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 ...
user64494's user avatar
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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: ...
Sean Svihla's user avatar
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)...
Mike Gotier's user avatar
4 votes
2 answers
420 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. ...
Vitaliy Kaurov's user avatar
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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 ...
Luca's user avatar
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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 ...
Rob_'s user avatar
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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^...
Torkoal's user avatar
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1 answer
56 views

How to collect specific terms in an equation and set them to new parameters?

I have this equation ...
Dr. phy's user avatar
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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}...
Cryme's user avatar
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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\...
João Paulo Melo's user avatar
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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 <...
ppp's user avatar
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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 ...
San's user avatar
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1 answer
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Incorrect results for Integrate[Cosh[x]/(Sinh[x] + Cosh[x]), x] [closed]

Input: ...
Boris's user avatar
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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 ...
larry's user avatar
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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. ...
Dotman's user avatar
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1 answer
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How can I get undefined unevaluated integrals to be treated like number?

I am working with commutators like this $$ \left(a \int f \, \mathrm dt\right) * a - a * \left(a \int f \, \mathrm dt\right),$$ ...
Luca's user avatar
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273 views

Symbolic integral with UnitStep functions

I want to symbolically evaluate the following integral (with real positive parameters L1, L2, ...
Giancarlo Creanza's user avatar
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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 ...
Endeavour 's user avatar
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, ...
Sidharth Ghoshal's user avatar
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 ...
elifcansu's user avatar
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: ...
Orian's user avatar
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1 answer
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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)...
Reality Check's user avatar
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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 ...
ShyPerson's user avatar
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1 vote
1 answer
153 views

How to solve the non-linear over-determined equations symbolically? [closed]

...
aamir farooq's user avatar
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1 answer
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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 ...
IntroductionToProbability's user avatar
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1 answer
58 views

Finding the maximum of a symbolic piecewise function

I have the function: coded as: ...
vivelesmaths's user avatar
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 ...
Mohamed Mostafa's user avatar
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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 <...
InFei's user avatar
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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 ...
Lagrenge's user avatar
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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 / ...
user3180's user avatar
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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. ...
Y. zeng's user avatar
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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 $...
Marvin Dippell's user avatar
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)....
Tom's user avatar
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-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 ...
algebroo's user avatar
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1 answer
44 views

How to define the following rule for all objects in a compact way?

Consider the following symbolic definitions: ...
John Taylor's user avatar
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1 vote
2 answers
126 views

How to define the following "derivative"?

Consider the following test expression: ...
John Taylor's user avatar
  • 4,681
2 votes
3 answers
124 views

How to extract specific terms from the polynomial?

Consider the following polynomial: ...
John Taylor's user avatar
  • 4,681
4 votes
2 answers
193 views

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 ...
John Taylor's user avatar
  • 4,681
2 votes
2 answers
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 ...
ertl's user avatar
  • 121
1 vote
0 answers
49 views

Operations on symbolic tensors

I have recently discovered the set of functions related to symbolic tensors, namely TensorProduct, TensorContract, ...
enzotib's user avatar
  • 1,054
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] & ...
Lain's user avatar
  • 133
1 vote
1 answer
215 views

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: ...
stefan_chem's user avatar
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}^´}{\...
user3011's user avatar
1 vote
1 answer
88 views

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+...
Mike D's user avatar
  • 113
4 votes
1 answer
96 views

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 ...
Robert Lee's user avatar
0 votes
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-...
Alex's user avatar
  • 755
3 votes
0 answers
130 views

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 $$D_{x,y}f_{ij}(x,y)=\lambda_{i,j} f_{ij}(x,y).$$ ...
user1620696's user avatar
3 votes
2 answers
181 views

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 ...
Kazi Abu Rousan's user avatar
1 vote
1 answer
90 views

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 $m\times m$ ...
EVC's user avatar
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1 vote
2 answers
105 views

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 ...
Tuong Nguyen Minh's user avatar

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