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

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3
votes
0answers
106 views

What is so special about variable s$?

I found a nice bug in Mathematica 9.0.1.0. Could anyone check to reproduce it? Create a file temp.txt with one line: ...
0
votes
1answer
238 views

Symbolic Constrained Optimization

I have a question regarding evaluating constrained optimization problems in symbolic terms. I would like to perform How can I implement the method of Lagrange multipliers to find constrained extrema? ...
4
votes
3answers
269 views

Running out of variables

I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ...
0
votes
2answers
124 views

How to display output as symbols?

I have this piece of code which populates a matrix following different rules depending on row and column number: ...
1
vote
1answer
89 views

Why TensorReduce not working here?

I would like to use TensorReduce to work on the tensor contraction $y_{ib}y_{ia}$ (where index $i$ is summed). However, ...
7
votes
1answer
270 views

Is there a way to see the result of NIntegrate's symbolic preprocessing?

NIntegrate can do a number of different types of symbolic preprocessing on the integrand before starting the numerical calculations, including changes of variables. ...
0
votes
1answer
293 views

Symbolic matrix simplification and solving

I am trying to expand or solve an equation that contains matrices for a certain matrix, but it is not working: ...
1
vote
1answer
361 views

Finding exact local extrema of simple functions

I want to exactly find all the local maxima of f[x_] := x^4/4 - x^2/2 over the interval [-Sqrt[2], 1 + Pi/10]. The correct ...
1
vote
1answer
157 views

How to perform a symbolic minimization?

Can Mathematica determine the symbolic expression in terms of τ that minimizes f[τ] ? ...
3
votes
2answers
298 views

Tweaking Solve for systems of polynomial equations

I am trying to solve the following system of $6$ quadratic equations in $6$ variables: ...
15
votes
2answers
860 views

Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
1
vote
2answers
267 views

Expansion with binomial coefficients

How can I get binomial coefficients in expansion of $(n x+i) (1+i x)^n+(n x-i) (1-i x)^n$, where $i=\sqrt{-1}$ and $n$ is an integer. I have no idea how to coax Mathematica to do something remotely ...
2
votes
1answer
116 views

Declaration of variables in large Linear Programming model with NMaximize

I want to solve a large LP problem using NMaximize. This is a small instance of my bigger problem: $$max \sum^{4}_{t=1}(\sum^{4}_{c=1} V_{c}*f_{c,t})\\ s.t\quad ...
3
votes
0answers
133 views

Do a gauge transformation for a Chern-Simons theory?

Suppose we have the following Lagrangian density: $$ L=\epsilon^{\mu\nu\rho}\big(\sum_a A^a_{\mu}(x) \partial_\nu A^a_{\rho}(x)-\sum_{a,b,c}\frac{1}{3} f^{bca} A^a_{\mu}(x) A^b_{\nu}(x) ...
0
votes
0answers
216 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
2
votes
2answers
86 views

Forcing RecurrenceTable + NIntegrate to evaluate lazily

I have a recurrence relation that grows exponentially if expressed in closed-form. I need to integrate this function. If I plot it, I think Mathematica evaluates the recurrence numerically at every ...
2
votes
2answers
282 views

Can Mathematica identify formulae or sequences of numbers?

Can Mathematica suggest what a formula means? For example if I input $$\sum_{i=0}^n i$$ can it infer that this is a sum of integer values from $0$ to $n$? Or if I enter $0,1,1,2,3,5,8,13$, can ...
5
votes
2answers
153 views

Equality and Quantifiers

I am new to Mathematica and to Math. I do not study math in English, so please bear with me as I try to state my questions.. This is what I am trying to "solve": $$∃!x : A(x) ⇔ ∃x : ¬A(x)$$ In ...
1
vote
1answer
109 views

Linearity of a function in Mathematica

I have a function which has something like myFunc[q,a state[c,d]] a could be anything, and I want to tell Mathematica that ...
10
votes
3answers
388 views

Reduce can't reduce an equation without appropriate assumptions

When there are three unknowns (x, y, z), Mathematica can solve it: ...
3
votes
0answers
71 views

How to combine DifferenceRoot objects for odd and even-indexed terms

I'm trying to analyze a certain infinite sequence $S$, indexed by positive integers starting from $1$. It can be split into two subsequences: $S^{odd}$ by removing all even-indexed elements and ...
4
votes
1answer
153 views

Volume within parameter space

Imagine a parameter space with variable 0<p<1, 0<e1<1/2 and 0<e2<1/2. ...
3
votes
1answer
103 views

Check that a relational expression is true for all complex numbers

How can I use Mathematica to check if a statement like $$\left| \frac{\sqrt{1+2z}-2}{2z-3} \right| \le 1$$ is true for all complex numbers $z$? Also, how can I use Mathematica to check such a ...
0
votes
0answers
68 views

Symbolic representation of bessel series derivative

I want to get symbolic expression for BesselJ derivative, where BesselJ is represented as series: ...
2
votes
1answer
196 views

Why FullSimplify doesn't work here?

Since the emphasis of this question is on finding a workaround, I decided to post this question with an emphasis on the explanation of the behavior of Mathematica. The Bessel function satisfies the ...
5
votes
1answer
68 views

How to bail out from a non-applicable transformation function?

I provide a custom function in TransformationFunctions options of FullSimplify that can do a transformation only for some values ...
6
votes
0answers
183 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special function are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
0
votes
0answers
77 views

How can I plot the characteristic polynomial? [duplicate]

For example, I have: CharacteristicPolynomial[m, x] 0.5 + 0.1 x + x^2 But ...
1
vote
1answer
147 views

How to apply a tensor to a list of arguments

The problem I have is the following: Let C be a list of coordinates, say, C = {x1, x2, ..., xn} and ...
18
votes
1answer
460 views

Incorrect result from Integrate

I attempted to calculate the following integral: ...
6
votes
2answers
236 views

How to implement a formal expectation operator over an unknown distribution?

I need to do some simplification of an expression involving averages over a stochastic variable (in order to verify a long analytical calculation). The easiest way to do that, I figured, were if I ...
4
votes
1answer
364 views

How to extract a possible closed form from WolframAlpha[] output

To find a possible closed form of a number, I can use the function WolframAlpha["6.38905609893065", IncludePods -> "PossibleClosedForm"] It returns a result ...
4
votes
2answers
478 views

Problems with Symbolic summation over unknown values

I'm having some real trouble with Mathematica wrongly evaluating various symbolic sums at the moment. I have this function: $$h_{ij}(x) = ...
5
votes
1answer
260 views

Symbolic linear algebra

I would like to know how I can ask Mathematica to expand (and simplify) such an expression : $$ (\alpha A + \beta B)^\top (\alpha A + \beta B) $$ where $\alpha,\beta$ are two real numbers and $A,B$ ...
1
vote
0answers
37 views

Matching Root[…] objects with patterns, unexpected hidden argument

I needed to write patterns that could distinguish between arbitrary-function and polynomial forms of Root objects, for example, ...
0
votes
1answer
89 views

Is there any automatic method for rating function arguments importance?

If I have a function: y = 2a + 5b + c It can be easily seen that b is the most important parameter, next ...
1
vote
1answer
293 views

Import symbolic variables from Matlab with MATLink

I'm trying to manipulate with Mathematica symbolic expression created in Matlab. I'm using the MATLink package, and I've succedeed in importing numerical variables, but not symbolic ones : ...
4
votes
2answers
284 views

How do I evaluate a symbolic integral involving Hermite polynomials?

I want to test a difficult integral : Integral on all reals of some complicated function involving the Hermitian polynomials, exponentials, squares, factorials, and being general considering any ...
6
votes
2answers
117 views

Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
3
votes
2answers
216 views

Mixed product identity between tensors in Mathematica 9

How can we simplify tensor expressions in Mathematica 9 using the mixed-product identity $(A\otimes B)(C \otimes D) \equiv AC \otimes BD$ ? Is it possible to implement this kind of evaluations using ...
2
votes
1answer
759 views

How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
15
votes
1answer
390 views

How to represent a continuous monotonic phase of Airy functions?

Note: In this question I am concerned only with real-valued variables and functions. DLMF, §9.8 Airy Functions, Modulus and Phase, formula $9.8.4$ defines the phase of Airy functions: ...
12
votes
1answer
482 views

Does anyone have experience with performing symbolic regression using Mathematica?

I understand that there is at least one Mathematica package, DataModeler commercially available for symbolic regression. I'm seeking any observations with this or any other similar tool. I'm ...
2
votes
3answers
199 views

How to code the following product?

I am trying to examine the properties of the following product for a given tuple $\vec \lambda = (\lambda_1, \lambda_2, \dots, \lambda_n)$, then the product is as follows: $$ \dim \Gamma_\lambda = ...
4
votes
3answers
207 views

Why the inequality does not take into account the domain?

I have this inequality: Reduce[(4000-1000k)/(k-4) < 0] and the answer is k ∈ Reals I would expect ...
2
votes
2answers
187 views

Transform Piecewise[] into sum of indicators

I'm interested in transforming a piecewise defined function into a sum of indicator functions, ultimately with the aim to be better able to integrate them. As an example I would like to transform the ...
9
votes
1answer
279 views

Mathematica: computing a difficult integral

I am trying to compute the following integral: Integrate[Exp[Sum[-((cw λ - b[i])^2/(2 σ^2)), {i, 1, n}]], {cw, 0, 1}] And currently Mathematica outputs ...
7
votes
1answer
95 views

Need a generalization of RootApproximant to recognize linear combinations over algebraic numbers

RootApproximant does a very good job when I need to recognize an algebraic number and when enough of its digits are known (or even when an unlimited number of ...
2
votes
1answer
85 views

Illogical failures of symbolic integration over Boole

Is there a way to work around integration over Boole being mysteriously flaky like examples show below? Is there a meaningful explanation for this behaviour? ...