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

learn more… | top users | synonyms

0
votes
0answers
57 views

Assigning values to variables with subscripts [on hold]

I'm wondering if there is a way to assign values to variables with subscripts. I have the following Manipulate function: ...
2
votes
2answers
121 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
votes
1answer
148 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 ...
0
votes
0answers
38 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
votes
3answers
373 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 ...
30
votes
1answer
633 views

How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
0
votes
1answer
74 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 ...
0
votes
0answers
40 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
vote
0answers
102 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...
8
votes
1answer
282 views

Is it possible to implement symbolic sub matrices?

The accepted answer in the question Symbolic matrices in Mathematica with unknown dimensions provides a functionality to create symbolic matrices which behave pretty much as the name suggests. ...
1
vote
1answer
56 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: ...
1
vote
1answer
138 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 ...
0
votes
1answer
49 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 ...
8
votes
2answers
292 views
4
votes
0answers
92 views

Symbolic integration of elliptic functions

Is there some clever way to integrate products of elliptic functions $\wp(z;g_2,g_3)$ or $\zeta(z;g_2,g_3)$ in Mathematica? Mathematica seems to be able to integrate functions like ...
6
votes
1answer
125 views

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

I found an unexpected behavior (that I think of as a bug) in evaluation of the equality operator applied to mathematical functions with exact arguments (i.e. not containing any approximate ...
16
votes
1answer
451 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: ...
7
votes
4answers
237 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
3
votes
0answers
68 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 ...
21
votes
2answers
281 views

Backslide of Limit

A friend of mine showed me this example: Limit[Sum[Sin[Pi*k/n]/(n + 1/k), {k, 1, n}], n -> Infinity] This sample calculates well in v8.0.4: but not in ...
1
vote
0answers
46 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 ...
10
votes
1answer
724 views
0
votes
0answers
32 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: ...
-2
votes
1answer
119 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: ...
29
votes
1answer
720 views

Proving the hairy ball theorem using xAct

I would like to formally prove the hairy ball theorem in Mathematica, initially just for $S^2$, and then see about generalizing. An approach I thought about to use the xAct package to define $S^2$ ...
3
votes
0answers
44 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
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
156 views

How to speed up a symbolic integration

I have a question about an integral. I wanna integrate this: ...
0
votes
0answers
44 views
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: ...
1
vote
1answer
95 views

Strange timings of integrals involving Hermite's polynomials

I have used Mathematica to calculate tunneling for quantum harmonic oscillator. The code is simple: ...
5
votes
0answers
57 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 ...
1
vote
3answers
70 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 ...
3
votes
3answers
95 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 ...
0
votes
1answer
56 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: ...
20
votes
1answer
597 views

Analogue for Maple's dchange - change of variables in differential expressions

Maple owns an interesting function called dchange which can change the variables of differential equations, but there seems to be no such function in Mathematica. ...
0
votes
0answers
41 views
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 ...
0
votes
0answers
47 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 ...
9
votes
2answers
223 views

How to implement symbolic Ramanujan's summation in Mathematica?

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 ...
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 ...
4
votes
1answer
62 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: ...
5
votes
0answers
95 views

Integral formula for the inverse Laplace transform doesn't work?

The direct implementation of the definition of the inverse Laplace transform using Integrate fails in the following case: ...
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} ...
4
votes
2answers
63 views

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? ...
0
votes
1answer
47 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. ...
5
votes
1answer
51 views

How do I perform exact unit conversions with irrational conversion factors?

Suppose I want to express $3h$ in units of $\hbar$ (where $h$ and $\hbar$ are the Planck constant and reduced Planck constant, respectively). By definition, $h = 2\pi\hbar$, but when I attempt this ...
5
votes
1answer
107 views

Checking if a symbolic matrix is positive semi-definite

As far as I can tell, there is no way to tell the builtin PositiveSemidefiniteQ about assumptions on symbols. For example, the matrix ...
0
votes
1answer
53 views

Is there a function or option to collect factors under one radical sign?

One of the things that frustrates me most about Mathematica's symbolic manipulations is the fact that output is often presented quite differently than most humans would write it. This is especially ...