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Questions tagged [symbolic]

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

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Doing symbolic manipulations — how-to literature tips [closed]

Is there a good how-to guide to doing symbolic manipulations in Mathematica so that it is really helpful --- I have found most aspects of symbolic manipulation in MMA to be tedious and in the end, I ...
atapaka's user avatar
  • 3,960
0 votes
0 answers
26 views

Calculating determinant and adjoint of a matrix of arbitrary dimensions

I am trying to compute the determinant and adjoint/adjugate of a matrix with each entry a polynomial in symbolic variables a[1],...,a[k] and dimension some ...
Curious Mind's user avatar
0 votes
1 answer
64 views

Asymptotic volume of intersection of n-cube with n-sphere [closed]

I would like to symbolically compute the following: $$\lim_{d\to\infty} \frac{\text{Vol}(C^d(1) \cap B^d(K\sqrt{d}))}{\text{Vol}(C^d(1))}$$ where $B^d(r) = \{(x_1, \dots, x_d) \mid x_1^2 + \dots + x_d^...
Capybara's user avatar
3 votes
3 answers
97 views

How to invert a series with two variables, where the series is expanded in the other variable?

I have defined an expression that is a series in powers of $1/c$: ...
Christopher's user avatar
3 votes
1 answer
107 views

Why does singular solution not satisfy the ode?

Should not singular solution also satisfy the ode itself? Since it is a solution. Why does Mathematica V 14 in this example generate a singular solution which does not seem to satisfy the ode itself <...
Nasser's user avatar
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1 vote
0 answers
56 views

Symbolic integral with piecewise functions

I want to compute the following integral as a function of some positive real parameters, $a, \rho, \lambda$ and three positive real variables $L_a, L_b, L_c$: ...
Ruth Murphy's user avatar
2 votes
2 answers
138 views

How to solve a matrix differential equation $\frac{d X}{dt} = i(X Y- Y^\dagger X)$?

In eq (21) on page-5 of this article, we have matrix HEP = (\[Omega]/2)*{{-2*I, 1}, {1, 0}}; and I am interested in finding matrix ...
User101's user avatar
  • 613
1 vote
1 answer
73 views

Symbolic Computation - Don't Evaluate Integral

I'm following a paper. I've been trying to get Mathematica to help me. Combining equation 1 and equation 2 should result in equation 3. Equation 1: \begin{equation} R=C k^2 T^2 \int_0^{\infty} \ln \...
Tomi's user avatar
  • 4,486
2 votes
1 answer
46 views

Intra-Symbolic Wild Card Pattern Matching

I have the following custom expression structure I am parsing: Theorema`Knowledge`Q$TM[ Theorema`Language`VAR$[Theorema`Knowledge`VAR$x$TM]] I already was able to ...
marie_antoinette's user avatar
0 votes
0 answers
49 views

Why is centerdot distributivity broken

Does anyone else have this problem? CenterDot[CenterDot[a, b] - CenterDot[b, a], d] returns -d b.a + (a.b).d It's not ...
Luca's user avatar
  • 93
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0 answers
34 views

How to symbolize code for ladder operators

As suggested in this answer, I am considering symbolizing the function "NonCommutativeMultiplyNew" from the following code: ...
Steven Sagona's user avatar
1 vote
1 answer
61 views

Defining a symbolic block matrix

I'm a total beginner in Mathematica and I have been struggling with defining the following symbolic matrix with entries in $\mathbb{Z}_2$ Here, $\mathbb{1}_{m_i}$ and $\mathbb{0}_{m_i}$ stand for the ...
Mohammed Sabak's user avatar
4 votes
2 answers
246 views

Can Mathematica return the closed forms of 'arbitrary' function compositions?

I have only just downloaded Mathematica, so I am entirely new to this software. Here is what I am trying to do: If $f(x) = \frac{x}{2}$ is an example function, and $f^{(n)}(x)$ is the composition of $...
Wisdom Iwueze's user avatar
2 votes
0 answers
39 views

Take symbolic derivative of summation expression and display as unexpanded sum

My main problem here is two-fold: Take symbolic derivative of summation expression Stop summations from being "unrolled"/expanded, e.g., displayed as the sum of terms I also have some ...
ImagineBaggins's user avatar
0 votes
0 answers
33 views

How to find the region in angles that match the following conditions?

Consider the following function: ...
John Taylor's user avatar
  • 5,827
3 votes
1 answer
71 views

Troubles with BlankNullSequence in the case of multiplication

I have some trouble to use the triple underscore notation to use definitions with or without a term. Consider the following toy example f[a___ x]:=1 {f[x],f[2x]} ...
Adrien Martina's user avatar
2 votes
1 answer
84 views

Defining custom operators for indexed objects [closed]

I have some symbolic indexed objects $A_i$, $B_{ij}$, $C_{ijk}$, $D_{ijkl}$, etc. I want to define a symbolic differential operator $\partial_{xy}$ that acts on these indexed objects in the following ...
Franz5217's user avatar
2 votes
1 answer
94 views

Need help in implementing q-SeriesToq-Product in Mathematica

In Mathematica Guidebook for symbolic computations (https://www.amazon.com/dp/0387950206/wolframresearch-20), in the Exercises, 30 (c)(p. 359), there is a question: I have no clue how to implement ...
Sangama's user avatar
  • 23
2 votes
1 answer
74 views

Inconsistent results when trying to solve an ordinary differential equation (ODE)

Introduction and problem I tried to solve, symbolically and numerically, the following ODE with Mathematica: $y’(t) = \sin(t) y’’(t)$, and I got strange results at different levels (either ...
mlpo's user avatar
  • 879
3 votes
2 answers
60 views

RSolve does not evaluate this recursion with two boundary conditions

I am using RSolve to solve for a function defined recursively, with two boundary conditions: First boundary condition describes the relationship between $f(1)$ and $f(0)$ Second boundary condition ...
Kuantew's user avatar
  • 131
2 votes
3 answers
210 views

Solving divergent Integral

I want to solve this integral. using Integrate I get it done, but the problem is it results in complex values, which is incorrect for my problem (has no physical meaning). I'd like to know if there's ...
lia's user avatar
  • 347
0 votes
0 answers
25 views

How to Factor Out Polynomial Terms which Have Same Coefficient Differing Only by Sign

I'm new to the Mathematica StackExchange. I am trying to simplify a polynomial in Mathematica. In the following, I only show a part of the polynomial Here I want to combine terms with the same ...
Kazuki's user avatar
  • 1
1 vote
1 answer
62 views

Finding constant term in product expression

I've an expression which is product of 20 or more factors of polynomial, something like $$\left(1-\frac{pq}{z^i}\right)(1+pq z^j+z^k)$$ and I want to find coefficient of $z^0$. SeriesCoefficient works ...
xandar's user avatar
  • 13
0 votes
1 answer
105 views

ExpToTrig conversion problem

Let we have some ODE solution: formExp = c1 E^(-I t) + c2 E^(I t) +c3 E^(-2 I t) + c4 E^(2 I t) It is known that this solution can be reduced to the form: ...
lesobrod's user avatar
  • 1,729
2 votes
1 answer
145 views

FourierCosCoefficient for function with singularity

FourierCosCoefficient is way more powerful than I expected. For example, ...
Leo's user avatar
  • 131
0 votes
0 answers
41 views

Perturbing a tensorial expression

I am new to Mathematica. I am trying to simplify an expression of the some form like: $$ n_i \sigma_{ij} n_j - \gamma n_i \hat{\sigma_{ij}} n_j = 2 + v_i x_i + \kappa E_{ij} \chi_{ji} $$ There are ...
fiarast11's user avatar
4 votes
1 answer
187 views

How to find a closed-form expression for this integral depending on parameter?

In 14.0 under Windows 10 I try to find the improper integral $$\int\limits_{\sqrt{1-\sqrt{1-\psi }}}^{\sqrt{1+\sqrt{1-\psi }}} \frac{1}{r^2 \sqrt{-r^4+2 r^2-\psi }}\,dr$$ under the assumptions $\psi &...
user64494's user avatar
  • 26.8k
5 votes
2 answers
137 views

Display of nested fractions as products of fractions

How do I get Mathematica to avoid displaying nested fractions in outputs, and instead automatically display them as parenthesized, factored-out terms? For example, I would like ...
Christopher's user avatar
3 votes
1 answer
115 views

Define a function whose variable is differential operator

I would like to act with a differential operator $D_x = x \partial_x^2+3\partial_x$ on a function $g(x)$ to compute something like $$ ((D_x)^2 +D_x) g(x) $$ Clearly, in this simple example, this does ...
bnado's user avatar
  • 413
2 votes
0 answers
174 views

How to perform the following deduction symbolically?

$$i \frac{d}{dt}a_n = (a_{n+1} + a_{n-1}) + |a_n|^2 (a_{n+1} + a_{n-1}), \; n \in \mathbb{Z}$$ In the above, $a_n := a_n(t)$. Consider $P = \sum\limits_{n}g(|a_n|^2)$ where $g$ is some function to be ...
KZ-Spectra's user avatar
2 votes
1 answer
69 views

Joint Moments of Stochastic Process at Different Times

Suppose I have a random process defined in Mathematica, e.g. h = TelegraphProcess[a] I know you can use Mathematica to calculate different statistics like the mean,...
Sahand Tabatabaei's user avatar
4 votes
1 answer
196 views

Solve taking infinite time

I have a system of equations that should determine the real coefficients {b[1], c[1], d[1],, e[1], f[1], g[1], h[1], a[1], b[2], c[2], d[2], e[2], f[2], g[2], h[2]}....
Slayer147's user avatar
  • 247
1 vote
1 answer
50 views

How to make the following replacement?

Consider the following symbolic expression: expr=mon[m,b]*kd[m,d]+band[a,c]alc[b,c]kd[a,d]+func[a,c]dum[a,c]kd[b,d] + f1[b,c]f2[d,c] It has three types of summands:...
John Taylor's user avatar
  • 5,827
4 votes
1 answer
190 views

Two integrals equal to Euler-Mascheroni constant not evaluating symbolically

I'm trying to compute: Integrate[(x - 1)/((1 - x*y)* Log[x*y]), {x, 0, 1}, {y, 0, 1}] and ...
Pinteco's user avatar
  • 141
3 votes
2 answers
168 views

Disagreement between symbolic and numerical integration

I am trying to get the integral of a rather complicated function: $$ \int_{t_1}^{t_2}m_{\text{basal}}+m_{\text{size}}\exp\left(\frac{1}{2}\left(\ln(S_{t_1})+\frac{u-t_1}{t_2-t_1}(\ln(S_{t_2})-\ln(S_{...
Vincent Wieland's user avatar
0 votes
1 answer
67 views

Make function with variable arguments from output of symbolic manipulations

I have a fairly intricate symbolic calculation, which outputs a list of formulae as functions of several variables. The final symbolic formulae are much less complex than the large number of complex ...
Paul Harrison's user avatar
1 vote
0 answers
64 views

Export data vertically

I have data that I want to export to a text file. ...
Alyasaa Jasim's user avatar
2 votes
1 answer
130 views

Symbolic multiple Integrals not delivering expected zero result

Consider the following function defined as a double-integral: $ int_{2D}(h)=\int_0^h \int_0^{t_1}f(t_1,t_2) dt_2 dt_1 $. Clearly, $int_{2D}(0)=0$ as long as $f(t_1,t_2)$ is well-behaved. The previous ...
Jam's user avatar
  • 71
1 vote
0 answers
37 views

Using DEigensystem with parametrized cuboid

The following code where Cuboid has a predefined dimensions {1, 1, 1} works fine: ...
Mirko Aveta's user avatar
  • 2,202
0 votes
1 answer
58 views

How to find the particular solution in symbolic form of an overdetermined system of equations

I want to use mathematica to reproduce a conclusion in a paper, which is solve an overdetermined system of equations, $$ \begin{array}{l} c^{2}(n-1)^{2}\left(a_{0}+a_{1} Y+a_{2} Y^{2}\right)^{3}+a(n-1)...
godspeed's user avatar
5 votes
0 answers
129 views

How to write down and check the Karush-Kuhn-Tucker conditions?

This is a simple touchstone for a serious matter. I try to solve with Mathematica 13.3.1 on Windows 10 problem 1278 from "The Kvant". Let real numbers $x_1,x_2,\dots,x_n$ satisfy the ...
user64494's user avatar
  • 26.8k
3 votes
2 answers
241 views

How can I solve this system of nonlinear PDEs?

How can I solve these PDE analytically for $z$ and $y$? \begin{eqnarray} 2 \dot{z} &=& \ddot{y}+ y^{-1}, ~~~ (1)\\ z' + \dot{z}' &=& - \dot{y}'. ~~~~~~~~~~ (2) \end{eqnarray} Where (....
Dr. phy's user avatar
  • 287
0 votes
0 answers
84 views

Break symbolic eigenvalue calculation early

I am computing eigenvalues of matrices with single monomial entries (x,y,z, etc.) and for efficiency, need to truncate calculations early if any eigenvalues contain non-linear (x^{2}, \sqrt(x),x*y etc....
JJJJJJJJJJJJJJJJ's user avatar
4 votes
2 answers
245 views

How to transfer a numerical value in Mathematica into a symbolic fraction with sufficiently large precision?

Suppose I have a number $0.26630939883535015$ and want to transfer it into a symbolic fraction by truncating it first. The way I do it is first Round it and then <...
narip's user avatar
  • 381
2 votes
3 answers
202 views

Are there exact solutions for the following system of nonlinear first order ordinary differential equations?

The two equations are: u'[t]== -(K + L v[t]) u[t] and v'[t] == -L u[t] v[t] where K and L are constants. At t=0, u(0)=a ...
TNEst's user avatar
  • 21
0 votes
0 answers
32 views

Issue with symbolizing all expressions of the form $x_k$ following recent update

A notebook that I created a while ago starts with the following two lines: ...
gen's user avatar
  • 195
0 votes
1 answer
101 views

Adding a symbolic tensor and a specific one

I need to add a symbolic tensor and a specific one, but it seems the symbolic tensor is always treated as a number and is added in very components of the specific tensor. Firsts I give assumptions <...
DarkGlimmer's user avatar
2 votes
3 answers
208 views

How to make Mathematica gives the right answer for this integral $\int_{-\infty}^\infty \frac{\mathrm dx}{(a^2 - x^2)^2 + (bx)^2}$?

I'm trying to compute the following integral with Mathematica: $\int_{-\infty}^\infty \frac{\mathrm dx}{(a^2 - x^2)^2 + (bx)^2} = \pi/ab^2$. Source . Somehow, even if I assume $a>0$ and $b>0$, ...
Syrocco's user avatar
  • 123
1 vote
1 answer
96 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 ...
user64494's user avatar
  • 26.8k
0 votes
0 answers
68 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: ...
Sean Svihla's user avatar

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