# Questions tagged [symbolic]

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

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### Showing symbolic equality up to some transformation of variables

I'm trying to show that there exists some transformation of variables between the following two expressions such that they are equivalent. ...
75 views

### How to Handle First Variation with Symbolic Computation in Mathematica?

Background I am currently working on a problem related to surface tension and found a research paper that appears to have the information I need. I am attempting to replicate the calculations in this ...
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### How to simplify and rearrange a mathematical expression with quantities that have subscripts

I'm trying to simplify and rearrange the mathematical expression $\text{d$\xi $} \left(k_1+k_2\right)+\text{dt} \left(k_1 \left(l_1-x_1\right)\right)+\text{dt} \left(k_2 \left(x_2-l_2\right)\right)$, ...
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### How to handle undefined Integral results for excluded conditions in Mathematica

I have a mathematical function where both input parameters x and y are real numbers within the interval [−π,π]: ...
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### Selecting only the quartic terms from an expression

I am trying to create a function that returns a list with every quartic term (in total, meaning that \[CapitalPhi]1^2 * \[CapitalPhi]2 ^2 would count). what I have ...
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### I need a link to Leonid Shifrin's" MathProgrammingIntro.pdf" example code

I have been reading and using the Shifrin text. I tried to get the example code he mentions, but his website is closed. Anyone have a link to these examples? I ask here because this seems to be the ...
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### Integrate diverges for convergent integral, and returns unnecessary condition

I'm trying to solve an infinite integral using Mathematica. For some reason, Mathematica claims the integral diverges although when solving to a finite limit L and ...
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### Finding kernel of a set of polynomial functions [closed]

I have a list of polynomials fi[x_] and polynomial fractions qi[x_] (with i as an iterator) ...
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### How to preserve symbols under brackets?

Consider, e.g., a symbol =>. In Mathematica, it gets automatically converted into $\ge$. However, if I put the converted symbol inside the "" brackets (...
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1 vote
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### Why the solution to this PDE, provided by DSolve, does not solve the PDE? (How to correctly use DSolve for such equations?)

This is a question about the correct way to use DSolve. In the image below, I wrote a partial differential equation. I asked Mathematica to solve it, and you can see the suggested solution. Plugging ...
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### What tools does Mathematica have for solving indefinite integrals?

I haven't used Mathematica regularly in about 15 years, so I'm a bit out of date on what the latest tools are for indefinite integration. I have Mathematica 11 on my computer. through searching online,...
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### How to get derivation of a function with respect to another function?

I often have this need: I have some functions that have the same variable and have inclusion relationships, like this. f[t_] := t^2 + 1 g[t_] := Exp[-I Sin[f[t]]] ...
358 views

### PolynomialQ behaviour

I am crafting some functions on polynomials that must be in x. But I checked that it is always True whatever variable I use: ...
1 vote
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### Why does functional form of integration output depend on variables used?

The following integration code is identical, except for the use of integration variables x vs k and constants ...
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### Solving difficult coupled PDEs with DSolve

I have used mathematica to find a set of dynamical equations with boundary conditions. I wonder if it's possible to solve these equations with DSolve. Could anyone help me with this? Here are my sets ...
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### 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 ...
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### 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 ...
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### How to find the region in angles that match the following conditions?

Consider the following function: ...
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### 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]} ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
1 vote
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### 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 ...
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### 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: ...
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### FourierCosCoefficient for function with singularity

FourierCosCoefficient is way more powerful than I expected. For example, ...
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### 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 ...
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### 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,...
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### 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]}....
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1 vote
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### 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:...
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