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

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2
votes
1answer
195 views

Difference between Map[f[#] + g[#] &, {a, b, c}] and Map[f[x]+g[x]&, {a, b, c}]

Map[f[#] + g[#] &, {a, b, c}] vs Map[f[x]+g[x]&, {a, b, c}] My question is: why is the output different? ...
2
votes
1answer
84 views

how to calculate the covariance of sample central moments

$\bar{x}= \sum_{i=1} ^{n} \frac{1}{n}x_{i}$ $m_1=\sum _{i=1} ^{n} \frac{1}{n} (x_{i}-\bar{x})$ $m_2=\sum _{i=1} ^{n} \frac{1}{n} (x_{i}-\bar{x})^2 $ $m_3=\sum _{i=1} ^{n} ...
2
votes
1answer
93 views

simplifying integrals for multiple exponentials

This is somewhat related to this question, but applied to products of Exp[]. For example, I have a symbolic expression containing terms like $Exp[\int_0^1 ...
2
votes
2answers
102 views

Let mathematica combine integral limits

Is there a way to teach mathematica to combine integral limits according to $\int_a^b f dx+\int_b^c f dx=\int_a^cf dx$ to simplify expressions like $\int_0^1 f[t] dt+\int_1^x (1+f[t]) dt$ to $\int_0^t ...
2
votes
1answer
45 views

Imaginary term in Integration procedure

How do you remove the imaginary term in the integrated output? Compare the outcome from the operations below. The first operation yields an imaginary term, while the second one has none. ...
2
votes
1answer
166 views

Compute symbolic Expectation of a summation

I am required to computed following Expectations : $E[\displaystyle\sum\limits_{i=1}^N \frac{X_{i}}{N}] = \bar{x}_{0}$ & $E[\displaystyle(\sum\limits_{i=1}^N \frac{X_{i}}{N})^2] = ...
2
votes
1answer
105 views

Symbolic multiplicative partitions

Let $p_n\#\equiv\prod_{k=1}^{n}p_k$ (primorial): p[n_] := Times @@ Prime[Range[n]] then the multiplicative partitions of $p_{1,2,3,4}\#$ are $$ \{\{2\}\},$$$$ ...
2
votes
1answer
534 views

Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
2
votes
2answers
225 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 ...
2
votes
2answers
288 views

How to find solutions that yield of root of unity?

I have a polynomial with coefficients that are integer polynomials in another (complex) variable. For example: 1 + (1 - v^2) #1 + (-3 - v^2) #1^2 + #1^3 & I ...
2
votes
1answer
161 views

Simplification of a symbolic manipulation involving functions of more than one variable

I am facing the following problem. f[x_,y_] = a[x] u[y] + b[x] v[y] Now I can ask Mathematica to calculate ...
2
votes
1answer
44 views

Pattern matching & simple replacement

I have a question about an expression that I want to modify. Here is the expression: ...
2
votes
1answer
117 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
2
votes
1answer
111 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
2
votes
1answer
47 views

A question about expanding complex functions of real arguments

I have the following problem. There is such an expression as: P[x_,y_] := z[y] E^(I beta x) + Conjugate[z[y] E^(I beta x)]; The variables ...
2
votes
1answer
279 views

How to make Mathematica try harder to perform symbolic comparisons?

(I suspect this question is a duplicate, but I didn't find a sufficiently similar question with an answer to it.) I'm having trouble with comparisons of symbolic ...
2
votes
2answers
444 views

Mass Symbolic Manipulation with Subscripts? (from plaintext Input)

The simplest example of the change being sought is a greek letter, typed in as plaintext nu, and its may be replaced by the symbol, ν: expr = 3nu*kx*ky+ ...
2
votes
1answer
128 views

Symbolic quadratic constrained maximization with non-negativity constraints?

Dear Mathematica users, I attempted to maximize the below quadratic function K, subject to x1+x2<=A, and a series of ...
2
votes
1answer
97 views

Typing (and executing) expressions with multiple superscripts

I am trying to type (and evaluate) expressions of the following form: $$ G^{a,b} $$ into a mathematica. I've tried the obvious G^(a, b) or ...
2
votes
1answer
473 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 ...
2
votes
1answer
236 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 ...
2
votes
1answer
91 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? ...
2
votes
1answer
277 views

Integral not simplifying

I specify a function in terms of an integral and then try to evaluate it with Simplify. However, the answer is not really simplified to what it should be. ...
2
votes
1answer
45 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 ...
2
votes
1answer
61 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 ...
2
votes
1answer
100 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 ...
2
votes
1answer
78 views

How to define the symbolic expression $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in Mathematica?

I want to define this expression symbolically: $V = \frac{1}{N} \sum_{i=1}^N ( y_i(g) - z_i)^2$ in which $\{y_i(g)\}_{i=1}^N$ is to be understood as a symbolic sequence that depends on a vector $g$. ...
2
votes
1answer
126 views

Extracting rational coefficients from an irrational sum [closed]

I have a function that returns results that always can be represented as $p+q\,\pi^2+r\ln2+s\ln^22+t\sqrt2$ where $p,q,r,s,t\in\mathbb Q$. But the actual Mathematica expression returned not always in ...
2
votes
2answers
339 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
2
votes
1answer
179 views

Integrate does not accept my integrand expression

I want to calculate the symbolic integral, but I could not obtain the final results from Mathematica. ...
2
votes
1answer
127 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 ...
2
votes
2answers
87 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
1answer
138 views

Differentiating with respect to vectors of unspecified length

Given a function defined by f[x_,y_] := Sum[ x[[i]] (g[y[[i]]] - g[Total[y]] - Log[x[[i]]]), {i, 1, Length[x]}] I can easily calculate the derivative for a fixed ...
2
votes
1answer
754 views

Variable name string to expression

I'm not sure how to name this problem appropriately. But anyway. I have, say, three variables (arrays in my case), which I call: A1, A2, A3 I would like to ...
2
votes
1answer
243 views

Can I reduce a matrix inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$?

I'm new to Mathematica. When I do linear algebra, I wonder if I can have an inequality such as $\mathbf x^\prime\mathbf A\mathbf x > \mathbf x^\prime\mathbf x$, where $\mathbf x$ is a column vector ...
2
votes
1answer
501 views

How can I solve an exponential inequality in Mathematica?

I would like to solve the equation: A Exp[m t + s Sqrt[t] x - 1/2 s^2 t] >= K with respect to x (which is in the exponent) ...
2
votes
1answer
472 views

Reduce/Solve an equation with symbols in powers

I am trying to solve the following equation with respect to x. eqn = x^z + y == a; But when I do ...
2
votes
0answers
69 views

Integrate with Subscript: does this crash your kernel too?

I encountered some strange behaviour running v10.0.1 on a Mac Pro, while working with Integrate and Subscript. Starting from a ...
2
votes
0answers
89 views

How does Mathematica resolve symbolic systems of inequalities?

Before getting into my (probably annoying) question, let me provide some context: I recently started using Mathematica to automatically perform stability analyses that I previously did by hand. A ...
2
votes
0answers
97 views

Result of symbolic integration changed drastically by making assumptions

I would like to know the underlying reason for different outcomes for the two integration operation below. One of them includes a few assumptions, otherwise both have the same integrand: ...
2
votes
0answers
310 views

Symbolic matrix calculus: What's new in Version 9

I have seen some of the related posts, which ask about doing matrix calculation on tensors unknown dimensions. One of the posts mentioned that version 9 has some capability, but it was concerned about ...
2
votes
1answer
862 views

How to simplify symbolic matrix multiplication results?

I've defined three symbolic abstract matrices X, M and S as shown below. ...
2
votes
0answers
140 views

Changing bounds of summation after differentiating symbolic sums

Suppose, I have a function written as Taylor-Maclaurin series f = Sum[c[n]*x^n, {n, 0, Infinity}] Now, I wish to differentiate this expression with respect to ...
2
votes
0answers
201 views

Problems with Simultaneous Equation Solving

Let me first explain what I am doing and then I will explain the problem that I can't figure out. I am basically trying to solve 2 equations for 2 unknowns (a1 and ...
1
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1answer
206 views
1
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1answer
327 views

Is this function convex?

How can I determine convexity of the function f = Log[ x, 1 + (x^a - 1) (x^b - 1)/(x - 1)] with the parameters $a,\,b$ belonging to the interval $(0,1)$ in ...
1
vote
2answers
554 views

How to make Mathematica use the chain rule?

Lets say I have the following PDE: $$x^2 u_{xx} - u_{yy} + u_y = 0$$ And I have the following change of variables: $$ s(x,y) = x e^y \, \, \, , \, \, t(x,y) = x e^{-y}$$ How can I use Mathematica ...
1
vote
3answers
133 views

Symbolic derivatives of special functions yield incorrect results

When I evaluate with Mathematica this expression D[ Abs[ Zeta[x + I y]], {x, 2}] + D[ Abs[ Zeta[x + I y]], {y, 2}] 0 the ...
1
vote
1answer
137 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 ...
1
vote
3answers
630 views

Sqrt — how to get negative branch?

One of the many attractions of Mathematica is that integers are generally treated as exact symbolic entities, and not just as numbers. I was just playing with Sqrt, and was puzzled by what appeared to ...