Questions tagged [symbolic]

For questions about symbolic computation, as opposed to numerical computations.

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0 votes
0 answers
38 views

Annoying Glitch when inserting symbols

Anybody else had this glitch when inserting symbols This should be ::Delta
2 votes
1 answer
106 views

Another solution to a simple DE given by DSolve: not the one I expected

Consider a simple 2nd-order differential equation with a parameter $a$, which can be solved with DSolve: ...
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0 votes
1 answer
79 views

When running code to compute a sequence, loop variable gets set to a constant

I would like to write Mathematica code to read in a list of sequences, and print the sequence definition ($a_n$), along with the sequence evaluated at a few values of $n$. ...
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3 votes
2 answers
174 views

How are Symbolic Vectors Defined?

It is my understanding that undefined symbols are considered scalars, so I can't index variables that aren't defined. It is possible to define a symbol as a vector of symbols as follows, allowing ...
1 vote
2 answers
58 views

How to print particular cases with Integrate?

I would like to perform the following simplification: ...
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0 votes
2 answers
93 views

Calculating an integral with a seemingly complicated integrand

I would like to calculate the following integral: $$ I=\int_{0}^{1} \min (1,(u-1)^{n-1}(u-v)^{n-1}) dv $$ where $u$ is a constant taking values between $1$ and $2$ and $v$ is variable whose range is $(...
4 votes
1 answer
127 views

DSolve solution for 1st order PDE involving complex number does not match initial condition

Bug introduced in 11.3 or earlier, persisting through 13.2.1. [Mathematica 12.0.0.0, MacOS X x86 (64bit)] Trying to solve ...
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1 vote
0 answers
31 views

Simplifying symbolic sums using KroneckerDelta

I am trying to use Mathematica to simplify a symbolic expression of the following form $$ S_i = \sum_{n_1 = 0}^\infty \sum_{n_2 = 0}^\infty \ldots \sum_{n_M=0}^\infty n_i \times \Big( \sum_{j = 1}^...
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0 votes
0 answers
37 views

Nest n-times a multi-variable function with only one of the variables being updated with previous function value

I have a function y1 of three variables, x, y, and z. (y1 also depends upon f1 defined previously). I would like to Nest or interate, such that on the nth iteration, the y1's 3rd variable, z, will be ...
2 votes
2 answers
83 views

Symbolic matrix tensor an identity without specifying the dimension?

I want to calculate an expression like $\left( M_1\otimes I+I\otimes M_2 \right) ^l$ with $M_i$'s symbolic matrices and $I$ the identity matrix with Mathematica. $M_i$'s are of the same dimension and ...
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1 vote
1 answer
67 views

TensoriaCalc does not display the correct output

I am trying to use TensoriaCalc to calculate the components of the Ricci and the Riemann tensor of the following metric: $R^{2} \left(d\theta^{2} + \sin^{2}\left(\theta \right)d\phi^{2} \right)$; ...
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2 votes
0 answers
47 views

SymbolicGPU documentation

I found an interesting files there $CUDALinkPath -> ../GPUTools here ...
0 votes
0 answers
42 views

Simplifying expresion with Defer and derivatives

I would like to simplify a complicated expression that contains some derivatives whose evaluation is halted with Defer, using some custom simplification rules. For ...
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0 votes
0 answers
31 views

Expanding a large dynamic expression involving roots of a degree 4 polynomial

I am trying to find the eigenvalues of a 4x4 Matrix symbolically. Below is the code I am using, ...
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1 vote
0 answers
76 views

Using DSolve to solve the Hypergeometric ODE in terms of Legendre Polynomials

I have been curious about if is it possible to "Force" DSolve to get solutions of differential equations in terms of another related functions. Eg. The ...
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0 votes
0 answers
62 views

Answer changes slightly when re-run

I am trying to resolve why I get slightly different answers when I re-run my notebook. Here is my full code: ...
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2 votes
1 answer
257 views

How to calculate infinitesimal analytic continuation?

Many problems in science and engineering are related to the analytic continuation and in particular infinitesimal analytic continuation to the upper or lower complex plane, i.e., a generic complex ...
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2 votes
2 answers
121 views

Collect with symbolic exponents does not simplify any further

I am trying to simplify a symbolic expression. Here is an example: ...
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1 vote
3 answers
76 views

Local variables in a module don't show their actual values

I need to do the following transformation that pick[a,b] -> ex[c|->{c[a],c[b]}] ex is a function that accepts a function as parameter which returns a list ...
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1 vote
1 answer
62 views

Reduce equations formed of symbolic matrices and vectors

I was defining the following assumptions $Assumptions = {A ∈ Matrices[{3, 3}, Reals], x ∈ Vectors[3, Reals], b ∈ Vectors[3, Reals]} ...
2 votes
1 answer
116 views

Solving differential eqation x''(t)+a x'(t) x(t)+b x(t)^3-c x(t)^2=0 symbolically [closed]

I can't solve the following differential equation: DSolve[{x''[t] + a x[t] x'[t] + b x[t]^3 - c x[t]^2 == 0}, {x[t]}, t] It returns the original input. How can we ...
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1 vote
0 answers
47 views

Finding the (symbolic) eigenvalues of a matrix with some assumption

I have the following 3$\times$3 symmetric matrix with symbolic entries. Meff = \begin{array}{ccc} 2 \beta \text{c12}^2 \text{c13}^2 \text{$\eta $11} \text{m1}+\alpha \text{c13}^2 \text{D31} \text{...
2 votes
1 answer
111 views

Pathological expression for field strength contractions in a curved background

I am trying to define in Mathematica the quantity $\star F^{\mu}=\frac{1}{2}\epsilon^{\mu\alpha\beta}F_{\alpha\beta}$, where $F_{\mu\nu}=\nabla_\mu A_\nu-\nabla_\nu A_\mu+\left[A_\mu,A_\nu\right]$. ...
24 votes
3 answers
777 views

Why does V 13.2 DSolve now return no solution instead of implicit solution for some differential equations?

V 13.2 DSolve now returns {} as solution for some ode's, while V 13.1 returns solutions for same ode's but with ...
  • 127k
2 votes
2 answers
121 views

Finding minimum of a symbolic function [closed]

Why does Mathematica fails to find the minima of the two variable function with real coefficients. The function and my attempt is given below. Input: ...
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2 votes
2 answers
81 views

Numerical solution to given equation involving one variable

Any neat way to solve this equation? ...
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0 votes
0 answers
29 views

Mixed system of PDE and integral equations is solved manually, but not solved automatically

I continue to study the issue raised here. There is one technical difficulty that requires a separate topic. I have a system of equations: ...
  • 2,304
0 votes
0 answers
40 views

How can I make Mathematica catch one-off cases where the answer is different? [duplicate]

I wanted to compute $$\frac{2}{L}\int_0^L\left(1+2\cos\frac{3 \pi x}{L}\right)\cos\frac{n \pi x}{L}\,dx,$$ so my input was ...
1 vote
0 answers
50 views

Replace original function inside its derivative

I'm trying to simplify a derivative calculation. I have the Zhs in function of x : ...
2 votes
3 answers
178 views

First order Differential equation with boundary condition

I'm wondering why it is not solving with the Mathematica?? ...
1 vote
2 answers
66 views

Integration gives very different answers when some variables are specified

When Matematica does this integral $\int \frac{k}{\sqrt{a^2 n^2 y^2+2 a n^2 y-k^2+n^2}} \, dy$ the result is $k \left(\frac{\log \left(\frac{a n y+n}{\sqrt{(a n y+n)^2-k^2}}+1\right)}{2 a n}-\frac{\...
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0 votes
1 answer
73 views

Integrating a function over the interval formed by the largest two real roots of a cubic equation

Description of the problem: Suppose I have a depressed cubic equation $-x^3+p^2x-q^2=0$ under the condition (the local max is larger than zero and local min is less than zero) $$-\frac{2}{3\sqrt 3} |p|...
  • 101
4 votes
0 answers
112 views

Differentiating with D vs. Derivative

I was tinkering with something and needed a high-order derivative of a function that, when differentiated, needs the product rule (and so, subsequent derivatives - without simplification - become ...
  • 2,661
6 votes
1 answer
214 views

Solve PDE system for Helmholtz decomposition

In the article Analytical Helmholtz Decomposition and Potential Functions for many n-dimensional unbounded vector fields on page 3 presents the formulas (6-8). If I understand these formulas correctly,...
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3 votes
0 answers
38 views

Why is TensorContract[x, {}] not always x?

If I use TensorTranspose on an undefined symbol, nothing happens unless the permutation is the identity. For instance, ...
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6 votes
2 answers
337 views

How to generate a horizontal histogram with words?

I have a dataset of the type: ...
  • 1,238
1 vote
2 answers
95 views

Symbolic derivative of transposition

I have an expression: expr = Transpose[x]+Transpose[f[x]]+Transpose[x+f[x]] I want to differentiate this expression and desired result looks like this: ...
  • 2,304
0 votes
0 answers
57 views

LaplaceTransform doesn't work

I have code: A = 1; ω0 = 5*10^6; τ0 = 3*10^-3*Sqrt[2/Log[2]]/(5.85*10^3); s0[t_] = A*E^(-t^2/τ0^2)*Cos[ω0*t]; Phi[ω_] = LaplaceTransform[s0[t], t, ω] The last ...
1 vote
2 answers
72 views

How to force mathematica to calculate the integral?

When calculate temp = Integrate[Integrate[f[x], x] + D[f[x], x], x] Mathematica gives $$ \int{({\int f[x]dx}+ f'[x])dx} $$ instead of $$ \iint{f[x]dx dx} +f[x] ...
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1 vote
2 answers
141 views

I want Mathematica to evaluate $\int(1 + \delta (x - \text {x0})) p[x] dx$ as $p[x0]+\int p[x] dx$, where $p[x]$ remains unspecified

I define the simple function: Simp[h_] := Integrate[h[x] p[x], {x, -∞, ∞}] where the function p[x] is continuous, but I want ...
  • 11
0 votes
3 answers
119 views

Calculation using symbols instead of assigned values [closed]

How can I calculate with the symbols itself not using assigned values? a = 2; Simplify[a + 2 a] This example returns 6 but I ...
2 votes
2 answers
96 views

Symbolic derivative about functional and substitute function

I have trouble with symbolic functional derivatives and substitute , for example, result1 =[D[f[x, y], x]] $result1 = \frac{\partial f[x,y]}{\partial x} $ next, i ...
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2 votes
0 answers
58 views

Asymptotic expansion for a function containing irrational exponents

I'm trying to find an asymptotic expansion of a function containing irrational exponents in the form of a power series (which also might contain irrational exponents). It works correctly if I request ...
2 votes
2 answers
204 views

Solve the Differential Equations of r and θ to find the r(θ)

There are some differential equations. $r''+r\theta'^{2}=0$ $r\theta''+2r'\theta'=0$ And $r=r(x)$ and $\theta=\theta(x)$. And I want to get the $r(\theta)$. I tried to solve the $r(x)$ and $\theta (x)$...
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1 vote
1 answer
69 views

Am I calculating the limit of this discrete time system correctly?

Background I have the following discrete-time system: (*System: x(t+1) = Ax(t)*) (*Conditions: Q1+Q2=1; Q1 >= 0; Q2 >= 0*) A={{Q1,1-Q1},{Q2,1-Q2}}; ...
0 votes
1 answer
94 views

Is there a way of calculating Expectation Values of tensor operators in Mathematica?

This Wikipedia article in on Bell's Theorem lists a whole bunch of expectation values for Bell states: $$\langle A_0 \otimes B_0 \rangle = \frac{1}{\sqrt{2}}, \langle A_0 \otimes B_1 \rangle = \frac{1}...
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4 votes
2 answers
438 views

Evaluating an integral symbolically seems impossible

I have an integral of general form $$ i_n(z)=\dfrac{z^2}{K_2(z)}\int_1^{\infty} \dfrac{\left(x^2-1\right)^{n+\frac{3}{2}}}{x^{2n+1}} \exp(-zx) dx $$ $K_2(z)$ is the bessel function and $0.01 \...
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6 votes
4 answers
340 views

How to simplify expression through variable substitution [closed]

I am trying to simplify a complicated expression through variable substitution and part of the expression looks like: $2A_1^2+A_1B_2+2B_1^2-B_1A_2+2C_1^2+C_1D_2+2D_1^2-D_1C_2$ I want to substitute $...
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0 votes
1 answer
60 views

I'm trying to solve the indefinite integral of a real function (with a bunch of real parameters inside) but the result is a complex function

The integral I'm trying to solve is $$ \int{\frac{12\left(c_3-R\ c_2\cos{(\frac{s}{R}})+R\ c_1\sin{(\frac{s}{R})}\right)}{l\ Y\left(\frac{H}{2}+4k\frac{s(s-\pi R)}{(\pi R)^2}\right)^3}ds} $$ but, when ...
2 votes
2 answers
99 views

Replacing symbolic variables inside of a compile

As the result of a symbolic integration, I have a very long array with symbolic variables u[i] which I would like to substitute for real number values. Moreover, I ...
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