Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,477
questions
0
votes
0
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38
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Annoying Glitch when inserting symbols
Anybody else had this glitch when inserting symbols
This should be ::Delta
- 163
2
votes
1
answer
106
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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:
...
- 1,217
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 $n$.
...
- 1,939
3
votes
2
answers
174
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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
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How to print particular cases with Integrate?
I would like to perform the following simplification:
...
- 232
0
votes
2
answers
93
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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 $(...
- 201
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
...
- 175
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}^...
- 219
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37
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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 ...
- 33
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 ...
- 135
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)$;
...
- 111
2
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0
answers
47
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SymbolicGPU documentation
I found an interesting files there
$CUDALinkPath -> ../GPUTools
here
...
- 597
0
votes
0
answers
42
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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 ...
- 255
0
votes
0
answers
31
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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,
...
- 15
1
vote
0
answers
76
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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 ...
- 36
0
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0
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62
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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:
...
- 1
2
votes
1
answer
257
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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 ...
- 4,584
2
votes
2
answers
121
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Collect with symbolic exponents does not simplify any further
I am trying to simplify a symbolic expression. Here is an example:
...
- 143
1
vote
3
answers
76
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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 ...
- 307
1
vote
1
answer
62
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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
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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 ...
- 21
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{...
- 11
2
votes
1
answer
111
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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
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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:
...
- 189
2
votes
2
answers
81
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Numerical solution to given equation involving one variable
Any neat way to solve this equation?
...
- 3,128
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,$$
so my input was
...
1
vote
0
answers
50
views
Replace original function inside its derivative
I'm trying to simplify a derivative calculation. I have the Zhs in function of x :
...
2
votes
3
answers
178
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First order Differential equation with boundary condition
I'm wondering why it is not solving with the Mathematica??
...
- 447
1
vote
2
answers
66
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Integration gives very different answers when some variables are specified
When Matematica does this integral
$\int \frac{k}{\sqrt{a^2 n^2 y^2+2 a n^2 y-k^2+n^2}} \, dy$
the result is
$k \left(\frac{\log \left(\frac{a n y+n}{\sqrt{(a n y+n)^2-k^2}}+1\right)}{2 a n}-\frac{\...
- 11
0
votes
1
answer
73
views
Integrating a function over the interval formed by the largest two real roots of a cubic equation
Description of the problem: Suppose I have a depressed cubic equation $-x^3+p^2x-q^2=0$ under the condition (the local max is larger than zero and local min is less than zero)
$$-\frac{2}{3\sqrt 3} |p|...
- 101
4
votes
0
answers
112
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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,...
- 2,304
3
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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, ...
- 228
6
votes
2
answers
337
views
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
$$
\iint{f[x]dx dx} +f[x]
...
- 69
1
vote
2
answers
141
views
I want Mathematica to evaluate $\int(1 + \delta (x - \text {x0})) p[x] dx$ as $p[x0]+\int p[x] dx$, where $p[x]$ remains unspecified
I define the simple function:
Simp[h_] := Integrate[h[x] p[x], {x, -∞, ∞}]
where the function p[x] is continuous, but I want ...
- 11
0
votes
3
answers
119
views
Calculation using symbols instead of assigned values [closed]
How can I calculate with the symbols itself not using assigned values?
a = 2;
Simplify[a + 2 a]
This example returns 6 but I ...
- 690
2
votes
2
answers
96
views
Symbolic derivative about functional and substitute function
I have trouble with symbolic functional derivatives and substitute , for example,
result1 =[D[f[x, y], x]]
$result1 = \frac{\partial f[x,y]}{\partial x} $
next, i ...
- 25
2
votes
0
answers
58
views
Asymptotic expansion for a function containing irrational exponents
I'm trying to find an asymptotic expansion of a function containing irrational exponents in the form of a power series (which also might contain irrational exponents). It works correctly if I request ...
- 7,058
2
votes
2
answers
204
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Solve the Differential Equations of r and θ to find the r(θ)
There are some differential equations.
$r''+r\theta'^{2}=0$
$r\theta''+2r'\theta'=0$
And $r=r(x)$ and $\theta=\theta(x)$.
And I want to get the $r(\theta)$.
I tried to solve the $r(x)$ and $\theta (x)$...
- 23
1
vote
1
answer
69
views
Am I calculating the limit of this discrete time system correctly?
Background
I have the following discrete-time system:
(*System: x(t+1) = Ax(t)*)
(*Conditions: Q1+Q2=1; Q1 >= 0; Q2 >= 0*)
A={{Q1,1-Q1},{Q2,1-Q2}};
...
- 515
0
votes
1
answer
94
views
Is there a way of calculating Expectation Values of tensor operators in Mathematica?
This Wikipedia article in on Bell's Theorem lists a whole bunch of expectation values for Bell states:
$$\langle A_0 \otimes B_0 \rangle = \frac{1}{\sqrt{2}}, \langle A_0 \otimes B_1 \rangle = \frac{1}...
- 243
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 \...
- 693
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votes
4
answers
340
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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 $...
- 73
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 ...
- 153