# 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 ...
143 views

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 ...
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

1 vote
156 views

### Converting expression to quadratic formula

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 ...
89 views

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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 ...