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

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0answers
88 views

Solve[] unexpectedly giving empty solution sets for extremely large problems

I was calculating the set of lattice vectors in $\mathbb{Z}^4$ which have taxicab norm $r$. For example, executing ...
3
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1answer
143 views

Faster Solve for Fermat 4n+1 conjecture

Assuming that Fermat 4n+1 conjecture (each prime of the form 4n+1 is the sum of two squares) is true then I like to solve the ...
0
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1answer
144 views

How to enter and solve this equation in finite fields?

Is there a way in Mathematica 9 to enter and solve the following equation $p(x) = r^x$ where $p(x)$ is a polynomial whose coefficients are drawn from a finite field, and $r$ is a primitive root of ...
1
vote
1answer
107 views

Decomposing a diagonal positive real matrix

I would like to 'decompose' a diagonal positive real matrix $E$ of rank $D$ onto $\sum_{i=1}^{D}c(i)N^i$: $$E = \left( \begin{array}{ccc} 0 & & & \\ & a & & \\ ...
2
votes
2answers
94 views

Quadratic Equations mod p^k

As part of a larger program, I need to solve $A x^2+B x+C \equiv 0 \mod p^k$ for prime $p$. Right now I'm doing this by calling ...
2
votes
3answers
138 views

Extracting coefficients from g=a*x+b*y+c*x*y

I have a Response Surface Equation (RSE) that I'm trying to extract coefficients from. It has a form similar to: g = a*x + b*y + c*x*y; I want to be able to ...
1
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0answers
63 views

No response from DSolve

Using optimal control theory, I am trying to find the optimal paths of d and k such that they will maximize profit as given by lc: ...
2
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1answer
170 views

Resonance Curve using NDSolve

I am trying to make a resonance curve like this one below, using NDSolve. I tried to use code as below. Basically I try to hold solution for a w (driving frequency value) using NumericQ and then ...
1
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1answer
120 views

Problem to solve an integral equation [closed]

I am new to Mathematica. I am trying to numerically solve for C in the following equation: $\begin{equation} \begin{array}{lcl} -\int_0^\infty (5000000+100000 x+ C)^{-1} ...
1
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1answer
72 views

Asymptotics of sum of binomials

I would like to find the asymptotics of Sum[Binomial[n,i]*1/i^((n+1)/2),{i,1,n}] I saw Find asymptotics of Sum[2^i*Binomial[n-i-1,2*n/3-1],{i,0,n/3}] but I ...
2
votes
1answer
76 views

Solving Complex Equation Over Reals

I want to solve the equation $\frac{abi}{a+bi}=4-2i$, where $a$ and $b$ are real numbers. I know from hand-solving the answer is $a=5$, $b=-10$. How do I get Mathematica to tell me this? I tried: ...
1
vote
1answer
175 views

General form of a linear transformation

Let $v_1 = \begin{bmatrix} 2 \\ -1 \end{bmatrix}$ and $v_2=\begin{bmatrix} 1 \\ -1 \end{bmatrix}$ and let $A= \begin{bmatrix} 3 & 2 \\ -2 & 1 \end{bmatrix}$ be a matrix for $T\colon \Bbb ...
0
votes
0answers
62 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
0
votes
0answers
97 views

Second-order DSolve overdetermined with only 2 boundary conditions

I was going through some circuit analysis problem and came up with a second-order differential equation, which I decided to solve with Mathematica: $$ L\frac{\mathrm{d}^{2} I}{\mathrm{d}t^{2}} + ...
3
votes
1answer
393 views

How do I solve $1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x))= 0$?

Consider the equation $$ 1 - (1 - (A x)^2)^\frac{3}{2} - B(1 - \cos(x)) = 0 $$ where $A,B \in \mathbb{R}$ are constants. What is the analytic solution?
11
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1answer
154 views

ToNumberField won't recognize Root as an explicit algebraic number

In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an explicit algebraic number. ...
5
votes
1answer
280 views
0
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3answers
324 views

How can I solve my system of two simultaneous equations?

How to solve the system {b - a*Sqrt[a^2 + b^2 + 1] - a^2*(a*b - Sqrt[a^2 + b^2 + 1]) == 0, a - b*Sqrt[a^2 + b^2 + 1] - b^2*(a*b - Sqrt[a^2 + b^2 + 1]) == 0} ...
0
votes
1answer
80 views

Failure message from Reduce

I am getting the message Reduce::nsmet: This system cannot be solved with the methods available to Reduce. while trying to solve the following equation: ...
0
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0answers
73 views

Issue with NDSolve

This could be a stupid issue, but I have been checking for ages. I cannot solve this apparently innocuous system of PDEs: ...
3
votes
0answers
126 views

How to get vertices of a polytope given by equalities and inequalities?

I have a polytope given by some equalities and inequalities, how can I get all the vertices of the polytope? If there's a way to deal with the one given by inequalities only, how can I reduce the ...
2
votes
2answers
141 views

Plotting double inequality only for integer values

RegionPlot is plotting for all values. And using ListPlot I can only evaluate one inequality. How can I plot this type of ...
0
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0answers
43 views

Store results of inequality [duplicate]

I eveluated some values using Reduce commend and I store them in a Table ...
0
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3answers
88 views

Reduce of a table [duplicate]

I have a table for example: t = Table[k,{k,5}] which returns {1,2,3,4,5} and for every element in this table I want to check ...
2
votes
2answers
164 views

Solve the system of equalities and inequalities

I have a system of expressions, in which each expression is an equality or inequality expression of the following form: Var = Var1 + Var2 Var $\odot$ number Var $\odot$ Var1 $\odot$ = $\leq | \geq | ...
2
votes
1answer
106 views

Solving problems with the floor function

I've got the following problem: If I want to calculate the following equation, ...
1
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3answers
111 views

Discrete inequality plotting

I have an equation like this: $${20 \choose k}\cdot \sum_{i=0}^k {k \choose i}\cdot i \leq 1+f$$. I want to plot this inequality as the dependency between k and ...
9
votes
3answers
339 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
3
votes
3answers
215 views

How can I calculate a combination of limit and sum?

How can I solve the above problem? I enter it as: Limit[Sum[Sqrt[1 + i^2/n^2]/n, {i, n}], n -> Infinity] but this is not working:
0
votes
0answers
73 views

Assigning the answer of Solve to a variable [duplicate]

If I enter Solve[(x-2)(x+2)==0,x] then the answer comes up as {{x -> 2}, {x -> -2}} I want to make two variables ...
0
votes
3answers
256 views

Solving a differential equation with mixed conditions using DSolve

I want to solve a differential equation $$ \frac{d}{dx}\left(k_0 \left(\frac{T(x)}{T_0}\right)^n \frac{dT(x)}{dx}\right)=0,$$ with boundary conditions: $T(l)=T_0$, $\;T'(0)=-\frac{q_0}{k_0 ...
4
votes
5answers
332 views

Problem using WhenEvent to constrain solution

Note: This question has also been posted at the Wolfram Community Problem: Simulate pressure in volume 1 and 2 for 1 second. The circuit is as follows: From this I set up the governing DE for ...
1
vote
1answer
122 views

Solve returns a wrong answer

I'm afraid the following is rather localized questions, but I don't know how to simplify and generalize it. I have the following two points (in the real plane): ...
1
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1answer
103 views

NSolve with numerical function

I would like to solve numerically an equation which involves a numerical function constructed by fitting some data: ...
2
votes
2answers
162 views

Check if integer has even number of digits

I want to check if a number has an even or odd number of digits. 10 would be even because it has 2 digits 300 would be odd ...
0
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0answers
67 views

Reduce - Most efficient expression - Using FullSimplify

I am trying to solve complicated inequalities using Reduce, in order to determine whether certain mixed equilibria in game theory are stable. My first question ...
1
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0answers
199 views

Differential equations: How do I solve a delay differential equation with 0-1 variables

How do I solve the following non-linear, delay-differential equations using Mathematica under the assumptions $$p(t) = 1 ,\; y(t) > k$$ $$p(t) = 0,\; y(t)<= \ k$$. $$ \frac{dw}{dt} = ...
9
votes
1answer
341 views

Mathematica implementation of Earth Movers Distance?

Has anyone implemented in Mathematica the Earth Mover's Distance (EMD)? A concept dating back to Monge 1871, used to compare histograms and images, e.g., the CIEDE2000 Color Difference algorithm. ...
2
votes
1answer
118 views

How can I exhibit the evaluation of formulas in a Mathcad-like way?

How can I create a function F that works like this: x = 2 f1 = x^2 + 3 f2=x+5 F[f1] x^2 + 3 = 2^2 + 3 = 7 ...
0
votes
1answer
99 views

NDSolve + FindRoot for Bessel Zeros

I am trying to use a solution given by Michael E2 in this topic: ...
6
votes
1answer
317 views

What are the algorithm details of FindRoot?

The Help page of FindRoot says: "by default, FindRoot uses Newton's method (Newton-Raphson) to solve a nonlinear system". But I ...
8
votes
2answers
461 views

Can Mathematica solve this sort of functional/differential equation?

I am looking for differentiable functions $f$ from the unit interval to itself that satisfy the following equation $\forall\:p \in \left( 0,1 \right)$: $$1-p-f(f(p))-f(p)f'(f(p))=0$$ Is there a way ...
1
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0answers
153 views

Why DSolve and NDSolve give different answer

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? Which one is ...
3
votes
2answers
285 views

How to solve a “tensor equation”?

I am trying to solve equations which looks like this: $$ T_{ab} - T_{bc} = a_1 T_{ab} + a_2 T_{ac} + a_3 T_{bc}, $$ where $T_{xy}$ are tensors. I want to get the $a_i$'s (in this simple example ...
0
votes
1answer
131 views

Small problem at equation solving

I have $2$ equations in $2$ parameters which involve integrations. The limits of the integrals can not be defined analytically. They also require equation solving and eventually I couldnt incorporate ...
2
votes
1answer
93 views

Plotting the solution of a 2nd order equation

I have got to solve a second order equation, where the coefficient depend on the parameter $k$: $$(A_k - \omega) (D_k- \omega) - B_kC_k = 0$$ so that also the solution $\omega=\omega(k)$ will depend ...
1
vote
1answer
120 views

Solving System of Inequalities Relatively

I have been trying to figure out how to solve a system of inequalities relatively. I don't care about values, I just want all possible ordering. An example system might be:$${b > r,\; p > r,\; c ...
7
votes
1answer
392 views

Issue with the NDSolve code

With this procedure, one may determine an eigen-value function $R(a)$ for any given $\Xi$ (say 0, 25, 50, 75, 100) ...
1
vote
2answers
118 views

Symbolic matrix equation

I am looking to a system of equations of the form $\pi =\pi P$, the one encountered in Markov chain theory. My $P$ variable is: ...