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

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3
votes
1answer
108 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 ...
3
votes
1answer
397 views

Define operator algebra

My objective is to work out commutators like this $$[f(x,y)\partial_x^2+g(x,y)\partial_x+h(x,y),a(x,y)\partial_x^2+b(x,y)\partial_x+c(x,y)]$$ or ...
3
votes
1answer
330 views

n-fold symbolic integral in Mathematica

I am trying to compute symbolically a n-fold integral (n is a parameter of a function) over, say, the cube [0,a]^n. My code looks like this ...
3
votes
1answer
60 views

Need help understandig the output of `DSolve`

I give Mathematica (10) the following command: DSolve[I D[P[x], {x, 2}] f[x] - (P'[x])^2 f[x] + 2 I P'[x] f'[x] == 0, P, x] And I have the following output: ...
3
votes
1answer
47 views

How to get Mathematica to make further simplifications to conditional expressions than it has already made?

I have the following Mathematica result under the assumption that {ax, bx, px, ay, by, py} \[Element] Reals, and after refinement by ...
3
votes
1answer
134 views

Can Mathematica solve this type of recurrence?

I have the following recursively defined equation: ...
3
votes
3answers
143 views

Differential equation with a Heavisidetheta function running for ever

So I'm trying to get the solution of the following differential equation: ...
3
votes
2answers
137 views

Eigenvectors of large symbolic matrix

I have large symbolic matrix of order 32 x 32 given as ...
3
votes
1answer
114 views

Strange integration

Bug introduced in 9.0 or earlier and fixed in 10.1 Note: Beginning with V10.1, this integral returns unevaluated but without error messages. I tried to evaluate this line ...
3
votes
1answer
595 views

Nested Sums to multiple sum

I would like to automatically "move nested sums to the left". I mean, just take out of an expression all the summations and go from a nested Sum to a multiple sum. Something like starting with: ...
3
votes
1answer
515 views

Mathematica 9 and later behavior with derivative of a sum

Bug introduced in 9.0 or earlier and persisting through 10.3.0 or later ...
3
votes
1answer
95 views

Symbolic Output after numerical computation

I have a small question about the symbolic output. I started to write a program that generates the coordinates of n-dimensional polytopes by Wythoff construction. For crystallographic groups, all is ...
3
votes
1answer
290 views

Sum of positive terms gives negative answer

Bug introduced in 7.0 and fixed in 9.0 Mathematica evaluates Sum[((n - y - 1)*(n - y)^2*n^y)/y!, {y, 0, n - 2}] as -2 e^n n. ...
3
votes
1answer
124 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 ...
3
votes
0answers
57 views

Simplifying between set theory and logical connectives

I'm trying to find out how to switch between set notation and logic, but am having difficulty. For instance, I know that the following two expressions are equivalent ...
3
votes
0answers
90 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
3
votes
0answers
65 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 ...
3
votes
0answers
80 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 ...
3
votes
0answers
58 views

Derive logistic choice probabilities symbolically

More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: ...
3
votes
0answers
63 views

Evaluating standard functions of general quaternions symbolically

Mathematica can easily compute exponentials and logarithms of concrete quaternions: ...
3
votes
0answers
486 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 ...
3
votes
0answers
153 views

Fourier transformation of HeavisideTheta functions

I want to find 2D-Fourier transformation of the function given below f = HeavisideTheta[y1]*HeavisideTheta[y2 - y1] For the purpose, I use built-in function in ...
3
votes
0answers
112 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: ...
3
votes
0answers
186 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) ...
3
votes
0answers
80 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 ...
3
votes
0answers
249 views

Malliavin Derivative with Mathematica is it possible?

Is it possible to define a Malliavin calculus with Mathematica 9? Consider a random variables on the Wiener-space $\Omega=\mathcal{C}([0,1])$ of the form ...
3
votes
0answers
244 views

Numerical-Symbolical Integration (Calculus)

I created a simple numeric-symbolic integration. Here you can use symbolical and numerical techniques at the same time. You can also interpolate numerical integrals. The problem with my function is ...
2
votes
2answers
517 views

Rewriting one expression using a variable representing another expression [duplicate]

I have two expressions: w1 = (a+b)/c^2; w2 = (a^3 + 3 a^2 b + 3 a b^2 + b^3)/c^6; How can I ask Mathematica to try to find an alternative expression for ...
2
votes
2answers
359 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 ...
2
votes
4answers
267 views

Working with symmetric polynomials

I have a question related to working with symmetric polynomials in some variables. Let us say, I have an expression ...
2
votes
1answer
346 views

Identifying the sign of an expression in an interval

My expression is the following: $$ \frac{(1-\alpha ) \alpha h^2 (h+2) \mu r}{(h+1) ((1-\alpha ) h+1) (\alpha h+1)}-\left(\frac{\alpha h \mu }{h+1}\right)^{\alpha } \left(\frac{(1-\alpha ) h \mu ...
2
votes
2answers
153 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: ...
2
votes
1answer
579 views

How to get (fg)' = f'g + g'f?

I am new to Mathematica so the my questions might be pretty much at the pupil's level. If I want to use differentiation to derive: (fg)' = f'g + g'f How can ...
2
votes
1answer
89 views

How does this code work to substract a set A from a set B?

In an answer to a question (as given here: code), the proposed function was to to subtract a set B from a Set A: ...
2
votes
1answer
180 views

How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
2
votes
2answers
173 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 ...
2
votes
1answer
207 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
2
votes
3answers
2k views

How to calculate partial derivative of an unknown function

How can I force Mathematica to calculate symbolically the partial derivative of a function u[x,y] with respect to a variable ...
2
votes
1answer
88 views

Boundary condition not fully taken into account in DEigensystem?

Context Mathematica 10.3 now has the very nice DEigensystem function. ...
2
votes
3answers
115 views

Symbolic integration conditional bug?

I just ran across this: Assuming[x > 0, Integrate[1/t^2, {t, 1, x}]] gives the output ...
2
votes
1answer
196 views

What's the differences between the shift-enter and MakeBoxes running?

I know the example usages of MakeBoxes in the Tutorial like this. but I want to know a subtle distinction between (1) and (3) ...
2
votes
1answer
174 views

Factoring terms out of a polynomial

I don't do much algebra in Mathematica and was surprised to discover, while attempting to answer this question, that I had no idea how to factor out an expression from a polynomial. The question was, ...
2
votes
1answer
76 views

Defining a function (but not explicitly)

I have a question that must have a simple answer, but googling and searching this website did not produce an answer, so I'm asking it here. I'm working with three variables $x, y, \theta$, and I want ...
2
votes
1answer
434 views

Prove (or check) an expression is positive given constraints on variables?

I'm trying to figure out whether an expression is always positive given positive parameters. When the expression is complicated, I can't do this by eye. Is there any way to make Mathematica prove ...
2
votes
3answers
206 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 = ...
2
votes
1answer
218 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
117 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 ...
2
votes
1answer
135 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
358 views

Working with derivative of conjugate of a complex number

I have a complex function, lets say $g(x)$. I want to take its and its conjugate's derivative. I need the solution of derivative which must be symbolically and computationally efficient. Lets take an ...