Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,538
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How to make Assumptions in IntegrateChangeVariables?
There is a new useful command IntegrateChangeVariables since 13.1.
The command has the Assumptions option which is very poorly ...
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0
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64
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Help implementing Lagrange inversion
I'm attempting to find the coefficients of generating functions using Lagrange inversion. I am finding the series coefficients with:
...
2
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2
answers
230
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The center of mass of a semiellipsoid
I am trying to find the center of mass of a semiellipsoid using cylindrical coordinates.
r^2/a^2+z^2/b^2 < 1, z < 0 the density = 1.
I know that the center of mass is (1/M int,int,int rcos(theta)...
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Largest integer between 1 and 1000 with no letter "n"
This problem is easy to solve logically - try it for fun if you want before you run the code and see the answer.
...
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39
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How to pattern match multivariate integral?
I have been using a pattern
Integrate[c_ f_, it:{x_Symbol, __}] :> c Integrate[f, it] /; FreeQ[c, x]
which matches an integral and pulls out c if c has no ...
- 83
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Seeking Wolfram Mathematica Techniques for Detailed Step-by-Step Solution of Integral Equation Transformation [closed]
Hello Mathematica Community,
I am working on a mathematical problem where I need to transform an integral equation into a simpler form using Euler's Formula and the Error Function. My current ...
- 1
2
votes
3
answers
143
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Find Generalized Series with Symbolic Variable
CoefficientList[Series[Exp[x], {x, a, 3}], x]
Gives the following expression,
$$
\left\{-\frac{1}{6} e^a a^3+\frac{e^a a^2}{2}-e^a a+e^a,\frac{e^a a^2}{2}-e^a a+e^...
- 123
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1
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56
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How to collect specific terms in an equation and set them to new parameters?
I have this equation
...
- 213
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1
answer
89
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Symbolic matrices
How does one declare a matrix of specific symbolic dimension? For instance, if $A,B,C,D$ are four $n\times n$ matrices, $M$ is the block matrix
$$
M=\begin{bmatrix}
A & B \\ C & D
\end{bmatrix}...
- 133
-1
votes
0
answers
40
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Out put of FeynCalc is not symbolic
When I run, for example:
LC[$\alpha$, $\beta$, $\mu$, $\nu$] MT[$\mu$, $\nu$]
the out put is
LC[$\alpha$, $\beta$, $\mu$, $\nu$] MT[$\mu$, $\nu$]
rather than
$\varepsilon_{\alpha \beta \mu \nu}g_{\mu\...
0
votes
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 <...
- 981
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0
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59
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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
...
- 1
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1
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84
views
0
votes
1
answer
56
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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 ...
- 695
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2
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156
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Converting expression to quadratic formula
I want to manipulate and represent the following expression in a more presentable way.
...
- 424
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1
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84
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How can I get undefined unevaluated integrals to be treated like number?
I am working with commutators like this $$ \left(a \int f \, \mathrm dt\right) * a - a * \left(a \int f \, \mathrm dt\right),$$
...
- 83
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0
answers
273
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Symbolic integral with UnitStep functions
I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ...
0
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0
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29
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How to extract subscripts in mathematica and apply a function on them?
For a bit of context, I am trying to evaluate an integration over Haar randm unitaries. I couldn't find any inbuilt function, so I am trying to implement a simple code for the Wingarten functtion in ...
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1
answer
152
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Why does Mathematica fail to compute $\int_{0}^{\infty} \sin(ax^2) dx$ whereas Wolfram Alpha seems to be able to do it? [closed]
I was symbolically computing
$$ \int_{0}^{\infty} \sin(ax^2) dx $$
Via the command:
Integrate[Sin[a*x^2], {x, 0, Infinity}]
But it seems to fail with mathematica, ...
- 133
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votes
1
answer
52
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Showing that the difference between two CDF functions is positive when CDFs are symbolic expressions
I'd like to check the sign of a symbolic expression conditional on some predefined assumptions. More specifically, first, I want to assume that the mean and variance of a normally distributed random ...
1
vote
1
answer
58
views
Adding symbolic functions and manipulating results of DSolve
I want to add a symbolic function and its second derivative.
The symbolic function is given by DSolve:
...
- 13
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votes
1
answer
34
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Piecewise integration doesn't evaluate
I'm trying to integrate the following function:
$$q(d, \theta) = q_x(d, \theta) + q_y(d, \theta) - 2q_x(d, \theta) q_y(d, \theta)$$
where $q_x(d, \theta) = \min\left(2 - d\cos\theta, d\cos\theta\right)...
0
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0
answers
38
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Symbolic solutions to systems of Boolean constraints?
Is it possible to solve a system of Boolean constraints symbolically? I'm trying to solve systems like the following, where $X$ is the unknown Boolean expression I'm trying to find, $a, b, c$ are the ...
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153
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58
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Function to generate analytic solution of StandardDeviation of a list given sublists
Motivation
I have the Mean and StandardDeviation of several lists of equal size but I don't know the elements of those lists.
I ...
0
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1
answer
58
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Finding the maximum of a symbolic piecewise function
I have the function:
coded as:
...
4
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3
answers
218
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Integration involving two DiracDelta with variable limit
I want to write a code to evaluate
$$ \int_0^{t-1}\frac{\delta(z-1)}{z}\frac{\delta(t-z-1)}{t-z}dz$$
which should gives the answer $$\frac{\delta(t-2)}{t-1}.$$
I tried to write the code
...
- 286
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0
answers
50
views
Symbolic computation using ``Reduce" does not give a result
Firstly, I have proved that γ = β^2/12 is one of the solutions of (A12 P312 + A13 P213 + A23 P123)/P123123 + A12 A13 A23==0
<...
- 115
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votes
1
answer
40
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How to define linear mappings on a vector space spanned by abstract symbols?
Say I have an infinite dimensional vector space $V$ with basis consists of abstract symbols $\{ a_j \}^\infty_{j=0}$, and consider a linear function $f$ on $V$ defined by its action on the basis ...
- 119
1
vote
1
answer
51
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Simplify to vectors and matrices [closed]
How do you simplify an expression:
$[r_1, r_2, r_3]^T [t_1, t_2, t_3] = r_1 t_1 + r_2 t_2 + r_3 t_3 = \vec{r}^T \vec{t}$
In other words, I want to group and simplify scalar expressions over vectors / ...
- 121
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How should I find out the bounds of the symbolic solution, since the numerical solution is 1 , but the symbolic solution cannot show 1?
There is a symbolic solution which doesn't show 1, but when replaced variales with values, there is 1.
...
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32
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Tensor Algebra of Symmetric Algebra with Symoblic Tensors
Given
$V=\mathbb{R}^3,$
I would like to work symbolically with elements of
$\mathrm{T}^{(k_1,\dotsc,k_n)}(\mathrm{S} V),$
i.e. vectors of the form
$$\phi = \phi_1 \otimes \cdots \otimes \phi_n$$
with
$...
- 101
1
vote
1
answer
88
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Multiplying abstract tensors in Mathematica
I want to do an operation like
$$ AA \otimes BB \times AA' \otimes BB' $$
and have
$$AA \times AA' \otimes BB \times BB' $$
without specifying the elements of $AA$s and $BB$s (and so are their primes)....
- 121
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votes
1
answer
53
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Difficulty in Proving Symbolic Equality in Mathematica [closed]
I'm currently working with the Mathematica software to verify the symbolic equality between two mathematical expressions. However, I've encountered a challenge where Mathematica's symbolic ...
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1
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44
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How to define the following rule for all objects in a compact way?
Consider the following symbolic definitions:
...
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3
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How to tell Mathematica to leave only terms not higher than X power?
Consider the following expression:
expr = a[x]*da[x,t]*db[x,t]c[x] + db[x,z]^2*a[x]^2*d[x] +d[x]^2*da[x,t]db[x,t]+ dc[x,z]^2 + c[x]*dc[x,z]^2*db[x,t]^6
Is there ...
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2
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91
views
Symbolic Indexing on Symbolic Arrays
Is there a way to use symbolic indices on symbolic vectors? The most barebones example I can think of is the following:
aV = Array[a,3];
aV[[m]]
which evaluates to ...
- 121
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0
answers
48
views
Operations on symbolic tensors
I have recently discovered the set of functions related to symbolic tensors, namely TensorProduct, TensorContract, ...
- 1,054
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1
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150
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Do symbolic integration of function including \[ScriptCapitalL]
I have done a symbolic integration in mathematica 13.2 as follow
Integrate[-((Sqrt[-r(r - 2 l)] l)/(r(r - 2 l) (-r + l))), r] // Simplify[#, r > 0] &
...
- 133
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1
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215
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Discrepancy with Hurwitz Zeta function
I've come across an issue while using Wolfram Mathematica that I don't quite understand.
Consider the following symbolic computation:
...
- 27
1
vote
2
answers
75
views
How to show result in reduced form?
Suppose that I define $$v(t)=\sqrt{v_1(t)^2+v_2(t)^2}$$ and I want to take the derivative of this with respect to time. The result that Mathematica gives me is $$v^´ = \frac{v_1{v_1}^´+v_2{v_2}^´}{\...
- 11
1
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1
answer
88
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Solving a Variable Number of Difference Equations with RSolve
I'm trying to solve a variable number of linear equations defined by
$$
\begin{align} x_0 &= A+Bx_1 \\ x_i &= C+\frac{B}{2}(x_{i-1}+x_{i+1}), \hspace{.25cm} 1\leq i \leq n-1 \\ x_n &= C+...
- 113
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How can I compute the $n$-th complete Bell polynomial?
I'm interested in computing the n-th complete Bell polynomial
$
B_n(x_1,..., x_n)
$ using the formula given as the last equation in the "Exponential Bell polynomials" section here (I tried ...
- 45
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0
answers
33
views
Solution to a vector recurrence equation
Suppose $n\ge1$ is fixed. Let $C_1,C_2,\ldots,C_n$ be given constants.
Consider the recurrence
$$
C_n[S_{1}^{(n)},S_{2}^{(n)},\ldots,S_{n-1}^{(n)}]=
\left[\binom{n}{1},\binom{n}{2},\ldots,\binom{n}{n-...
- 755
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How to find a power series expansion of a function obeying a certain PDE?
Let us suppose that I have some differential operator $D_{x,y}$ acting on functions of two variables $(x,y)$. I want to solve one eigenvalue equation
$$D_{x,y}f_{ij}(x,y)=\lambda_{i,j} f_{ij}(x,y).$$
...
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2
answers
181
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Decoupling a system of four linear $1$-st order ODEs
I have a system of four $1$-st order ODEs. $$ \dot{p_1} = -2\beta^2 q_1 - \gamma p_1 + \Delta p_2 $$ $$ \dot{p_2} = -2\beta^2 q_2 - \gamma p_2 + \Delta p_1 $$ $$ \dot{q_1} = 2\alpha^2 p_1 + \gamma q_1 ...
- 132
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How can I solve/verify the following matrix?
Given $ZFZ’ = C$, I have the following set of symbolic matrices:
$Z$ of order $m\times q$
$Z’$ is the transpose of matrix $Z$ of order $q\times m$
$F$ of order $q\times q$
$C$ of order $m\times m$
...
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2
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105
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Why mathematica Minimize function cannot handle Integers constraint in this case?
I am an electrical engineer and sudenly a problem of this form appear during my research
For this kind of problem, Mathematica can work just fine. But as soon as I as the Integers option then I ...
