mathematica and my function has been running for over a month now. I am beginning to think I may never get a solution or that there is a mistake in the code, which means a ...
131 views

### On the solvability of the Diophantine equation $a(x^2-y^2)+2bxy=1$

Take two integers $a,b$ with $\mathrm{GCD}(a,b)=1$ and $a$ odd. Consider the Diophantine equation $$a(x^2-y^2)+2bxy=1,\qquad x,y\in\mathbb Z$$ Is there any efficient way to determine whether such ...
371 views

### FindInstance with a symbolic constant

Please consider FindInstance[m >= 0 && x >= 0 && x <= m, {x}] for which, I would like a parametric answer ...
105 views

### FindInstance within a range

I am trying to find particular solutions to my inequality for two positive integers $a$ and $b$: FindInstance[a<f[etc...]*b,{a,b},Integers] However I want $a$ ...
133 views

### Checking Rationality Using FindInstance

I need to find example if $x,\sqrt{x^2+6},\sqrt{x^2+12}$ all can be rational at once or not. But the following command ...
373 views

### Problems with FindInstance in v. 11

I have been trying to solve a system of linear equations and linear inequalities with 18 unknowns. I would think that for Mathematica giving an answer to such question will be a matter of milliseconds....
588 views

### solving linear systems with parameters

I am trying to solve simple, small linear systems, with parameters. I would like to have the result shown for various values of the parameter. RowReduce[], ...
88 views

### What is the algorithm used in FindInstance? [closed]

Is FindInstance guaranteed to find an instance if one exists? Conversely, if it does not find an instance, does that mean an instance does not exist at all? Finally, is there a way to change the ...
388 views

### Faster way to pick pairs of integer coordinates from a "region"

I am trying to find a faster way to do this than what I have put together or by looping through a bunch of points. I want to select all pairs of integer points ((x1,y1),(x2,y2)) such that: Point (x1,...
134 views

### Get a feasible solution

Link : Reduce time taken to get feasible solution I have 18 inequations with 4 variables vars2 = {arb, arb, arb, arb} , To get a feasible solution, NMinimize and Nmaximize were used as ...
187 views

### Error using NMinimize/NMaximize : The initial region specified may not contain any feasible points

Link : Reduce time taken to get feasible solution An example of 18 non linear inequations with 4 variables is given in the image. But I have a set of 32 non linear inequations with 9 variables (I ...