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

learn more… | top users | synonyms (4)

11
votes
2answers
916 views

Trying to fit an unknown extreme distribution

First up, I'm quite new to Mathematica so any hints on better code would be greatly appreciated. I have some histogram frequency data from an unknown distribution that I'm trying to fit. Here's the ...
4
votes
1answer
1k views

Solve system of equations related to perspective projection

I'm trying to solve system of equations. I have 4 points before perspective projection and after and I whant to obtain matrix of perspective projection $m_{i,j}$ ($x,y,u,v$ are known , $m_{i,j}$ ...
1
vote
1answer
3k views

solve non-linear system of equations

I have a system of equations and I want to solve it to get x, y $$\begin{cases} u= C_{1}+(x-C_{1})(1+k_{1}((x-C_{1})(x-C_{1})+(y-C_{2})(y-C_{2}))) \\ \\ v= ...
3
votes
2answers
174 views

Why didn't Reduce give me the right result?

My code: Clear[r1, r2]; par[r1_, r2_] := r1 r2 / (r1 + r2); Reduce[{5 par[r2, 32000]/(r1 + par[r2, 32000]) == 1.8 && par[r1, r2] == 5000}, {r1, r2}] ...
2
votes
1answer
1k views

Solve matrix equation A*X=X*B using LeastSquares

I want to solve matrix equation A*X=X*B using LeastSquares method, but it is suited for equation like A*X=B. All matrices are 3x3 ...
1
vote
2answers
2k views

Find the dimensions of a cylindrical can that will minimize the cost of the material

A cylindrical can is to be made to hold 1 L of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. This is a standard calculus problem. The volume of the ...
9
votes
4answers
643 views

Finding the roots of Hypergeometric1F1[]

I am trying to find the roots, λ, for this equation: Hypergeometric1F1[1/4 (2 -  λ /β), n + 1, β] for certain ...
5
votes
1answer
1k views

How Can I use Solve/Reduce Output

Suppose I want x and y to be rationals Solve[ x^2 + y^2 == 1, {x, y}, Rationals] I am ...
12
votes
2answers
1k views

How do I split up a curve into segments of equal length?

I have a curve that is defined as f[x] and what I'm attempting to do is to divide the curve into equal straight lengths for a number of segments of my choosing that I've defined as nSeg. I've created ...
6
votes
2answers
436 views

How to work out the parameter in a definite integration which has an exact value while the integration doesn't have an analytical solution?

Here is the equation I'm trying to solve: NIntegrate[1/(E^(1/(λ T)) - 1), {λ, 200, 220}] == 1000 T is the parameter I'm ...
5
votes
1answer
232 views

Incompleteness of FindInstance

I've been playing around with Resolve and FindInstance. I know that Resolve should always ...
6
votes
1answer
327 views

Buggy Reduce/Resolve function?

It seems to me that this is a clear-cut case of Mathematica actually producing the wrong answer (with no warnings). I'm trying to express the fact that for any integer, there exists a factorization ...
3
votes
2answers
3k views

How to convert a system of parametric equations to a normal equation?

For example, I have a system of parametric equations (R is a constant number) : ...
9
votes
3answers
715 views

Using FindInstance to Prove No Solutions Exist

For a small amount of background, I am currently working on an undergraduate research project in Combinatorial Geometry and I'm working on a case analysis for embedding spherical simplicial ...
2
votes
2answers
1k views

How to plot an inequality?

I need some help in plotting the following inequality using Mathematica: $$\frac{1+(x/100+0.1)\times y/100}{1.15+1.15\times(x/100)\times(y/100)}\geq 1$$ assuming $x,y\in \mathbb{Q}$, the set of ...
7
votes
1answer
655 views

Getting an InterpolatingFunction from a ContourPlot

I have a function, say minimizeme[Ω_][β_][ϵ_] = ϵ^2 Ω - Log[2 (Cosh[2 β] + Cosh[2 β ϵ])]/(2 β); I want to find its critical points in $\epsilon$ for a given ...
10
votes
3answers
287 views

Problems Computing (in a reasonable amount of time) Solutions to a System of Inequalities

For my Cryptography research I am interested in finding solutions to the following inequalities in terms of $r$ and $s$, where $p$ is some fixed constant. $$\begin{align} 2^{p - s + 4} + 2^{p - r} + ...
1
vote
2answers
345 views

solving for one solution to a system of polynomials

I'm trying to solve a system of equations: ...
6
votes
3answers
1k views

Why won't Mathematica Solve a set of two equations for one variable?

For example, if I try to Solve this set of equations Solve[y == 3 x + 5 && y == -x + 7, {x, y}] Mathematica gives the right values for ...
7
votes
4answers
444 views

Defining a Unique Domain for Solving Diophantine Equations

I am working on a research problem in discrete geometry to do with sphere packings, and believe it or not, I have been able to reduce it to finding the solutions to the Diophantine equation, $$n = ...
7
votes
2answers
194 views

Why does Solve and Sum give different answers when according to Table it is the same sequence?

I have been thinking about a piece of code today, but I don't understand why I get different outputs from two in my mind similar Mathematical sums. First I observe that the Table command for this: ...
8
votes
2answers
3k views

Inverse of a complicated function

Mathematica is struggling to find the inverse of this function f(r): ...
5
votes
4answers
388 views

Manipulating Equations

I would like to be able to manipulate algebraic equations. For example, let's say I enter 3x+5==2 I would next like to be able to manually subtract $2$ from both ...
6
votes
1answer
627 views

How to Simplify equations over a Ring with Mathematica?

For example, when we work over a ring, the equation x^3=0 does not imply x^2=0 or x=0, but ...
7
votes
0answers
186 views

What Method options does FindInstance accept?

While answering Trouble getting FindInstance to return multiple results for certain constraints it became clear that for this problem FindInstance would be better ...
8
votes
2answers
314 views

Trouble getting FindInstance to return multiple results for certain constraints

I'm having a hard time getting FindInstance to return multiple results. Consider this simple example: ...
8
votes
3answers
1k views

Checking if the roots of a function are real

I'm trying to determine if the roots of a function are real. How would you do that? (In particular I'm interested in verifying that the roots of LegendreP[6, x] ...
12
votes
1answer
765 views

Proving inequalities with Mathematica

Question summary: I would like to learn some tips and tricks on how to prove inequalities with Mathematica. I'm studying various inequalities in triangle that have the form $R+ar + bs\geq 0$, where ...
17
votes
4answers
11k views

Assign the results from a Solve to variable(s)

I understand Mathematica can't assign the results of a Solve to the unknowns because there may be more than 1 solution. How can I assign the 4 values of following result to variables?
11
votes
2answers
613 views

Google Code Jam: Mountain View code review

After participating in Google Code Jam 2012 Round 2, it occurred to me that the Mountain View problem boiled down to solving a set of linear inequalities, which could be done in Mathematica. I've only ...
4
votes
1answer
3k views

Why can't Mathematica “Solve” my equation?

I am trying to get Mathematica to solve the following equality in terms of $w_i$ $\displaystyle \frac{\sum_{i = 1}^{n} x_i }{\sum_{i = 1}^{n} y_i} = \frac{\sum_{i = 1}^{n} ( (\frac{x_i}{y_i}) w_i ) ...
7
votes
3answers
2k views

How to solve an overdetermined system in Mathematica

I would like to understand the reasons and find a way to avoid such behaviour of the Solve function in Mathematica 8. ...
0
votes
2answers
202 views

Constraining two points, a specified distance apart, to a line

Suppose that I have two points in the xy plane: pt1 and pt2init. pt1 is fixed in space, ...
2
votes
1answer
451 views

Inconsistent initial and boundary conditions

I have a 4th order nonlinear PDE with the following BCs and IC: ...
3
votes
3answers
401 views

Animate a position change along the curve for every iteration

I've only had few previous experiences on Mathematica before. So basically an entry-level question that harasses a rookie like me. I made the following attempt using bisection method to calculate ...
4
votes
3answers
923 views

Replace function and its derivatives found with Solve

If I have an equation eq = f[x] + g[x] == 0 and I solve for f[x] sol = Solve[eq,f[x]] ...
8
votes
5answers
5k views

How to get rid of warnings when using Solve on an equation with inexact coefficients?

When I solve this equation in Mathematica 8, I can get the right answer, but with some uncomfortable warnings. Equation: ...
2
votes
1answer
415 views

Reduce/Solve an equation with symbols in powers

I am trying to solve the following equation with respect to x. eqn = x^z + y == a; But when I do ...
2
votes
2answers
263 views

How to find solutions that yield of root of unity?

I have a polynomial with coefficients that are integer polynomials in another (complex) variable. For example: 1 + (1 - v^2) #1 + (-3 - v^2) #1^2 + #1^3 & I ...
3
votes
2answers
578 views

Solving a linear equation in Mathematica

This should be easy but I can't seem to find the right way to do it. I have an equation of the form $a x + b x + c y + a z + d z = 0$, and I'd like to solve for relations between the parameters ...
5
votes
2answers
2k views

Select Solution with real (positive, etc) coefficients - ignoring variables

I often need to solve equations for numerical coefficients while preserving numerous variables (e.g. to preserve scaling relations). Thus I end up with a set of solutions like $$ ...
0
votes
1answer
131 views

Numerical rule evaluation -> {True, False} to deviation of target equation

I solve some equations numerically with FindRoot[] returning a quadruple {1,2,3,4}. Because the solver sometimes do not find any roots depending on parameterization of these equations I select only ...
5
votes
2answers
1k views

Error (NSolve::ifun) when using NSolve, I need help interpreting the error

I wrote the following code to observe how the solutions to the equation $(e^{i a})^2 = e^{i b}$ varied as $b$ varied between 0 and $2\pi$ ...
18
votes
6answers
4k views

About multi-root search in Mathematica for transcendental equations

I have some questions for multiroot search for transcendental equations. Is there any clever solution to find all the roots for a transcendental equation in a specific range? Perhaps ...
2
votes
3answers
847 views

Finding roots of nontrivial equation

I am trying to solve the following nontrivial equation: ...
2
votes
2answers
119 views

Solving an equation and finding a couple of results given that they are integer

My problem is to find all solutions to an equation with 2 variables between two values that define the range of my search. e.g., $(x+y-y²)/(1-y-x²)=0$ with solutions ${x,y} \in \mathbb{Z}$.
7
votes
1answer
858 views

How to find the smallest root

I have a continuous, differentiable, monotonic, bounded function called F[t]. If t -> Infinity then ...
4
votes
4answers
3k views

Solving complex equations

I feel like I am missing a basic, but key point when using Mathematica's Solve or Reduce. ...
1
vote
3answers
897 views

Conditional expression

How do I evaluate a conditional expression in order to convert the solutions that are in terms of $x$ to a new variable $c$ depending on $x$? The conventional method I have been using with eliminate ...
5
votes
1answer
537 views

Solving recurrence relation using Mathematica defined in a piecewise way

I have a recurrence relation defined as following: RSolve[ { p[0] == p0, p[1] == λ p[0]/μ, p[i + 1] == λ p[i]/(2 μ) }, p[i], i ] Note that the relation ...