Questions tagged [symbolic]
For questions about symbolic computation, as opposed to numerical computations.
1,538
questions
2
votes
1
answer
79
views
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 ...
- 3,548
9
votes
3
answers
2k
views
Mathematica gives wrong answer for an integral
Bug introduced in 9.0 or earlier, persisting through 13.2 or later
When I execute the following,
Integrate[ Exp[-w^2 + I w^3], {w, -∞, ∞}]
I get
...
- 13.1k
9
votes
3
answers
392
views
DSolve—different solutions for same set of equations using different symbols?
I happen to find that DSolve can give different solutions, even a different number of solutions, for a set of differential equations just by making a change in the ...
- 63.8k
3
votes
1
answer
150
views
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] &
...
- 63.8k
2
votes
2
answers
230
views
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)...
- 47.3k
2
votes
2
answers
195
views
Alternatives to NumericQ that allow symbols to be considered numeric
I am writing a program in which I am using NumericQ. I am trying to allow symbols to also be considered Numeric, so I have been using NumericQ[a]=True for all of ...
CommunityBot
- 1
0
votes
0
answers
64
views
Help implementing Lagrange inversion
I'm attempting to find the coefficients of generating functions using Lagrange inversion. I am finding the series coefficients with:
...
- 24.4k
4
votes
2
answers
419
views
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.
...
- 384k
0
votes
1
answer
84
views
How can I get undefined unevaluated integrals to be treated like number?
I am working with commutators like this $$ \left(a \int f \, \mathrm dt\right) * a - a * \left(a \int f \, \mathrm dt\right),$$
...
CommunityBot
- 1
0
votes
0
answers
39
views
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 ...
- 24.4k
0
votes
0
answers
54
views
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
views
Find Generalized Series with Symbolic Variable
CoefficientList[Series[Exp[x], {x, a, 3}], x]
Gives the following expression,
$$
\left\{-\frac{1}{6} e^a a^3+\frac{e^a a^2}{2}-e^a a+e^a,\frac{e^a a^2}{2}-e^a a+e^...
- 40.6k
0
votes
1
answer
56
views
How to collect specific terms in an equation and set them to new parameters?
I have this equation
...
- 152k
0
votes
1
answer
89
views
Symbolic matrices
How does one declare a matrix of specific symbolic dimension? For instance, if $A,B,C,D$ are four $n\times n$ matrices, $M$ is the block matrix
$$
M=\begin{bmatrix}
A & B \\ C & D
\end{bmatrix}...
- 4,999
4
votes
1
answer
965
views
Calculate the algebraic multiplicity of known eigenvalues of a large, sparse matrix
I have a large (and sparse) matrix with size 1000x1000 -- 10000x10000. I believe i know all eigenvalues for the matrices. All entries are integers and so are the eigenvalues.
I want to check this by ...
0
votes
1
answer
185
views
Symbolic partial differentiation of a Lagrangian function including a summation
I'm using Mathematica to double-check that I correctly derived first order conditions for the models I'm researching. Before I get started, I wanted to actually teach myself how to use Mathematica, ...
CommunityBot
- 1
-1
votes
0
answers
40
views
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
views
`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 <...
- 24.4k
0
votes
0
answers
59
views
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
...
- 24.4k
0
votes
1
answer
84
views
2
votes
0
answers
272
views
Symbolic integral with UnitStep functions
I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ...
0
votes
1
answer
56
views
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 ...
- 4,750
2
votes
1
answer
311
views
Ordinary differential equation with variable (polynomial) coefficients -form of solution
If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation
$ y''(t)+b y'(t)+\left(\...
CommunityBot
- 1
1
vote
2
answers
156
views
Converting expression to quadratic formula
I want to manipulate and represent the following expression in a more presentable way.
...
- 46.2k
0
votes
0
answers
29
views
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 ...
- 11
0
votes
1
answer
52
views
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 ...
CommunityBot
- 1
1
vote
1
answer
152
views
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, ...
- 24.4k
0
votes
1
answer
58
views
Finding the maximum of a symbolic piecewise function
I have the function:
coded as:
...
CommunityBot
- 1
11
votes
1
answer
1k
views
Expanding derivatives of hypergeometric functions
Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
- 1,604
2
votes
1
answer
89
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]}
...
CommunityBot
- 1
1
vote
1
answer
88
views
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)....
CommunityBot
- 1
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:
...
- 152k
1
vote
1
answer
153
views
0
votes
1
answer
34
views
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)...
- 152k
0
votes
0
answers
38
views
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 ...
- 440
0
votes
1
answer
58
views
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 ...
- 124k
5
votes
1
answer
261
views
Issue with definite integration by parts using IntegrateByParts
Introduced in 1.0.0 of ResourceFunction["IntegrateByParts"], persisting through 2.0.0.
I am trying to prove Cauchy's identity with Mathematica ...
- 63.8k
4
votes
3
answers
218
views
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
...
- 49.6k
2
votes
1
answer
161
views
Partial Trace with KroneckerProduct
I have some symbolic expression of the form
X=KroneckerProduct[A,B]+KroneckerProduct[G,F]+...
How can I define a partial trace for this, i.e. a function f:
...
CommunityBot
- 1
1
vote
1
answer
51
views
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 / ...
- 2,857
0
votes
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
<...
- 41.9k
0
votes
1
answer
40
views
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 ...
- 24.4k
8
votes
6
answers
241
views
Adding elements to some sublists of unequal length
Complicated title for a simple problem:
I have list
a = {{1, 3, 5, 2}, {2, 6, 2}, {3, 5, 6, 1, 2}, {4, 2}}
In which the first element of each sublist is ...
- 12.4k
12
votes
2
answers
487
views
Why do I get a wrong result from SeriesCoefficient?
Bug introduced in 7.0.1 or earlier and fixed in 13.3
Consider the following code:
func[x_] = Sin[x^3]/(x - 1/3);
c[n_] = SeriesCoefficient[func[x], {x, 0, n}]
<...
- 7,122
0
votes
0
answers
19
views
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.
...
- 465
0
votes
0
answers
32
views
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
$...
- 18.9k
1
vote
1
answer
117
views
Checking the consistency of a variable change
This question may have a simple solution. I did a change of variables and I'd like to check it; what do you recommend?. Altough I believed there's a way to compare term-by-term doing
...
CommunityBot
- 1
-1
votes
1
answer
53
views
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 ...
- 63.8k
0
votes
1
answer
44
views
How to define the following rule for all objects in a compact way?
Consider the following symbolic definitions:
...
- 18.9k
1
vote
2
answers
126
views