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8 votes
3 answers
651 views

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 ...
josh's user avatar
  • 2,412
2 votes
5 answers
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 ...
138 Aspen's user avatar
  • 1,393
1 vote
1 answer
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: ...
Steve237's user avatar
  • 435
3 votes
2 answers
193 views

FindInstance taking very long

Trying to solve this equation: ...
Steve237's user avatar
  • 435
1 vote
1 answer
89 views

Why FindInstance does not find this solution?

Do you think FindInstance should have found this solution? ...
Nasser's user avatar
  • 145k
0 votes
0 answers
47 views

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-...
SHR's user avatar
  • 1
5 votes
2 answers
526 views

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: <...
Nitra's user avatar
  • 347
1 vote
1 answer
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 ...
RudyJD's user avatar
  • 121
0 votes
0 answers
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 ...
supragyan priyadarshinee's user avatar
1 vote
1 answer
69 views

Randomized values for FindInstance

...
mdansfo's user avatar
  • 21
0 votes
0 answers
28 views

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 ...
Mihir's user avatar
  • 1
4 votes
4 answers
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 ...
Jason Roell's user avatar
3 votes
2 answers
307 views

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. ...
John Paul Peter's user avatar
4 votes
1 answer
84 views

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 ...
RF_1's user avatar
  • 672
0 votes
1 answer
85 views

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?
sam wolfe's user avatar
  • 4,863
1 vote
0 answers
89 views

Finding the similarity transformation between two symbol matrices

I have two symbol matrices mA and mB, which are similar matrices. ...
lotus2019's user avatar
  • 2,141
3 votes
0 answers
75 views

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 ...
Carlo Beenakker's user avatar
1 vote
0 answers
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: ...
Wiki's user avatar
  • 11
0 votes
0 answers
50 views

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 ...
lotus2019's user avatar
  • 2,141
2 votes
1 answer
115 views

Mathematica generating 'incorrect' Cuboids

Mathematica 13.1 for some reason gives an error for the following code: ...
Liam Baker's user avatar
1 vote
1 answer
98 views

Finding a (sufficient) condition for an inequality - Solve takes too long

I have the following inequality $ 2 \sqrt{2} n^2 \sqrt{\frac{r}{r-1}} \exp \left(2^{-\frac{\sqrt[3]{\log (n)}}{10 \sqrt[3]{\log (r)}}} \left(\frac{1}{r+1}\right)^{-\frac{\sqrt[3]{\log (n)}}{10 \...
black's user avatar
  • 251
9 votes
5 answers
859 views

Solving a Simple 'Sum and Product' Problem

I am trying to solve a simple 'sum and product' problem. Basically, the sum of four prices and the product of those four prices are numerically equal (you must, of course, disregard the units). The ...
JoeMarino's user avatar
  • 151
1 vote
2 answers
142 views

How to find a set of solution of the inequality?

There exists a,b,c,d,e such that ...
lapcal's user avatar
  • 531
2 votes
1 answer
139 views

Strange error in FindInstance result

I was running the following code ...
user58955's user avatar
  • 617
3 votes
1 answer
130 views

FunctionDomain and FindInstance problem

I have some functions including many real parameters as follows: For example, ...
Eric_Jansen's user avatar
2 votes
0 answers
98 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: ...
2132123's user avatar
  • 657
3 votes
1 answer
148 views

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: ...
Eldar Sultanow's user avatar
4 votes
3 answers
181 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 ...
dtn's user avatar
  • 2,404
0 votes
0 answers
71 views

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 $...
2132123's user avatar
  • 657
0 votes
0 answers
48 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 ...
GaloisFan's user avatar
  • 405
2 votes
0 answers
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 ...
Matthew Crawford's user avatar
0 votes
1 answer
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: ...
Levin Koo's user avatar
0 votes
2 answers
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 ...
David G. Stork's user avatar
2 votes
4 answers
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 ...
David G. Stork's user avatar
8 votes
2 answers
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 ...
David G. Stork's user avatar
3 votes
1 answer
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 ...
Oliver Miller's user avatar
1 vote
1 answer
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 ...
algal's user avatar
  • 113
0 votes
2 answers
63 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 ...
user3558075's user avatar
1 vote
0 answers
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 ...
florin's user avatar
  • 1,798
2 votes
1 answer
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 ...
user73722's user avatar
1 vote
1 answer
97 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(\...
sam wolfe's user avatar
  • 4,863
3 votes
0 answers
134 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 ...
sam wolfe's user avatar
  • 4,863
6 votes
4 answers
311 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 ...
Jesper Johansson's user avatar
1 vote
1 answer
43 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-...
hxiao's user avatar
  • 887
1 vote
1 answer
63 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, ...
naomig's user avatar
  • 343
2 votes
0 answers
166 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 ...
Penelope Benenati's user avatar
1 vote
2 answers
214 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 ...
Gabi Gayer's user avatar
0 votes
0 answers
133 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 ...
LCH's user avatar
  • 189
1 vote
1 answer
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 \...
LCH's user avatar
  • 189
1 vote
1 answer
201 views

FindInstance runtime is too long

...
mtheorylord's user avatar