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

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126 views

Finding Values of All Nine Constants in q-hypergeometric Equation

I suspect that an identity of the form $$\sum_{j=-n}^{j=n}(-1)^jq^{j(5j+1)/2}=\sum_{r=0}^{n}f_{ar+bn+c}(-1)^{n-r}q^{(n-r)(dr+en+f)/2}\frac{(q;q)_{gr+hn+j}}{(q;q)_{n-r}}$$ for $a, \dots , j$ integer ...
3
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1answer
202 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
0
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1answer
207 views

Center Manifolds

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7
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2answers
222 views

How to correct this, `f[a_] := FindRoot[eq == 0, {x, 0.5}]`, where `eq` contains a parameter $a$, without using `eq[a]`?

I want to solve an equation with a parameter $a$, and define the result as a function of $a$. It is something like this: ...
2
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1answer
340 views

why doesn't NSolve find all the solutions that Solve finds?

Define d[p1_, p2_] := (p1 - p2).(p1 - p2) to be the square of the distance between two points. I am trying to solve equations like: ...
2
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2answers
161 views

Graphical solution of a a two-variable system containing an equation and an inequality

I'm currently studying atmospheric-gravity waves and their dispersion relations. I want to have look at values of $(x,y)$ that solve the following system : \begin{equation}\label{}(1) \left\{ ...
0
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0answers
115 views

Can't Solve a system of differential equations, Solve takes too long

My question is probably not really interesting but I really need help on this because I won't have access to a more powerful computer. So my model contains 7 equations : ...
1
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2answers
2k views

Solve within a range?

Is it possible to solve an equation in which some some of the parameters have defined ranges? Example: ...
1
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2answers
712 views

Projection of curve 3D (x,y,z) on the x-y plane

I have a following systeme : \begin{equation} \left\{ \begin{array}{rcr} (\beta+\frac{1}{2}\delta^{2})\nu_{1}(u)-\delta\nu_{2}(u)+\nu_{3}(u)& = &0\\ ...
0
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1answer
100 views

RSolve works slow and does not give an analytical solution for solving high order linear difference equations

RSolve@@{{a[n]-a[n-10]==101}~Join~Table[a[i+1]==101+10i,{i,0,9}],a[n],n} I want to get the exact form of general formulas, but ...
0
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2answers
409 views

Symmetric function of the roots of a polynomial

First, I'm a beginner. I can compute the sum of roots with the follwing: Roots[x^7 + 5 x^6 + x^5 + x + 1 == 0, x] Plus @@ (x /. {ToRules[%]}) // Simplify Of ...
3
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3answers
231 views

Can Mathematica solve $x^{b^2} + ax^b -1 = 0$ for $x$ with $a>0$, $b>1$?

I have a problem that I can't seem to solve neither analytically nor with Mathematica. Namely, I have the expression $$x^{b^2} + ax^b - 1= 0,$$ which I want to solve for $x$ with $a>0$, $b>1$. ...
0
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1answer
355 views

Solve function doesn't work

I have the following system of equations that I need to solve: ...
0
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1answer
183 views

Nonlinear system of equations

I have been working to find an equilibrium solution for a Hamiltonian dynamical system. I have reduced the problem to the simultaneous solution of 3 equations: ...
0
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1answer
176 views
0
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1answer
115 views

NSolve cannot find the solution

I have some data which looks like: ...
0
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1answer
57 views

NSolve stalls when given an equation containing Log

Why does NSolve not work for this type of equation? ...
8
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2answers
234 views

What are the Method options Solve command accepts?

What are the Method options Solve command accepts? Solve has the Method option, however documentation contains no methods that it accepts...
3
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0answers
168 views

Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
2
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1answer
92 views

Strange behavior using variable in Exists

I came across a behavior that doesn't make sense to me when I tried to use Exists in Reduce. If I run commands: ...
2
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3answers
399 views

Is there a way to specify custom domains?

I want to solve for all solutions to the system of equations $a_1 a_2 a_3 b_4 + a_1 a_2 b_3 + a_1 b_2 + b_1 = 0$ and $a_1 a_2 a_3 a_4 = 1$ where the $a_i$'s and $b_i$'s take on values from $\{-1,1\}$. ...
2
votes
1answer
109 views

Problem with SquareWave in NDSolve

I would like to have a triangulare signal drive a ODE system, using SquareWave[]. Something seems to go wrong though during integration. Uext'[t] and ...
3
votes
1answer
521 views

What algorithms does NSolve use?

I've been using NSolve to find roots and now I've been wondering what underlying algorithm Mathematica uses. It's probabaly similiar to ...
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1answer
205 views

How to solve a non-linear equation?

I am trying to solve the following non-linear equation: $\frac{i e^{-x^2} \sqrt{\pi } x}{K^2}+\left(-0.131251-0.0379031 x^2-0.0151154 x^4-0.0100462 x^6+0.5 \left(0.00273859 +0.0400003 K^2\right) ...
0
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1answer
692 views

Solving a large system of non-linear equations

I am new to Mathematica, and I am currently trying to use it to solve a large symbolic system of non-linear equations. I began the code below about 30 hrs ago, and the Mathematica Kernal has been ...
3
votes
0answers
307 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 ...
0
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0answers
43 views

Verify “Type” of solution [duplicate]

I've written some Mathematica functions which allow the user to verify if a mathematical function has certain properties. What I'm basically doing is generating "random" functions in respect of ...
0
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1answer
216 views

Notebook keeps running when Solve for variable

This might be a simple question for the most of you, but I am very new to mathematica so please bear with me. I'll refer to the code below: ...
4
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2answers
1k views

What is the efficient way to code Successive Over-relaxation (SOR) method in Mathematica?

I have written a SOR method (SOR is this method) code using C-style procedural loops. However, I think there might be (much) better ways to achieve the same end in Mma avoiding these loops. So my ...
1
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1answer
307 views

How can I find a root of my transcendental equation near a certain point?

What function could I use to solve this equation for x: E^(-x^2) = 1 - Cos[x] I tried Solve, ...
1
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0answers
27 views

Minimizing roots of a transcendental equations [duplicate]

I'm trying to use the solution of FindRoot with parameters for further calculations. Annoyingly enough it always gives me trouble with replacing the parameters. As an example I'm attaching a simple ...
0
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1answer
137 views

Two questions on strategies for quantifier elimination

With the help of people here I was able to solve several cases similar to IC3 but this case - unlike the other cases - does not return an answer. I will try to run it for a day with 8 processors but ...
11
votes
3answers
855 views

Finding “Maxima” and “Minima” on a B-Spline

I need to find the "Maxima" and "Minima" on a B-Spline or more correct the points where the 2nd components of the derivate equal zero. For example: ...
1
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0answers
37 views

Correct use of Mathlink's MLGetRealList

I am attempting to use Mathlink from C. I have managed to return single values from mathlink to my c program, but I am having trouble with lists. Consider the Mathematica operation: ...
2
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0answers
893 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 ...
4
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3answers
445 views

Finding parameters making real part of eigenvalues vanish

I have the following $\;3\times3$ matrix: $\left( \begin{array}{ccc} 0.04 -0.4 b & 0 & 0.04 -0.4 b \\ 0 & -0.08-1.2 b & -0.06-0.9 b \\ 1.04 -0.4 b & 2.08 -0.8 b & 0 ...
0
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1answer
63 views

Help with Reduce, quadratic system of inequalities

I'm trying to obtain an equivalent system of inequalities to the one below but without the variables x and z. Somehow Reduce just repeats the command. ...
0
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4answers
159 views

RSolve fails on a two-equation non-linear system

I have a system of just two recurrence equations, I need to solve them and so I use RSolve: ...
1
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1answer
475 views

Why my differential equations become True? [duplicate]

I've been trying to solve a system of nonlinear differential equation, but the conditions are a bit weird. Two of the differentials equate to the same equation, but have different boundary ...
1
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1answer
298 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
0
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1answer
109 views

Equation in implicit form

This is simple example: v = {1.48622576, 1.53444276, 1.42299438} v/(v + 1) Out[1]:= {0.597784, 0.605436, 0.587288} In the above case expression v/(v + 1) is ...
0
votes
1answer
567 views

Solving a system of equations where two variables can only be one of several discrete values

I want to solve a three-equation system, but I need to constrain two of the variables so that they can only take one of several discrete values that I would specify (this is a circuit design problem ...
3
votes
0answers
143 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 ...
-1
votes
1answer
199 views

Mathematica Compute Time Is Extremely Long (Integrate simple function with parameter scan)

I was wondering if you can help. I have a set of equations I need to solve for a list of parameters; entering each parameter value and solving anew each time is simply not economical. I found a way ...
2
votes
0answers
49 views

How can I select two lists from a list of lists so that I receive the system of equations has only rational solutions?

I want to make a sytem of equations has the form $$\begin{cases} a_1x^2+b_1y^2 + c_1xy+d_1x + e_1y+3=0,\\ a_2x^2+b_2y^2 + c_2xy+d_2x + e_2y+3=0. \end{cases}$$ so that the given system of equations has ...
1
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1answer
77 views

Solve never terminates with simultaneous equation set

I have the following set of simultaneous equations that I want to solve symbolically. The two unknowns are $a$ and $d$. $a=\frac{c*(d/10)}{1 + (f/130) + (d/50)} - \frac{a}{1 + (a/100) + (d/100) + ...
0
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0answers
139 views

Solving a single equation with multiple parameters

If I wanted to solve equations like Cos[x]^2 = A Cos[Bx + C] + D what function should I use? The Solve function seems to only solve for as many variables as there are equations. Please note that my ...
1
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1answer
347 views

Marking the points of x-intercept on a plot

OK, I have a nice plot of some oscillating motion. I can read some stuff off the graph, but I thought it would be cool to show a dot where the curve hits the x-axis and a little label showing the ...
1
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1answer
158 views

How do assign an interval of values to a variable in order to use them in a function?

From my code (below) I have K1 and K2 set to zero in order to test this numerical method. However, K1 is on an interval from 0 to 32, and K2 is on an interval from 0 to 8. I would like to know if ...