# Tagged Questions

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

199 views

### Solve a symbolic underdetermined Linear System

Dear StackExchange Community, I'm trying to solve an indeterminate linear system of equations, with $n+1$ variables and $n$ equations; therefore, I need to express all $n$ other variables a function ...
59 views

### How to take the second derivative of a complicated function using limits [closed]

I have a very complicated function of one variable consisting of exponential and error functions combined in various ways. Mathematica can't take the derivative of this function in the usual way (...
135 views

### How does one verify the derivative of $f(x) = \sum^{K_2}_{k_2=1} c_{k_2} \exp\left(- \big(a^{(2)} - t^{(2)}_{k_2}\big)^2\right)$

I wanted to verify the derivative of the following equation: $$f(x) = \sum^{K_2}_{k_2=1} c_{k_2} \exp\left(- \big(a^{(2)} - t^{(2)}_{k_2}\big)^2\right)$$ for that I wanted to write a symbolic ...
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### How can I find the formal derivative of a polynomial w.r.t. to its coefficients [duplicate]

I want to define a function $f(x)$ as in $\quad \quad f(x) = \sum^{n}_{i=0} c_i x^i$ as a symbolic expression. Then I'd like to do operations on it. For example, take derivatives of it with respect ...
57 views

### Why can not the vector be transposed in integrating over a region? [duplicate]

Clear[x, A]; A = {{2, -1, 0}, {-1, 2, -1}, {0, -1, 1}}; Integrate[Exp[-x.A.{x}\[Transpose]/2], x \[Element] FullRegion[3]] This code raises an error Transpose:...
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### Multivariate Equation solving [closed]

I have the following equation: r^(1 + Rho) - r^Rho (-1 + Mu) - z Rho == 0 I searched the list but I couldn't come up with a solution. Any help is appreciated. ...
66 views

### Dropping rational coefficients

I have a list of expressions (they all are exact numeric quantities, not containing any variables), some of them have integer or rationals coefficients, or complex coefficients with rational or ...
61 views

### How to apply Simplify only to elements of list that cause specific Warning

I have a set of replacement rules I use to analytically compute nested integrals of very long symbolic expressions since Integrate literally takes forever. To do ...
121 views

### Parallel evaluation of symbolic matrix eigenvalues

I'm trying to find eigenvalues of symbolic hermitian 40x40 block matrix. It is made from 20 2x2 matrices like this: ArrayFlatten[Table[M[m,n],{m,1,20},{n,1,20}]] ...
140 views

### Identify a scalar, a list

I have a symbolic scalar m2 and a symbolic list (representing a 3x3 matrix) A. I want a function which does something like: <...
84 views

### Analytical Fourier Transforms with convolution rule [closed]

The task is the following, how to extend Mathematica's FourierTransform command in order to be able to analytically deal with non-linear differential equations. To do so it should be able to deal with ...
452 views

### Symbolic area calculation for a parametric self-intersecting closed curve

The parametric equation of the curve is: $$\begin{cases} x &= -9 \sin (2 t)-5 \sin (3 t) \\[6pt] y & = 9 \cos (2 t)-5 \cos (3 t) \end{cases}\quad t\in[0,2\pi]$$ which can be easily ...
167 views

### How to speed up an optimization with very long symbolic expressions?

I have 8 very long symbolic expressions (each having around 200,000 summands) - Simplify will run forever, so that is unfortunately not an option. Each of those ...
171 views

### MaxValue of a periodic function

I want to find the maximum of a periodic function on the interval [-Pi,Pi]. What I tried is the following: ...
203 views

### Defining a function implicitly and calculating its derivatives

I'm interested in using Mathematica's symbolic manipulation to obtain, for a particular function $f$, derivatives of arbitrary order evaluated at zero. Normally I'd use the ...
157 views

### How to convert a rational parametric plane curve into implicit form?

This problem is generated from another Green's theorem related question of mine. And here is a forward of the same problem in math.stackexchange. The original equation of the plane curve is not in ...
565 views

### Solve a trig equation system

Background of the problem In the same plane, P is a fixed point, A,B,C are moving point, PA=a, PB=b, PC=c, find the maximize perimeter of △ABC. let ∠BPC=A, ∠CPA=B, ∠APB=2*Pi-A-B, then the perimeter ...
67 views

### Recurrence relation for multivariate polynomials

I am trying to define a function which recursively computes a polynomial associated to every binary string: ComputePoly[s_]:=(** Recurse on the string s**) For ...
130 views

### Factor terms by kets

I have an expression that contains several kets with numerical factors. I would like to retrieve the individual kets and store each individually as a list element. The expression is as follows: <...
170 views

### Handling minus signs in mathematica

I am doing symbolic manipulations in Mathematica where expressions like $(-1)^{1/3}\left(-\log z \right)^{2/3}+\log z^{2/3}$ We see that clearly this expression is zero. But Mathematica does not ...
99 views

### How to order a polynomial in descending powers of x? [duplicate]

This should be very simple, even silly If I ask this mathematica Expand [(x + 1) (x + 2) (x + 3)] Mathematica delivers me well ...
426 views

### Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
183 views

### Comparing exact expressions for equality — is it really OK if I get wrong answer?

Bug introduced in 7.0 or earlier and fixed in 10.2.0 I found an unexpected behavior (that I think of as a bug) in evaluation of the equality operator applied to mathematical functions with exact ...
88 views

### Symbolically Minimizing a Max function

I'm having a tough time with seemingly simple symbolic Minimization/Maximization in Mathematica. I would like to use the Maximize function to work on some unknown random variables and so use min/max ...
50 views

### Analogue of Maple's identify command in Mathematica [duplicate]

In Maple there is a useful command identify that tries to find a closed form expression based on its numeric approximation. As far as I know there is no built-in ...
54 views

### Mathematical symbol and name for Symbolic Replacement

(Originally from math.SE, but might be better here) I'm searching for a mathematical symbol, that describes the symbolic replacement done for instance in Mathematica: ...
77 views

### Interval Arithmetic with Symbolic Intervals

I've run into a problem with IntervalUnion and IntervalIntersection when dealing with symbolic intervals. The following code ...
101 views

### Series of square root of exponential [closed]

my problem concerns the Series command applied to Sqrt of an exponential, and it can be presented in a simplified version as ...
73 views

### How to write a function that returns the combined output of several built-in functions

I am trying to make a module that takes a Boolean function, and prints the following: the function's truth table the function's NOR epxression the function's minimal Disjunctive normal form So far ...
184 views

### Mathematica's steps towards the result of a definite integral

I am interested in this definite integral: \eqalign{\int_0^\infty {x^2 \log(1-e^{-x})}\; dx\cr } That is: ...
194 views

### How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
78 views

### CharacteristicPolynomial returns 0

I have a following matrix. ...
54 views

### Pattern matching & simple replacement

I have a question about an expression that I want to modify. Here is the expression: ...
78 views

### Operator which can be interpreted as binary and unary

I'm a bit lost with the way how e.g. the + operator is implemented in Mathematica as binary (infix) and unary (prefix) operator depending on the context, since I would like to define a similiar ...
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### Using LeviCivitaTensor

I have 2 questions about using LeviCivitaTensor, based on the following session: The signs for the cross product seems to come out "opposite" of what I expected. Why is that? Did I miss anything? ...
123 views

### Root: Simplifying symbolic expression

I'm doing calculations with a lot of symbols, which don't always gives nice expressions. Now I have a solution with a Root-expression, where the coefficients are symbolic, e.g. ...
81 views

### Subtracting Series

When I input the following $$\sum_{n=0}^{m+1}x[n]-\sum_{n=0}^{m}x[n]$$ which in InputForm is: ...
How to implement Ramanujan's summation in symbolic form in Mathematica? For instance, I want as input the function $f(x)=x$, as output $-1/12$, as input $f(x)=1/x$, as output $\gamma$ (Euler's ...