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

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7
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0answers
464 views

Creating and using an explicit piecewise function in a convenient way

I have a set of data points that define a function in the form curvePts = {data1,data2,...} where ...
7
votes
0answers
187 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 ...
6
votes
0answers
138 views

FindRoot kills kernel

Bug introduced in 7.0.1 or earlier. Persists through at least 10.0.2 I'm having problems with FindRoot killing the kernel. In my real application, I want to FindRoot on a black-box function ...
5
votes
0answers
81 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite ...
5
votes
0answers
1k views

Solve huge symbolic system of linear equations

I have a system of 76 symbolic linear equations (i.e. some coefficients are symbolic) with a sparse coefficient matrix. However, neither Solve[] nor ...
5
votes
0answers
90 views

Faster way to perform SameQ[Reduce[…], Reduce[…]]

I'm have some expressions that I need to confirm the equality of. SameQ[Reduce[...], Reduce[...]] works like a charm for the more simple expressions, however when ...
4
votes
0answers
226 views

What is the algorithm behind Mathematicas Reduce in this equation?

Mathematica can use Reduce to arrive at an answer in this equation ...
4
votes
0answers
256 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 ...
4
votes
0answers
156 views

Solving a nasty equation

Here's an equation that I need to solve for $t_k$ $$ \theta_0 = \tan^{-1}\left(\frac{2(w_x - m)}{p - g {t_k}^2 - 2 t_k w_y}\right) - {\frac{1} {r}} \left( \left(\frac{m}{t_k}\right)^2 + \left( ...
4
votes
0answers
117 views

Symbolic solution to ODE, pure InverseFunction not evaluated

I'm new to Mathematica and I don't understand why in the solution of the following ODE, the #1 in the pure function is not immediately replaced by the corresponding ...
3
votes
0answers
132 views

Nonlinear FEM and FindRoot

I'm trying to develop a kind of nonlinear FEM application using mathematica to solve a bvp like the following: $$ \gamma(u') ~u^{iv} + 2 \gamma'(u') u''' u''+ u''^3 = f(x) $$ where $u = ...
3
votes
0answers
261 views

Function with a sharp resonance which Mathematica fails to integrate. Why?

I'm a new user of Mathematica and I'm trying to use it to calculate the collisional cross-section as a function of energy for a given potential and decay rate. I know that the resulting function ...
3
votes
0answers
110 views

Solving huge equations

I have this expression: $d=-\frac{\sqrt{\frac{780 (f+130) \left(5 d^2 (13 c+f+130)-5 d (c (f+1300)-325 (f+160))+125 \left(2 (2 c+725) f+5 f^2+104000\right)+13 d^3\right) \left(5 d^2 (52 c+17 ...
3
votes
0answers
95 views

Deciding whether a semi-algebraic set is empty. Which command is best?

[Update] I was able to prove that the "larger" set $ 1\ge x \ge y,w \ge 0$ and $p(x,y,w)>0 $ is empty with another computer algebra system in my slow laptop in few minutes but in Mathematica even ...
3
votes
0answers
524 views

FindRoot gives a wrong solution which obviously should not be there

I got stuck on FindRoot and I didn't see any similar problem posted, so let me explain what I am trying to do and what problem I meet here. I try to find roots of a particular function, which in the ...
3
votes
0answers
152 views

RSolve not returning known solution

I have the following recurrence relationship for which I know the solution is given by a binomial distribution: ...
3
votes
0answers
1k views

Solving a system of nonlinear equations self-consistently

I am trying to solve a set of three non-linear equations in Mathematica. I need help with them. The Mathematica code (in plain text format) is attached below. If you copy & paste the code below ...
2
votes
0answers
48 views

Simplify large fractions

Hi i'm quite new with Mathematica and i'm experiencing some problems with Simplify and FullSimplify. I'm dealing with a sistem ...
2
votes
0answers
55 views

NDSolve is running an extremely long time: how can I save the existing data?

I am trying to solve a PDE by the following code. It takes 1 hour or so to reach t=25.72 but about 20 hours to reach t=25.72404031638060174049337306126853310997. Actually, the time step is extremely ...
2
votes
0answers
116 views

Proving large inequality in 6 variables

I have arrived at a very large inequality in 6 variables that I would like to prove is true. The command I have tried is the following: ...
2
votes
0answers
86 views

Apart for complex roots?

Let p[x] be a polynomial in x and consider the partial fraction decomposition of 1/p[x]. ...
2
votes
0answers
121 views

What are the steps using boolean algebra for transforming one equation into another?

I have a special case where I have two equations, which I have solved in a better and quicker way, but I need to solve with Boolean algebra. Using the laws of Boolean algebra, I have to prove that ...
2
votes
0answers
127 views

Volterra integral equation

I have to find an approximate numerical solution for the equation $$ F(x) - \lambda \int\limits_1^{x} \text{d}s \;s^2 F(s) Z(x-s) = G(x) $$ $$Z(s) = (\psi''(1-2\ h\ i\ s)- 0.5 \psi''(1-2\ h\ i\ s))$$ ...
2
votes
0answers
74 views

How does Mathematica resolve symbolic systems of inequalities?

Before getting into my (probably annoying) question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A ...
2
votes
0answers
178 views

Solving a system of two nonlinear equations with many symbolic parameters

I have two nonlinear equations with two unknowns, $x$ and $y$, and many symbolic parameters, $a, b, c, d$. They look someting like: $\frac{1}{x}(1+x)^a (1-b)(cx+dy)=0$ ...
2
votes
0answers
102 views

Solving a system of difference equations in an exponential steady-state growth setting

I have a system of difference equations in an exponential steady-state balanced growth setting; all variables grow at the same steady-state rate, say, $g$. I use the notations as follows: Variable $X$ ...
2
votes
0answers
98 views

Error when using EquationTrekker

I just got to know EquationTrakker because I need to do phase graphs for my classes. When I load it ...
2
votes
0answers
65 views

How to solve for exponents in an infinite product?

Say I have a power series, $f(x,y) \in 1 + x\mathbb{Z}[[x,y]]$ Then it admits a unique expansion $$f(x,y) = \prod_{i=1}^\infty \prod_{j=0}^\infty (1 - x^i y^j)^{n_{i,j}}$$ for some integers, $i, ...
2
votes
0answers
94 views

Quartic equation

After using Solve I am choosing the physical root of my equation and dealing further with this root. However, when I am changing parameters using Manipulate, I clearly see not smooth behaviour. Is ...
2
votes
0answers
91 views

How to handle infeasible points in FindRoot?

I am calling FindRoot[f[x,y],{{x,xInit,xMin,xMax},{y,yInit,yMin,yMax}}] where for some points {x,y}, ...
2
votes
0answers
402 views

FindRoot in range

I am trying to find all roots in a range, using y /. FindRoot[Sin[y] == 0, {y, #}] & /@ Range[7] which gives ...
2
votes
0answers
54 views

Equation involving hypergeometric functions

I want to solve this equation but nor NSolve nor Solve are able to do this. ...
2
votes
0answers
117 views

Question about Solve

I don't understand what Mathematica is doing to get these solutions. I ask it to solve two equations, the left hand side of both expressions are the same, the right hand sides differ by a ± sign. I ...
2
votes
0answers
122 views

Equation Solving: Solution in terms of predefined functions

Is there a way that I can have Mathematica give me the solution of a problem it has solved in terms of functions that I have predefined? The specific problem I'm trying to solve is: ...
2
votes
0answers
197 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
2
votes
0answers
485 views

I can't solve this set of equations

I am having trouble solving a set of equations in mathematica. I do not get any errors, but i don't get any answers as well. I have some restrictions on my parameters and variables in the equations ...
2
votes
0answers
136 views

Nest for large value of n

I am working on a problem to find the Feigenbaum constant. In this problem I have to get $f^{2^n}(1/2)$ with $f(x) = kx(1-x)$. I use Nest to get $f^{2^n}(1/2)$ but ...
2
votes
0answers
306 views

Conditional statements in intial conditions?

This is potentially a daft question, but I thought I'd ask it; I have some material free to diffuse in a boundary between rn and ro; I've been able to get it working nicely for neumann type boundary ...
2
votes
0answers
339 views

differential equations with implicit functions

I have an ordinary differential equation that contains coefficient functions that depend implicitly on the independent variable via an algebraic equation. I am trying to go ahead and use NSolve to ...
2
votes
0answers
162 views

Why is FindRoot initial value far from the specified one?

I am trying to numerically find the root of a function that looks a bit like: 1/x - (SchurDecomposition[A[x]][[2]])[[1]], where ...
2
votes
0answers
189 views

Solving $k\log(n) - k\log(k) \leq u$

How can I persuade Mathematica to help me find solutions to the inequality $k\ln(n) - k\ln(k) \leq u$ over the reals, assuming $u \geq n \geq k \geq 1$. When I evaluate ...
2
votes
0answers
221 views

Am I entering this 2-variable recurrence correctly?

I'm trying to solve this recurrence with two variables. ...
2
votes
0answers
297 views

FindRoot - Speed and errors

I am using FindRoot[] to solve a complicated equation. It seems I get the correct answer even though I get errors about an ...
2
votes
0answers
411 views

Numerically/Analytically Solving a System of Equations

I have $6$ functions $f_i(x,y,z)$, $(i = 1, \ldots, 6)$ in three variables $x,y,z$, and I would like to find a simultaneous instance of these variables, say $(x_0, y_0, z_0)$, such that $f_i(x_0, y_0, ...
1
vote
0answers
66 views

Using Solve without introducing extra variables

First post here. I've tried searching for an answer for this for a few days now, but it seems the search terms (solve, slot, etc) are too generic to be helpful. I'm struggling with understanding how ...
1
vote
0answers
31 views

Trouble using Solve and NSolve with functions involving Erf

I have the following functions: R[k_, x_, t_] := -.5*(k - x)*(1 + Erf[-(k - x)/t]) L[k_, c_, x_, t_] := .5*c*(k - x)*(1 + Erf[(k - x)/t]) I'm interested in ...
1
vote
0answers
61 views

How to find Pauli matrices

I wanted to find the Pauli matrices, so i wrote down this code: z = {{a, b}, {c, d}} i = {{1, 0}, {0, 1}} Solve[z.z == i, {a, b, c, d}] and mathematica gave me ...
1
vote
0answers
88 views

Mathematica reading my mind - Solve knows which variable to solve for

I was checking some of my algebra with the following code; ...
1
vote
0answers
43 views

Equation solving: Solve returns a periodic solution

I have a very simple trigonometric equation, that I've been trying to solve for a variable for a few hours now: (I couldn't find how to correctly format this) ...
1
vote
0answers
40 views

Input `Reduce[Mod[a + x, l] == 0, x]' and output `x == -a + kl`?

Reduce[a + x == k l && k > 0, x] (* k > 0 && x == -a + k l *) I think a + x == k l and ...