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

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0answers
45 views

Legendre expansion of functions [on hold]

I am given the expansion for the Legendre function of the first kind. It is just $$f(x)=\sum_{n=0}^{\infty}A_{n}P_{n}(x).$$ I have found the expression for the coefficient $A_{n}$. However I would ...
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1answer
71 views
45
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5answers
2k views

Advice for Mathematica as Mathematician's Aid

I use Mathematica mainly as an aid in symbolic attacks on problems, usually intermediate or harder and often number theoretic. While Reduce, ...
3
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2answers
96 views

How to deduce the Ramanujan's summation of this series?

I have already asked a similar question about Ramanujan's summation in general but received no good answers. Now I am interested in this exact series: $$\sum _{n\ge1}^\Re (24 n + 12 n^2)$$
4
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0answers
93 views

Simplest identity that cannot be proved by FullSimplify [closed]

Apparently, FullSimplify is not able to prove all true identities, but usually it does pretty well when it comes to elementary functions. I'd like to know what are ...
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3answers
185 views

How to simplify symbolic expressions with KroneckerProduct

Having $X,Y$ being symbols for matrices, I was wondering if there is a way to simplify expressions like KroneckerProduct[X, X] + KroneckerProduct[-X, X] to ...
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2answers
141 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 ...
4
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0answers
44 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 ...
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0answers
43 views

Partial derivative of recursive exponential $f(x)=\sum^{K_2}_{k_2=1}c_{k_2}\exp(-z^{(2)}_{k2})$ w.r.t. the deepest parameter

I was trying to take the derivative of the following equation (which can be depicted nicely in a tree like structure, look at the end of question for diagram): $$f(x) = f([x_1, ..., x_{N_p}])= ...
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1answer
117 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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0answers
55 views

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 ...
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1answer
41 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 ...
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1answer
64 views

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. ...
2
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1answer
56 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 ...
1
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1answer
49 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 ...
2
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0answers
50 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}]] ...
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3answers
74 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: ...
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0answers
32 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 ...
14
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2answers
382 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 ...
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1answer
135 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 ...
2
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2answers
127 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: ...
6
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1answer
159 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 ...
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1answer
72 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 ...
14
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3answers
403 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 ...
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1answer
59 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 ...
1
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1answer
89 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: ...
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1answer
143 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 ...
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1answer
60 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 ...
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0answers
76 views

Solve is too slow with this system of equations

The definitions are: ...
11
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2answers
359 views

Why Mathematica cannot apply The Fundamental Theorem of Calculus automatically?

For some reason Mathematica cannot evaluate this definite integral: ...
9
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1answer
167 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 ...
3
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0answers
71 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 ...
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0answers
49 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 ...
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0answers
37 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: ...
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0answers
55 views

Interval Arithmetic with Symbolic Intervals

I've run into a problem with IntervalUnion and IntervalIntersection when dealing with symbolic intervals. The following code ...
2
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1answer
52 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 ...
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1answer
130 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: ...
2
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1answer
163 views

How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
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0answers
48 views

CharacteristicPolynomial returns 0

I have the following matrix. ...
2
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1answer
48 views

Pattern matching & simple replacement

I have a question about an expression that I want to modify. Here is the expression: ...
5
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0answers
61 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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1answer
76 views

Symbolic matrix calculation [closed]

I have question about a matrix calculation like $\mathbf{b}^{t}\,\Sigma\,\mathbf{b}$, where $\Sigma$ is a 7 by 7 matrix, and $\mathbf{b}$ is vector of 7 elements, and each element in the vector ...
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3answers
93 views

how to create, print and use variables using a loop in Mathematica?

I want to create, print and be able to use (i.e. do symbolic operations) variables in Mathematica using a for loop or equivalent. So, I have a bunch of variables of this form: $$dS_i = -\beta_i ...
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1answer
65 views

Symbolically solve system of equations involving matrix

I need to solve the following system of equations symbolically for a_i, b_i, and c_i: ...
3
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3answers
103 views

Factoring a separable integral with a product of independent integrands

I would like to input someFunction[Integrate[p[x] p[y], {x, -1, 1}, {y, -1, 1}]] and to get the following output ...
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0answers
50 views

Computing symbolic surface normal of a surface point on a semialgebraic set

Consider a semialgebraic set; such as reg below: ...
2
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1answer
63 views

Algebraic Manipulations with Indices

I am absolutely new to Mathematica, but I've heard it is a pretty powerful tool for symbolic calculations. My problem (stated generally): I have three dimensional array. I define a symbolic operator ...
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0answers
52 views

Is there a way for me to get Mathematica show its steps? [duplicate]

I have seen similar questions but they were quite dated (3+ years). When performing, say an Integration, it would be beneficial to see the major steps such as variable substitution, change the order ...
4
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1answer
66 views

Factoring out parts of an expression

I'm looking to factor out the parts of a multiplication type of expression. For example for the expression: $$20 e^{-t^2}\frac{t^2}{\sqrt{t^2+a}} erf(b+t)$$ I'd like to get a list in the form of: ...
2
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1answer
108 views

Fundamental question about capabilities of Mathematica to represent abstract mathematics [closed]

I have an fundamental question about what Mathematica can and cannot do. I have a book which presents a certain physical theory in an axiomatic manner. The axioms make heavy use of mathematics. Some ...