Questions tagged [findinstance]

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How to find a set of solution of the inequality?

There exists a,b,c,d,e such that ...
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2 votes
1 answer
101 views

Strange error in FindInstance result

I was running the following code ...
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  • 617
3 votes
1 answer
116 views

FunctionDomain and FindInstance problem

I have some functions including many real parameters as follows: For example, ...
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2 votes
0 answers
79 views

How to find rational roots of a polynomial in 5 variables in a cube

I am trying to find rational numbers $m,k,l,o,z,R$ such that R^12 - (k l^2 m - l m^2 o - k^2 l z + l o z) R^6 + o^3*z^3 == 0 in the following cube: ...
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  • 553
3 votes
1 answer
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How can I solve this system of 6 simple quadratic diophantine equations in four variables?

I generated this text file containing tuples $(\sqrt{s}, \sqrt{t}, \sqrt{u}, s,t,u,t+u,t+u-s,t-s)$ where the six variables $s,t,u,t+u,t+u-s,t-s$ are all squares. An excerpt of the data set is: ...
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4 votes
3 answers
158 views

Challenges and Opportunities of `FindInstance` Command

I'm testing the FindInstance capabilities and ran into one problem that behaves similarly with different types of inequalities. I calculate two points satisfying ...
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FindInstance specifying reals increases the time significantly and gives errors

I was wondering if there is any way to put time constraint on FindInstance. My problem is as follows: I want to find two, $2 \times 2$ matricies $A,B$ given $Tr(A)$, $Tr(B)$, $TR(AB)$, $Det(A)$ and $...
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  • 553
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0 answers
58 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; ...
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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 ...
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  • 353
2 votes
0 answers
52 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 ...
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0 votes
1 answer
66 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: ...
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2 answers
131 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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2 votes
4 answers
132 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 ...
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8 votes
2 answers
155 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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3 votes
1 answer
74 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 ...
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1 vote
1 answer
66 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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2 answers
52 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 ...
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1 vote
0 answers
54 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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2 votes
1 answer
79 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 ...
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1 vote
1 answer
76 views

How to show all global minimizers?

This is a follow-up to this question and I'm aware of this question for the local minimizers case. Consider, for $0\leq \epsilon\leq 1$ and $0<q,p<1$, the function $$ \begin{align} f(\...
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3 votes
0 answers
86 views

Finding multiple minimizers

Is it possible to find all (or as many as possible) minimizers of a given function? For example, minimizing the function $\cos(\pi(p-q))+\cos(\pi(q+p))$ for $-3\leq p,q\leq 3 $ can be done using ...
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  • 4,138
6 votes
4 answers
282 views

FindInstance won't compute this simple expression

I want to find instances where this standard 3x3 symmetric matrix has only positive eigenvalues. So I run ...
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1 vote
1 answer
40 views

Find a non-convex instance for a non-convex set function with FindInstance

Let $f$ be a non-convex set function defined on a set $L$. Hence there are subsets $A,B\subseteq L$ such that $$f(A)+f(B)>f(A\cup B)+f(A\cap B).$$ I tried to use FindInstance function to find a non-...
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1 vote
1 answer
60 views

Obtain fairly sampled data set subject to a condition?

I need to obtain a random distribution of some parameters {t1,t2,t3} subject to a set of conditions. For example, ...
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2 votes
0 answers
92 views

FindInstance taking too long

I just started to use Wolfram Alpha Notebook Edition. I am using FindInstance command to evaluate the sign of an expression with $8$ variables, under simple constraints, but it takes too much time. Do ...
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0 votes
2 answers
179 views

My Program using NSolve and FindInstance has been running for days without a solution

I have a system of 5 non-linear equations and 5 unknowns (p1,p2,p3,p4,p5 bellow), and a few inequalities. I am trying to understand whether the solution is unique. For this purpose, I tried to run ...
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125 views

System of 15 equations in 23 variables

$$ 1-k_0^2=0, \frac{1}{2} \left(-7 \alpha ^2+38 \alpha +2 c_3 (\alpha +\beta-3)+2 c_6-2 k_1^2-2 k_5^2-48\right)=0, c_5-k_2^2-k_{10}^2=0, c_8(\alpha +\beta -5)+5 c_{10}-k_3^2-k_6^2-k_8^2-k_{11}^2-2 k_2 ...
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  • 189
1 vote
1 answer
90 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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  • 189
1 vote
1 answer
142 views

FindInstance runtime is too long

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0 votes
2 answers
63 views

How can I find some values for which an expression is real?

I've a complicated expression which depends on several variables. I want to find some values for those variables such that the complicated expression is real. How can I do that? The obvious command ...
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  • 605
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0 answers
62 views

Turning FindInstance into True or False

I have a function where I input a certain vector of parameters and it gives me the output of 16 FindInstances. So, a typical output will look something like this ...
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0 answers
58 views

Finding a solution to a modular problem efficiently

I want to find a naïve hash function of the form Mod[a x + b, 2^p] which would produce a value less or equal to v for all ...
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3 votes
1 answer
179 views

Why does FindInstance take so long: It is faster with more restrictions than with less?

A support case with the identification [CASE:4347836] was created. I just noted this little puzzle on twitter by Brillant.org: \begin{align} A B C\\+ BCA\\ = CDE \end{align} Given that $A$ is even ...
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  • 12.3k
2 votes
1 answer
48 views

FindInstance confused by CoprimeQ

For some reason when I type FindInstance[a + b == c && CoprimeQ[a, b, c] == True, {a, b, c}, Integers] Mathematica just immediately returns my input as ...
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1 answer
83 views

How FindInstance can find all the solutions over a given range of parameters

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1 vote
0 answers
55 views

FindInstance Returns "Aborted" [closed]

Edit: Apologies, the question needs to be reworked, because I cannot reproduce the original problem using this code. I don't delete the question, in case someone is preparing an answer at the moment. ...
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1 vote
2 answers
66 views

How to use a given list of values for a parameter in FindInstance?

How should I specify a discrete range for a parameter as one of the conditions in FindInstance? MemberQ/Element functions don't seem to work. For example, ...
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3 votes
1 answer
93 views

FindInstance and cosine system of equations

I'm intrigued by Mathematica indisposition to find an example of the following system of equations $$ \cos(x) + \cos(y) + \cos(z) = \lambda_1, $$ $$ \cos(x+u) + \...
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  • 299
6 votes
1 answer
94 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 ...
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0 votes
0 answers
78 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 "...
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  • 373
1 vote
1 answer
84 views

Reducing system of 10 inequalities

I have the following system of inequalities of real variables ...
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  • 1,578
3 votes
2 answers
171 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 ...
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2 votes
2 answers
133 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 ...
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0 votes
1 answer
417 views

FindInstance with a symbolic constant

Please consider FindInstance[m >= 0 && x >= 0 && x <= m, {x}] for which, I would like a parametric answer ...
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  • 101
2 votes
1 answer
112 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 $a$ ...
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1 vote
3 answers
143 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 ...
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3 votes
4 answers
383 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....
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  • 641
2 votes
0 answers
645 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[], ...
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1 vote
0 answers
96 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 ...
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  • 153
6 votes
5 answers
411 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,...
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