Questions tagged [equation-solving]
Questions on the analytic and numerical equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
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Maximizing a function that is only defined numerically
I have a function of multiple variables that is only defined numerically. I am trying to maximize the function and find the critical points as fucntions of two parameters p and s using FindRoot but I ...
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Speed up this computation involving NSolve many times?
Can you think of a way of speeding up this computation ? I don't.
...
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Plotting an integral with solving for a specific constant [closed]
Given an Integral I(t) which is a function of a constant tc, this constant is determined with the condition I(tc)=0, how can I add this condition?
- 115
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Strange behavior of GroebnerBasis
Recently I tried to solve a multivariate quadratic equation over the reals, but with a parameter value. Since that took too long, I decided to try GroebnerBasis, ...
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How do I find roots of a third degree polynomial? [closed]
expr = G^2 X^3 -
2 Δ G X^2 + Δ^2 X + ((ℏ *G*η*
k*Subscript[E, l]^2)/(m*Subscript[Ω, m]^2)) == 0
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2
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How to modify the order of symbols to make the result more logical [closed]
Simplify[(1 - a) (1 - b)]
(-1 + a) (-1 + b)
How to modify the order of symbols to make the result more logical.
(1-a)(1-b)
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2
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Solution of a sixth degree polynomial
I want to get the solution to a 6th degree polynomial in a certain range.
I have the following code
...
- 117
2
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2
answers
105
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FindRoot with input as a list
I have three equations: eq1, eq2, eq3 with variables a,b,d,k. I wish to find the roots of these equations by assuming ...
- 379
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1
answer
77
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Adding Points on an Elliptic Curve
How do I do this in Mathematica?
The curve given by the equation $y^2 = x^3 + 29x + 7$ defined over the integers modulo $10007$
Adding the first pair of points $P = (3737, 4549)$ and $Q = (8286, 6097)$...
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2
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3
answers
240
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Getting all solutions to an equation on condition the variables are either 0 or 1
Given a list of 3-bit binary lists
b={{0,0,0},{0,0,1},{0,1,0},{0,1,1},{1,0,0},{1,0,1},{1,1,0},{1,1,1}};
I would like to have all possible solutions to
...
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1
answer
140
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Numerical solving diffusion equation in spherical coordinates
Mathematica nicely solves Poisson's equation in spherical coordinates as
...
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1
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53
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First order differential equation with two conditions
I want to produce all possible solutions for this equation:
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- 153
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1
answer
62
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Problems with Solve. Only works for specific parameters. Solve function do not "start"
I have the following problem I want to solve the following equalities.
My used code:
...
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2
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1
answer
141
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How to solve this integral equation numerically?
I am encountering difficulties while trying to numerically solve an equation in Mathematica that involves an unknown function and an integral. Specifically, the equation takes the form of
\begin{...
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2
votes
2
answers
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Selecting Solve results according to conditions
When using the Solve function I get four possible answers. How can I automatically get the option in which x and y are positive? Where to insert the conditions x>=0 and y>=0?
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How can I choose the integer numbers a, b, c, d, t so that the equation $\sqrt{a x^2+b x+c}=d x+t$ has two integer solutions?
The equation $\sqrt{x^2+36 x+180}=2 x+15$ have two integer solutions are $x = -5$ and $x = -3$. How can I choose the integer numbers $a, b, c, d, t$ so that the equation $\sqrt{a x^2 + b x + c} = d x +...
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Why this Solve cannot be solved [duplicate]
Solve[Sum[p*a[i], {i, 1, n}] == 0, p, Reals]
Solve[p*Sum[a[i], {i, 1, n}] == 0, p, Reals]
The first line of code cannot be solved, but when the variable ...
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Solving A System of Two Implicit Equations
I am solving a system of 6 equations, and I am interested to know the solution for different rhoBar values. Here is the input parameters:
...
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2
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Can a redundant condition be removed from a solution?
A solution to this equation:
Solve[{(p-x)^2 + (q-y)^2==d, p/q==t}, {p,q}, Reals]
has this repetitive condition:
$\displaystyle\quad d > \frac{x^2 - 2txy+t^2y^2}{...
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votes
1
answer
51
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How can i create an equation with a sum? [closed]
I have a list of $p_i$ and the condition that $\sum_{i=0}^{i=69} p_i = 1 $
I also have a list of 69 other different equations. I want to use NSolve to solve for the ...
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1
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How to find the variable $k$ which minimizes the function $\Omega^2$?
$$\Omega^2(k) = 4(\sum\limits_{m=1}^{\infty}\frac{1-\cos(km)}{m^{1+\alpha}})(\sum\limits_{m=1}^{\infty}\frac{1-\cos(km)}{m^{1+\alpha}} - A^2)$$
Let $A = 1$ and $\alpha = 1$ and write $w(k) := \sum\...
- 321
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50
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Get curve equation from parametrization
I am quite new to Mathematica and I have been wondering how to do this one very specific thing.
I have two functions $x(t)$ and $y(t)$ that are the parametrization of a curve, how would I get the ...
- 101
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2
answers
82
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`Reduce` is running forever
I'm trying to solve the last inequality in Reduce in the code below in terms of rmax under the parameter conditions included in <...
- 979
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How to speed up maximization of the Solve output?
I am trying to maximize the solution of the system of algebraic equations for different values of parameters. The problem is related to the absorbing times in Markov chains.
Here is the code
...
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3
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1
answer
143
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Cannot solve this polynomial equation
I'm trying to solve the following polynomial equation for $x$:
$$ (qx)^\alpha (1-qx)^{1-\alpha} = [(1-q)x]^\beta [1-(1-q)x]^{1-\beta} $$
where $\alpha, \beta, q, x$ are all strictly between 0 and 1.
...
2
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3
answers
129
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Multiple solutions from NSolve
I have a list of polynomial equations which I can solve using NSolve. However, it gives me a large number of similar solutions. The solutions are largely identical ...
- 16.1k
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1
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63
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Solving a non-algebraic equation at the symbolic level [closed]
Versions 10, 11, 12, 13.0.0.0 and 13.2.0.0 solves the following system of equations
...
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1
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1
answer
60
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Newton Raphson apply to Van der Waal Equation
I need assistance with this problem. I have two functions, where f1 corresponds to the dimensionless van der Waals equation of state, and function 2 corresponds to the dimensionless chemical potential ...
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1
answer
62
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Find an instance satisfying equation
I have the following equation with two variables xi and nu.
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1
answer
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Solving Nonlinear Algebraic Equation
What is wrong with the code below? Mathematica is taking a long time trying to solve it.
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71
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Solving inequality with `Reduce` doesn't work
I'm trying to solve an inequality in terms of one variable under some conditions for parameter. Here is the code.
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108
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Newton-Raphson Method Errors
I need assistance with this problem. I have two functions, where f1 corresponds to the dimensionless van der Waals equation of state, and function 2 corresponds to the dimensionless chemical potential ...
2
votes
2
answers
181
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Real zeros of complex function
I must find the zeros of a complex function $\xi$ that depends upon two real variables $B$ and $k$. The function is obtained by evaluating the determinant of the identity matrix of dimension $2n$ ...
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How to solve differential equations in just in reals? [closed]
I am working on a variation problem:
My goal is to find the curve that connects a point $(x_1, y_1)$ to another point $(x_2, y_2)$. When this curve is revolved around the x-axis, it should generate a ...
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How to solve this integro-differential equation in Mathematica?
I am a new user of Mathematica, and I am trying to figure out how to solve the following integro-differential equation in Mathematica:
$\frac{\partial c(x,t)}{\partial t} = -2 \mu x c(x,t) + 4 \mu \...
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1
answer
126
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Solve[] isn't producing a correct result
I want to find the exact algebraic roots of the following function in terms of Z, P, Q, <...
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Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation?
I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ...
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How does Mathematica select principal roots of complex numbers?
When I do
I^(1/3)
I get
Out[]:= (-1)^(1/6)
which is one of the solutions of $z^3=i$. There are two more solutions which are ...
- 4,137
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1
answer
141
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Solving system of first order PDEs
I am trying to solve the 1st order PDE system
\begin{align}
\xi_u^2+\eta_u^2&= \left(1+\frac{\xi^2+\eta^2}{4} \right)^2\\
\xi_v^2+\eta_v^2&=\left(1+\frac{\xi^2+\eta^2}{4} \right)^2
\end{align}
...
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How to convert the equation into this two forms?
The equation is:
x0^2/a^2 - y0^2/b^2 == 1
How to convert to this two forms:
b^2 x0^2 - a^2 y0^2 -> a^2 b^2
and
...
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Attempt to find a solution (out of potentially many) to a system of equations with FindInstance runs forever or crashes
I have a system of equations that in principle should have a solution (I would think not a unique one), which I want to solve. I am not interested in all solutions; I just want to locate one, assuming ...
- 561
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Computing Displacement Potential functions
I am new to Mathematica.
I am trying to compute the displacement Potential functions. My code is as follows.
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2
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How to interpret the solution and how to work with it further?
Please help me understand the solution to the following problem:
...
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1
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77
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Minimization of an implicitly specified function
exp - an experimental data, where expT - temperature, expChi - magnetic susceptibility
I ...
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1
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How to simplify? [closed]
The original formula is:
Abs[(a b)/x0]/(2 Sqrt[1 + y0^2/x0^2])
How do you convert operations to get this result?
...
- 2,879
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How can the process of hyperbola problems achieve the desired results?
As shown in the picture above, in the hyperbola x^2/a^2-y^2/b^2==1, point P is any point on the hyperbola, through the point P respectively do two asymptotes of the hyperbola parallel line PA, PB. The ...
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Calculate Bernoulli numbers ( with a twist) [closed]
Mathematica has an inbuilt function BernoulliB that calculates $B_n$ for which,
$$\frac{t} {\left(e^t-1\right)}=\sum_{n=0}^{\infty} \frac{B_n}{n !}t^n $$
I need to ...
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answer
49
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How do I plot a 2D function with an intermediate variable?
I have a function
$c\cdot\frac{x^2}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}} + x = c\cdot\frac{10^{-6.367-10.32}}{x^2 + 10^{-6.367}*x + 10^{-6.367-10.32}}+\frac{10^{-14}}{x}$, where $0 < x < 10^{...
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