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

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2
votes
1answer
101 views

Exclusions found but Solve and Reduce don't find exclusions

I have the following from Stan Wagons Mathematica in Action. ...
4
votes
1answer
141 views

Dealing with 6 VERY large equations. Am I doing this correctly, and can I expect a solution?

I'm new to Mathematica, but so far, everything seems straight forward and intuitive, which is really nice. However, I've come to use this software since I have to show a rather nasty 3x3 matrix is ...
2
votes
1answer
53 views

“Reduce” an expression in terms of a sub-expression

Newbie here. I've been trying to use Reduce to solve a rather long equation. The evaluation has been running for more than hour now, but still hasn't stopped. I've got an inkling that if I were to ...
11
votes
2answers
632 views

Is there a way to symbolically invert a piecewise function

I have a piecewise function that is continuous and strictly monotonic, like this: f[t_] = Piecewise[{{t/4, t < 0}, {t/2, t < 3}, {3/2 + (t - 3)*3, True}}] ...
0
votes
1answer
66 views

Why does this evaluate to {}?

I'm stuck with what seems to be an extremely simple issue, still, I just can't seem to find the solution or even the cause of the problem. So my issue is that I have the following surfaces: ...
5
votes
2answers
108 views

How to stop solving after one solution is found?

With[{P = 12}, Solve[{a^2 + b^2 == c^2, a + b + c == P, 0 < b <= a, c > 0}, {a, b, c}, Integers]] {{a -> 4, b -> 3, c -> 5}} ...
3
votes
1answer
70 views
0
votes
1answer
73 views

Solving an NODE in series

How can I solve this NODE in series y''[x]^2 + (1/2)*y'[x] + (1/2) y[x] == p x + q. `p` and `q` are constant. But do not know how to actually solve it with ...
13
votes
1answer
338 views

ToNumberField won't recognize Root as an explicit algebraic number

Bug fixed in 10.0.0 In Mathematica 9.0.1, it appears that ToNumberField will not always recognize a Root object as an ...
3
votes
0answers
154 views

Is FindRoot wrong about its WorkingPrecision?

I noticed an odd mismatch between the behaviors of NDSolve and FindRoot. If you give NDSolve an equation of a certain precision, say 20, and tell it to use a higher WorkingPrecision, say 30, it will ...
5
votes
1answer
329 views
0
votes
1answer
60 views

how to simplify -1 to shared power (produced by Solve)

I want a real solution to look real. But this solution does not: ...
3
votes
1answer
178 views

Solve problem: Inconsistent or redundant transcendental equation

I would like to mechanically Solve[a y == (1 - a) x && u0 == x^a y^(1 - a),{x,y}], given 1>a>0 and u0>0. The emphasis is on mechanically: I know it is ...
5
votes
2answers
162 views

How to find an estimated root efficiently with binary stochastic estimation of the function?

I am trying to construct certain nice geometric patterns, and one particular feature I'm trying to optimize is the balance of black and white corresponding to point being inside, or outside a ...
5
votes
2answers
2k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
-2
votes
1answer
54 views

Generic approaches for multivariable polynomials across different domains [closed]

Mathematica newbie here. So I don't have a lot of time to read through the whole library of functions and language rules. So I'm trying to settle in on generic ways of doing the math that I'm going to ...
4
votes
2answers
278 views

Can I solve a certain equation?

Neither Mathematica nor Wolfram|Alpha can resolve the following. How else can I reach a solution? Reduce[(1 + x)^(2/m) - (1 - x)^(2/m) == (1 - x^2)^(1/m), x]
2
votes
2answers
158 views

Plotting the solution of a cubic equation against a coefficient in the equation

I have to plot the solution of the following equation against the coefficient $L$. Since it's a cubic equation, I'd like to filter out the real solution first and plot that then. The equation is $L r^...
2
votes
1answer
72 views

How to solve an equation given certain parameters?

I am new to Mathematica so please bear with me. I have an equation that has around 7 parameters and one unknown. I was able to use FindRoot to solve it; however, I ...
4
votes
2answers
230 views

Plotting results from Findroot

I know this has been asked, but I cannot seem to understand the solutions. What I need to know, because I have my first domiciliary test this Monday, is how to plot the output from ...
6
votes
2answers
237 views

NSolve erroneously gives no solution to a polynomial system

I have a polynomial system with three equations in three unknowns, the maximum degree is 26. Two equations are symmetric, i.e. eq1(x,y,z)=eq2(y,x,z). If I search ...
0
votes
1answer
87 views

Find all degenerate eigenvalues of a cubic equation

I have an equation that is cubic in w. The three solutions correspond to bands in a bandstructure, and are a function of wavevector ...
5
votes
3answers
250 views

Finding the conditions for degenerate solutions to a cubic equation

I have a cubic equation (corresponding to the band structure of a physical system) given by w in the code below. ...
1
vote
1answer
86 views

NSolve or Reduce for obtaining the results and connecting roots

Here I have one problem how to solve numerically equation for different values of one parameter x. I used just two digits because of length, but for x=0.57 I should have one real root and for others 0....
5
votes
2answers
416 views

Solve for x given an interpolation function, y

Given a list of data, lst={{x1,y2},{x2,y2},...,{xn,yn}} and the interpolation function fun, y=Interpolation[lst] which ...
1
vote
1answer
263 views

How to solve a certain coupled first order PDE system

I would like to find the solution $(U,V)\equiv (U(x,t),V(x,t))$ of the following system. \begin{equation} \displaystyle\left\{\begin{array}{l} \frac{\partial U}{\partial t}+(a+b x)\frac{\partial U}{\...
5
votes
2answers
353 views
19
votes
2answers
2k views

How do I split up a curve into chords 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 ...
5
votes
2answers
526 views

Finding Points of Tangency of a Circle and a Parametric Curve

I have the following Parametric plot Generated from the following: ...
1
vote
1answer
115 views

cross point of intersecting lines [duplicate]

What is the easiest way to find the crossing point of two intersecting lines passing lets say through points line1 = {p1,p2}, line2 = {p3,p4}?
5
votes
0answers
100 views

Using quantifiers with free indices as declarative conditions in equation solving

This is a toy example: Is there a way to rewrite Reduce[{Norm@{c[1], c[2], c[3]} == 1, 0 <= c[1] < c[2] < c[3]}, {c[1], c[2], c[3]}] ...
2
votes
3answers
289 views

Solve a transcendental equation in Mathemathica

I believe it is called a "transcendental equation", and I would like to find the best possible sollution. I tried to use Solve: ...
3
votes
1answer
191 views

Finding closest point to implicitly defined curve

I'm facing the following problem: Given an implicit curve given by $f(x,y)=0$ and an initial guess $(x_0,y_0)$ which is hopefully close to the curve, I want to find the point $(x,y)$ on the curve ...
4
votes
1answer
613 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 ...
23
votes
2answers
1k views

Using the Krylov method for Solve: Speeding up a SparseArray calculation

I'm trying to implement this Total Variation Regularized Numerical Differentiation (TVDiff) code in MMA (which I found through this SO answer): essentially I want to differentiate noisy data. The full ...
3
votes
1answer
213 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 ...
2
votes
1answer
628 views

Solving a transcendental equation

I want to solve the a transcendental equation, e.g. NSolve[-(1-x)*Log[1-x] - x*Log[x] == 0.5, x] Mathematica is not able to solve, wheres WolframAlpha -- is able ...
1
vote
1answer
88 views

Reduce Inequality

How can I reduce the inequality in terms of modulus of alpha. ...
2
votes
1answer
101 views

Implicit derivatives in one line. How do I do it?

I have this little script to derive implicitly $PrePrint = # /. {D[y_, x_, NonConstants -> {y_}] :> y'[x]} &; Example: ...
1
vote
0answers
182 views

How to solve a nonlinear overdetermined system of equations

i'm trying to solve a nonlinear overdetermined system of equations (124 equations, 123 variables) i tried this procedure (newton raphson) ...
2
votes
2answers
236 views

Finding integral points on a surface

Suppose I have a dimension formula (for a Lie algebra representation) that is as follows: $$ d(a,b) = {(a+1)(b+1)(a+b+2) \over 2} $$ Now consider the surface $F(a,b,n) = 0 = d(a,b) -n$ where $n \in \...
24
votes
6answers
7k views

Finding the intersection of a curve with an interpolation function

There are no issues trying to find the intersection points of two defined curves. ...
0
votes
2answers
132 views

Significantly different results between Mathematica and Wolfram Alpha with large radicals and small numbers [closed]

I have some code which involves tiny numbers being put to the power of very large numbers. The function I'm looking at is $\varphi = \omega(T) \left(1 - (1 - \epsilon)^{n_{e}(T)} \right)$ when $\...
2
votes
2answers
160 views

Solving a system of weird equations

I'm trying to have Mathematica solve a system of equations for a friend's work in Computer Vision. I'm essentially going in blind to this and am not very familiar with Mathematica syntax, so would ...
2
votes
1answer
103 views

Can't NSolve system of exponential and linear equations in several variables

At the moment I am stuck with the following code, when specified to use root , quadratic or log utility functions all it fine, only exponentials like: $\small \left\{-e^{-c_{0,1}}-0.25 e^{-c_{1,1}}-0....