Questions tagged [symbolic]

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

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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 ...
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 ...
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 ...
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] & ...
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)...
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 ...
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: ...
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. ...
84 views

How can I get undefined unevaluated integrals to be treated like number?

I am working with commutators like this $$\left(a \int f \, \mathrm dt\right) * a - a * \left(a \int f \, \mathrm dt\right),$$ ...
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 ...
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 ...
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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 ...
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, ...
40 views

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 $\varepsilon_{\alpha \beta \mu \nu}g_{\mu\... 0 votes 2 answers 82 views Reduce is running forever I'm trying to solve the last inequality in Reduce in the code below in terms of rmax under the parameter conditions included in <... 0 votes 0 answers 59 views How to speed up maximization of the Solve output? I am trying to maximize the solution of the system of algebraic equations for different values of parameters. The problem is related to the absorbing times in Markov chains. Here is the code ... 0 votes 1 answer 84 views Incorrect results for Integrate[Cosh[x]/(Sinh[x] + Cosh[x]), x] [closed] Input: ... 2 votes 0 answers 272 views Symbolic integral with UnitStep functions I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ... 0 votes 1 answer 56 views Is it possible to get rid of the square root in the solutions of the following symbolic quadratic equation? I have a quadratic equation, which I want to solve, but don't want the square root to appear within the solutions. I tried converting the discriminant into a quadratic form but failed, not sure if ... 2 votes 1 answer 311 views Ordinary differential equation with variable (polynomial) coefficients -form of solution If you have a differential equation with polynomial coefficients then quite remarkably Mathematica can find a solution. For example for the second order differential equation$ y''(t)+b y'(t)+\left(\...
1 vote
156 views

I want to manipulate and represent the following expression in a more presentable way. ...
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 ...
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 ...
1 vote
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, ...
58 views

Finding the maximum of a symbolic piecewise function

I have the function: coded as: ...
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 ...
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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 ...
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 ...
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 ...
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 ...
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: ...
1 vote
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 / ...
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 <...
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 ...
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 ...
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}] <...
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. ...
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 \$...
1 vote
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 ...
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 ...