# Questions tagged [findinstance]

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### How to improve code finding x+y+z+w=40 to generate numbers 1 through 40?

Edit: Appended work to find generators for any number as per azerbajdzan and ubpdqn. See below Ran into this problem and was wondering if there is a more elegant and concise way of coding this if ...
• 2,412
297 views

### Why doesn't FindInstance work in finding Heronian triangle?

I was trying to find a triangle whose side lengths are all positive integers and area is rational number (similar to Heronian triangle) with FindInstance, but it ...
• 1,393
1 vote
50 views

### FindInstance for Reals

I am trying to find the total number of solutions to: Floor[x]*Ceiling[x]=x^2 between 0 and 100 Now when we do this for Integers, it's just fine with a 100 result: ...
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### FindInstance taking very long

Trying to solve this equation: ...
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1 vote
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### Why FindInstance does not find this solution?

Do you think FindInstance should have found this solution? ...
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### Checking Positivity

This is my matrix: H = {{2*a1*p4, -p5*a2, p3*a1, 0},{-p5*a2, 2*a2*w1, -p2, -p1},{p3*a1, -p2, 2*a3*w2, 0},{0, -p1*a4, 0, 2*a4*w3}} Where a1,a2,a3,a4 are non-...
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### Wrong solution in a geometry problem

I try to solve the simple problem of finding (integer numbers) for the sides of a triangle when its perimeter is 90 and its area is twice, three times or four times this number. My approach is this: <...
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1 vote
152 views

### How to return only the negative complex solutions of DSolve or using FindInstance?

I am using DSolve to find the solutions to two differential equations. The problem is from the first solution, I only want the solution that includes a negative ...
• 121
55 views

### Problem in solving the non-linear equation

Is there any other way to solve an equation rather than solve command also without findroot command in Mathematica? Because the Solve command is not returning any ...
1 vote
69 views

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### How to solve inequality equations of kappa modifiers using FindInstance command?

Here, ub are signal strength values while ube is error value. similarly, other values. THbb and other are higgs decay width values. these values are required values for making inequalities mentioned ...
207 views

### How can I formulate this simple mathematical riddle into a computable Wolfram Language query?

I'm trying to formulate the below question into a computable wolfram language solution, but can't seem to get it right. Question: Place three piles of matches on a table, one with 11 matches, the ...
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### How can I reduce the time to compile this solve?

I want to find five integer numbers $a, b, c, d, e$ so that $a+ b+ c + d + e = 9 k$ and none of two number in which are equal. I tried. ...
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### How can we find the appropriate values of unknowns such that the following expression must be a real number? FindInstance

Question: I have some mathematical functions including various parameters. I want to find instances for the parameters such that the function must be in a real domain after substituting the values of ...
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### Finding only non-negative roots with FindRoot

Given an arbitrary function F, how do I force FindRoot to look only for non-negative roots, returning nothing otherwise?
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1 vote
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### Finding the similarity transformation between two symbol matrices

I have two symbol matrices mA and mB, which are similar matrices. ...
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### Can I use FindInstance to prove an algebraic identity?

This question arose from a [now removed] MathOverflow discussion, where a Null result from a FindInstance query was used to prove that $f(x_1,x_2,\ldots x_n)\neq 0$ has no solution in $\mathbb{R}$. My ...
1 vote
57 views

### Calculating eigenvalues and solving inequalities with parameters

I would like to calculate b in terms of c and a, in order to satisfy the following conditions: ...
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### An error occurred while using FindInstance to find a matrix that meets the constraint conditions

I want to use MMA to prove an exercise in textbook: mA is a n-level square matrix. Proof: mA.mA==mA is true if and only if ...
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115 views

### Mathematica generating 'incorrect' Cuboids

Mathematica 13.1 for some reason gives an error for the following code: ...
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1 vote
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### 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 ...
• 405
100 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 ...
73 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: ...
199 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 ...
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156 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 ...
• 41.5k
196 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 ...
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149 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 ...
1 vote
100 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 ...
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### Restrict FindInstance to exact value

I would like to restrict the FindInstance function to exact values (ex. 2Pi/3) The following doesn't work ...
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1 vote
61 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 ...
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110 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 ...
1 vote
97 views

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110 views

### Solve inequalities

I use FindInstance to find a set of real parameters to satisfy the following inequality $-3 c_{11}-k_4^2-k_7^2-k_9^2>0$,  -4 \alpha^6+84 \alpha^5-721 \alpha^4+3228 \alpha^3-7924 \alpha^2+10080 \...
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1 vote