# Questions tagged [symbolic]

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

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### How to get a logical expression instead of a value [closed]

Suppose I want to write out the terms of the binomial distribution: Sum[ Binomial[n, k] q^k (1 - q)^(n - k), {k, 0, n} ] This obviously gives me 1, however I ...
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### Computing symbolic form of trigonometric integral

To calculate symbolically this integrale $$I(s)= \int\limits_0^{\pi/2} \dfrac{\cos t}{\sin^2 t-R^2} \; e^{-s/\cos t}\; dt$$ which has already been asked Here, @yarchik has suggested to me to post ...
267 views

### Computing symbolic form of integral

I am trying to calculate symbolically the integral of the form: $$I(s)= \int\limits_0^{\pi/2} \dfrac{\cos t}{\sin^2 t-R^2} \; e^{-s/\cos t}\; dt$$ where ...
279 views

### DSolve + basis solution

DSolve can't solve this system of differential equation by DSolve. But the basis solution is known. How I can help DSolve to use this basis solution? WM code: ...
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### Numerical vs Symbolic contour integration get different result

When I test the symbolic integration along a contour, I want to let the answer to be the residue of the integrand. Here is the code: ...
61 views

### Define a new coordinate chart and do algebra/calculus in it

I've stumbled across a very nasty problem: define a toroidal coordinate chart and calculate Laplacian in it. As I'm going through it manually, I wonder if this can't be made in Mathematica. Sure, MMA ...
63 views

### Symbolic variable assignment

I looked around and didn't see this question on the forum, so my apologies in advance in case this has been answered here. My question can be concisely described by the following example: ...
97 views

### How do I tell Mathematica to assume a symbol is bound to a matrix?

Is it possible to tell Mathematica to treat symbols as matrices instead of scalars? For example, instead of getting Solve[r == c*n*r + d, r] ...
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### Linear programming with parameters

I am trying to run LinearProgramming with a vector and a matrix that depend on some parameters, but it's not working. The message I get is that my code "contains ...
135 views

### Symbolically Minimizing Expression with Multiple Piecewise Functions

Following up my previous question about ArgMin, I now face a situation where the solution to an ArgMin call, where the output is ...
157 views

### Hertzian contact mechanics: symbolically calculating the required force for a specific displacement

Consider two parallel Cylinders with Diameters of $R_1$ and $R_2$: The contact width can be calculated from 2D Hertz formula: $$a=2 \sqrt{\frac{PR}{\pi E_c}} \tag{1}$$ Where $P=\frac{F}{L}$ is ...
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### Integration of a function with 3 parameters

Integrate[Y^(b - 1) (1 - Y)^(a - 1) (-Log [Y])^-k, {Y, 0, 1}, Assumptions -> {0 < a, 0 < b, k != 0}] ...
313 views

### How to do nonlinear substitution?

Suppose, I have an expression. For example: $$\cos^5(\phi) \sin^3(\theta)$$ And I want to change variables to $(x, y, z)$, knowing that the new variables are related to $\theta$ and $\phi$, via ...
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### why can't Mathematica solve the wave PDE on string when adding a dispersion term?

Could someone possibly gives an insight as to why DSolve can solve $$\frac{\partial^{2}u}{\partial t^{2}}=\frac{\partial^{2}u}{\partial x^{2} }\qquad t>0$$ ...
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### how to obtain general solution for Laplace PDE in spherical coordinates using DSolve?

Can DSolve given a general solution to Laplace PDE in spherical coordinates without given boundary conditions? I tried, but not able to get a solution. Do I need ...
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### Symbolic solution to a constrained optimization problem

Can anyone tell me why this method (Symbolic Constrained Optimization) works but not the following for obtaining symbolic solutions of a constrained optimization problem: ...
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### Problems with DEigensystem

I have the following problem $\frac{c_p q_m}{A}\frac{\partial T(x,t)}{\partial t}+\rho c_p \frac{\partial T(x,t)}{\partial x}-\lambda \frac{\partial^2 T(x,t)}{\partial x^2}=0$ I want to find the ...
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### Decomposing a product of “monomials” to list

Definition of the problem I wish to solve equations of the form ...
281 views

### Integration of Booles and Gaussians in high dimensions

Context As a follow up of this question, I would like to predict the connectivity of the so-called cosmic web in arbitrary dimensions. The connectivity $\kappa$ is defined as the number of ridges ...
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### Some indefinite integrals evaluate in 11.2 but not in 11.3 - what can be done?

Bug introduced in 11.3 and fixed in 12.0.0 Reported to Wolfram: [CASE:4032137] These integrals evaluate in version 11.2 on windows but when I tried them under version 11.3 they returned unevaluated.,...
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### Laplace PDE inside a disk

I can't get Mathematica to solve this standard textbook PDE, which is Laplace inside a disk of some radius. One of the boundary conditions needed is that the solution is finite (bounded) in center of ...
49 views

### Function definition interrupts pattern matching?

I'm trying to redefine NonCommutativeMultiply (NCM) to behave like an anticommuting operator, based on the question here. This involves calling Unprotect on NCM and adding a definition that leaves <...
64 views

### Multivariate hypergeometric functions

Anybody knows of any Mathematica implementation of multivariate hypergeometric functions? It requires Jack polynomials, or at least Schur polynomials for the real case. In addition it requires ...
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### Using Refine function and take real part of a symbolic expression

I am trying to take the real part of the a complex expression using Refine function. However, the result doesn't come out as expected. The final result still ...
114 views

### Problem with SeriesData

Problem: I need to find the leading order term in an expansion whose leading order behavior is a priori unknown. I can of course go with Series and try different orders, say ...
120 views

### Symbol Order for Built-in Functions such as TrigReduce

I’d like to use the TrigReduce function on a sum of n sinusoids to any power, and am running into an issue with Mathematica’s default ordering of symbols. Is there a way that I can specify an order ...
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### Rank of symbolic matrix [duplicate]

I can't figure out why Mathematica can't calculate rank of a symbolic matrix. Please take a look at the attached screenshot below. If you need the full source code then you can find it in the "...
400 views

### How can I solve my system of differential equations

I have 3 differential equations and I want to obtain an analytic expression for f[r]. It does not matter what equations are and I just need the command to solve ...
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### RegionMember not returning analytical result

From this question I'm using a function by kglr to find the inequality constraints for a shape. The function is this ...
59 views

### Make ConjugateTranspose distributive

Related to 123974, is there a way to make the ConjugateTranspose function, input as esc-hc-esc distributive for all symbols? For ...
51 views

### Define rules for derivatives of integrals

I want to create a computational rule like, $\frac{\partial}{\partial h_{i}}\int f\left(h_{i}\right)di:=\frac{\partial f\left(h_{i}\right)}{\partial h_{i}}$. This rule is somehow useful when doing ...
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### Defining a list without knowing the number of elements

Let $N$ be a natural number $\ge 1$. I have two questions: How can I define a list with variables $p_1,...,p_n$? How can I define an element $a\in\mathbb{C}$ such that $a⁶=(-1)^n?$
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### Solving a PDE with its boundary condition expressed as a piecewise function

All I want to do is solve the PDE pde = D[y[x, t], t] + y[x, t] D[y[x, t], x] == 0 with the boundary condition expressed as a piecewise function, say, ...
194 views

### how to obtain solution for $u_t+u=u_{xx}$

I was trying to verify my hand solution for this PDE using Mathematica. Is a trick to help Mathematica obtain solution to $u_{t}+u=u_{xx}$ with initial conditions $u(x,0)=f(x)$ and boundary ...
67 views

### Change order of evaluation in Plot[] nested with NDSolve[]

I noticed that in Plot the function is evaluated at each sample point Plot[func@x,{x,rStart1,rEnd1}] which is fine for a ...
245 views

### Symbolic calculation with generators and relations

Is it possible to do the following in Mathematica: Define an algebra $A$ via generators and relations and multiply some tensors in $A\otimes A$ (and of course simplify the relations via the relations)...
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### Symbolic summation with variable bounds and variable number of indices

I wish to compute compute terms like Sum[f[t[j[1]],t[j[2]],...],{j[1],m},{j[2],n},...] for arbitrary positive integer n and any ...
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### Integration with parameter

I want to integrate this integral $$\int_0^{\pi}d \theta\sin ^{d-2}(\theta ) \left(-1+e^{i k x \cos (\theta )}\right)$$ So first I tried ...
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### Transform expression involving Erfc back and forth with Laplace transform and its inversion

It's a problem I encountered when answering this question and I think it's worth starting a new question for it. Consider the following expressions: ...
280 views

### Separate or order the positive and negative terms of an expression

I am using Mathematica to manipulate/keep track of a long series of symbol manipulations. One thing that I would like to do is separate or order the terms of an expression by positive and negative ...
56 views

### Defining my own operator that Simplify will recognize

I would like to define my own operator and have Mathematica simplify expressions using it. Say I have an operator $\qquad P = \frac{d}{dt} + f(x,t)\frac{d}{dx}$ and I have an expression like \$\...
132 views

### DSolve and coupled linear first order PDEs

Does any one know a trick to make DSolve find solution to this coupled linear first order PDE system: (these are Cauchy-Riemann PDE equations, but with one of them ...