Skip to main content

Questions tagged [algebraic-manipulation]

The art of manipulating an algebraic expression into the desired form.

Filter by
Sorted by
Tagged with
0 votes
0 answers
61 views

Is there an easy way to understand how to manipulate summations?

I'm working in a very very long calculation that could be done by hand but it might be tedious. Moreover, when doing by hand that amount of calculations I'm subject to errors, of course. Then I ...
Felipe's user avatar
  • 111
2 votes
3 answers
158 views

Converting an algebric expression into a matrix form

Consider the following expression: a1 b1 c1 + a4 b2 c1 + a7 b3 c1 + a2 b1 c2 + a5 b2 c2 + a8 b3 c2 + a3 b1 c3 + a6 b2 c3 + a9 b3 c3 Can Mathematica convert it ...
SciJewel's user avatar
  • 484
0 votes
1 answer
69 views

Separable decomposition $F(r,\theta) = A(r) + B(\theta)$ [closed]

Is it possible in Mathematica to take a function $F(r, \theta)$ and ask it to rewrite it as $F(r,\theta) = A(r) + B(\theta)$? In particular, I have the expression: $$ \frac{g^{2} (r) f^{2} (r) \sin^{2}...
Dayzk's user avatar
  • 147
3 votes
2 answers
100 views

Multiple replacements in a long expression

Why does the replace /. not work on the second argument in the following expression: ...
SciJewel's user avatar
  • 484
-1 votes
1 answer
100 views

How to write an expression as a ratio of polynomials [closed]

I have the following Mathematica expression as a result of some calculations: ...
Mark's user avatar
  • 327
1 vote
0 answers
66 views

Function to express Piecewise as UnitStep functions

Is there a documentation for the function Simplify`PWToUnitStep? This is a function which can be used to express a Piecewise ...
Ruth Murphy's user avatar
4 votes
1 answer
163 views

What's the reverse operation of TransferFunctionExpand?

Given a transfer funtion TransferFunctionModel[1/(s + I) + 1/(s - I) + 1/(s + 1) + 1/(s - 2)^2,s] we can obtain the polinomial form by using TransferFunctionExpand ...
metroidman's user avatar
2 votes
1 answer
117 views

Is it possible to express $\text{Li}_2(-\frac18(-i+\sqrt{15})+\text{Li}_2(\frac18 (i+\sqrt{15})$ as an explicit real expression (not numeric)? [closed]

I obtain this expression in my calculations, and numerically I am sure that it is a real number. ...
MsMath's user avatar
  • 195
0 votes
1 answer
56 views

Convergent Taylor series unrecognized by Sum

I am trying to understand why Sum does not recognize a particular Taylor series as convergent. I have defined a function 'series' like this, that computes the Taylor series of a function 'f' at 'x', ...
Glenn Welch's user avatar
10 votes
4 answers
445 views

Visualizing Wicks' contractions using brackets

Given a string like MMMM, what is the easiest way to draw all Wicks contractions similar to the diagram below (from Ch. 2 of Eynard paper)? Example below is for (MMMM), but I need it to work for other ...
Yaroslav Bulatov's user avatar
1 vote
0 answers
34 views

Separate exponentials [duplicate]

Good afternoon, I have an expression Exp[2 I (t - tau) + a] + 2 Exp[2 I t + b] + 3 Exp[-I t + b] And I want to write it as a summation of powers of Exp[I t]. So, <...
Bou's user avatar
  • 11
2 votes
0 answers
59 views

Equivalent of `MomentConvert` for free moments/free cumulants? [closed]

I'm looking for Mathematica implementation of conversion between free moments and free cumulants. For instance, for traditional moments we have from ...
Yaroslav Bulatov's user avatar
3 votes
2 answers
100 views

Closed-Form Solution for k-ary Tree Traversal Order

I was reading this blog post (https://research.swtch.com/treenum) that proposes a new base-k ordering for k-ary trees - I found myself wondering: is it possible to use Mathematica to solve a ...
Torkoal's user avatar
  • 153
5 votes
1 answer
250 views

Quantum Field Regularization: Choice between ExpIntegralE and Gamma for Casimir Effect

For the Casimir effect with exponential regularization, we compute the vacuum energy between the plates (somewhat simplified) with: $$\omega = c\ \sqrt{q^2+k_z^2}$$ $$ E = \sum_{k_z=n\pi/a} 2 \int\...
Jos Bergervoet's user avatar
2 votes
1 answer
177 views

How can I get stronger simplification than FullSimplify?

Short description: Is there a simplification that can for a>1 simplify ...
Jos Bergervoet's user avatar
4 votes
2 answers
199 views

Putting a term under the square root

I want to put a term under the square root (but with Mathematica), such that $$(1+t)^2\sqrt{1+\frac{t^3}{(1+t)^3}}$$ is transformed to $$\sqrt{(1+t)^4+(1+t)t^3}.$$ I've tried all the forms of ...
lesobrod's user avatar
  • 1,729
7 votes
4 answers
363 views

Getting formulas like $E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+10n^2+4n$

Suppose $A$ is an random $n\times n$ matrix with standard normal entries. A user was able to obtain the following formula by enumerating all diagrams by hand: $$E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+...
Yaroslav Bulatov's user avatar
0 votes
1 answer
42 views

How to factorize high-order polynomials that have only complex roots?

I have polynomials like this: ...
homocomputeris's user avatar
2 votes
1 answer
68 views

Algebraic replacement [duplicate]

How do I replace an algebraic expression with a symbol? I'm trying to replace repeated terms such as $(a+b)$ with c, for example, so that $x(4a + 4b) + x^2(6a + 6b)$ becomes $x4c + x^26c$ .
PoemTechnology's user avatar
3 votes
1 answer
67 views

Expressing equation in terms of a ratio between two variables

I have x = (-2 h^2 k - 2 h k^2 - k^3 - Sqrt[8 h^4 k^2 + 16 h^3 k^3 + 14 h^2 k^4 + 6 h k^5 + k^6])/(2 h^2 + 2 h k + k^2) which has ...
Sang Dhong's user avatar
3 votes
1 answer
108 views

Factor constants out of multiple dot products

I have expressions of the type (-y A.A).(-y A.A).(A x).(A x) (* Example 1 *) (-y A.A).(-y A.A).(A x) (* Example 2 *) The number of parenthesis factors can vary, ...
Ben's user avatar
  • 249
1 vote
0 answers
42 views

Simplify argument of Logs

I have the following expression ...
BabaYaga's user avatar
  • 1,888
4 votes
3 answers
183 views

Automatically extract a factor from a sum of terms and rewrite the sum

I would like to automatically extract the same factor of each term, and thus write a sum such as: $$\frac{4 \sin (2 \pi x)}{\pi }+\frac{4 \sin (6 \pi x)}{3 \pi }+\frac{4 \sin (10 \pi x)}{5 \pi }+...
David G. Stork's user avatar
2 votes
3 answers
86 views

How to factorize $x+y$ in this kind of example?

Consider the following simple polynomial in two variables 5 + 2x + 2y. Suppose I want to simplify it to 5+2(x+y). I have no idea ...
user1620696's user avatar
4 votes
5 answers
315 views

How to make ReplaceAll recognize what to be replaced in a situation like this?

I'm a bit confused on how ReplaceAll works. For example ReplaceAll[2x+2y, x+y -> 1] just gives ...
user1620696's user avatar
1 vote
0 answers
89 views

Output a 24 by 24 Leech lattice

Input a rank-8 $E_8$ lattice, $$ M_{E_8}=\begin{pmatrix} 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ -1 & 2 & -1& 0 & 0 & 0 & 0 & 0 \\ 0 &...
zeta's user avatar
  • 251
0 votes
1 answer
47 views

Transform a list of delayed rules with conditions to a new list of delayed rules

I have a list of rules that implement some abstract algebras, for instance, that of the Pauli matrices, ...
Lelouch's user avatar
  • 543
5 votes
1 answer
437 views

Present a logarithm in terms of two logarithms

If $\log _8 3=p$ and $\log _3 5=q$ then, in terms of $p$ and $q$, what does $\log _{10} 5$ equal? I tried by my hand, I get the answer is $\dfrac{3pq}{1+3pq}$. How can I tell Mathematica solve ...
Laurenso's user avatar
  • 1,054
5 votes
1 answer
211 views

How to Replace 'delta t' with 'a' in Mathematica Without Affecting Separate Instances of 'delta' or 't'?

In Mathematica, how can I replace instances of delta t in an expression with a, while keeping instances of ...
Tokubara's user avatar
  • 215
1 vote
2 answers
162 views

Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
Dotman's user avatar
  • 456
0 votes
1 answer
136 views

Kernel Crash Using Solve

The following code crashes the Kernel with no error message. ...
Just Some Old Man's user avatar
0 votes
0 answers
49 views

On MacOs, I cannot use Needs["QDENSITY`Qdensity`"]

I am trying to get Needs["QDENSITY`Qdensity`"] from (https://library.wolfram.com/infocenter/MathSource/5715/), however, it failed and I get this error: ...
Xui Lao's user avatar
4 votes
5 answers
339 views

Most concise code for tangent and normal line of implicit algebraic curve

Can you make the code for tangent line and normal line of implicit algebraic curve cu more concise than mine? The code for tangent line at ...
azerbajdzan's user avatar
  • 18.9k
1 vote
3 answers
124 views

Selecting coefficients of multivariable polynomial

We have polynomial in three variables x, y, z. How to list all coefficients of odd powers of z or ...
azerbajdzan's user avatar
  • 18.9k
0 votes
1 answer
59 views

Function to generate analytic solution of StandardDeviation of a list given sublists

Motivation I have the Mean and StandardDeviation of several lists of equal size but I don't know the elements of those lists. I ...
IntroductionToProbability's user avatar
7 votes
1 answer
102 views

Unexpected behavior of `Exponent`

Fixed in Version 14.0 According to Exponent: Exponent[expr, form] gives the maximum power with which ...
user688486's user avatar
0 votes
2 answers
73 views

How to define an infinite dimensional algebra with a known basis and multiplication rule?

My goal is to do symbolic calculations in the noncommutative associative algebra generated by two elements $x,y$ satisfying the relation $x.y=q~y.x$. This infinite dimensional algebra has the basis $...
Lagrenge's user avatar
  • 119
2 votes
1 answer
56 views

Creating a boolean expression of assumptions between variables

I'm trying to create a boolean expression from a list of lists of variables such that the elements of one list are not equal to the elements of all other lists. I thought this might work: ...
David's user avatar
  • 159
2 votes
2 answers
243 views

How to approximate the distance from {x,y} to a hyperbola?

I can get a good approximation, but making this into a MMA algorithm is getting complicated. Consider this example: ...
Ted Ersek's user avatar
  • 929
1 vote
1 answer
157 views

How to factor a quartic equation whose coefficient has unknown parameters?

i'm trying to see if a quartic equation I obtained can be factored into simpler forms, such as the product of two quadratics. The problem is that their coefficients are some complex expressions in ...
larry's user avatar
  • 735
4 votes
1 answer
220 views

Working in Mathematica over a cyclotomic ring [closed]

How can I simplify expressions in $\mathbb Q[x]/(x^7-1)$ in Mathematica, i.e. make Mathematica transform $x^{20}+x^8+x+3$ into $x^6+2x+3$.
Adam's user avatar
  • 153
17 votes
4 answers
785 views

What is Mathematica's equivalent to Maple's collect with distributed option?

Given a polynomial in $x,y$, I want to collect on $x,y$ and any products of these also. As given using Maple's collect with the distributed option. Currently Mathematica will collect on $x$ then ...
Nasser's user avatar
  • 145k
1 vote
1 answer
33 views

Validate equalities among Square roots for a simple expression

I am trying to validate this property: $\sqrt{1-z}=\sqrt{-(-1+z)}=(\text{}\pm i) \sqrt{-1+z}$ FullSimplify[Sqrt[1 - z] == I Sqrt[(-1 + z)]] I have seen how we need ...
Jmtz's user avatar
  • 113
1 vote
1 answer
104 views

How to obtain approximate form for a calculation using Mathematica with specific approximations?

I am currently working on a calculation in Mathematica that involves various parameters, including Nb, k, and Ns. I want to obtain an approximate form of the calculation by considering the following ...
Sagar's user avatar
  • 11
2 votes
2 answers
85 views

Grouping expressions by their $O(..)$ rate of growth around 0

Given a list of expressions like $3 x^2,\frac{\sqrt{x}}{\sqrt{2}},\frac{2 \sqrt{x}}{\pi },\frac{9 x^3}{2},x,$, how could I group them based on their rates of growth around 0? IE, $2x$ and $3x$ are ...
Yaroslav Bulatov's user avatar
3 votes
0 answers
46 views

Can we ask Mathematica if a reduction of a system to one scalar equation in one variable+ rational representations of the other variables exists?

Nonlinear determined systems have typically several solutions involving square or higher order roots. Instead of solving them, it may be more profitable to reduce them to smaller systems with fewer ...
florin's user avatar
  • 1,798
3 votes
2 answers
253 views

Decoupling a system of four linear $1$-st order ODEs

I have a system of four $1$-st order ODEs. $$ \dot{p_1} = -2\beta^2 q_1 - \gamma p_1 + \Delta p_2 $$ $$ \dot{p_2} = -2\beta^2 q_2 - \gamma p_2 + \Delta p_1 $$ $$ \dot{q_1} = 2\alpha^2 p_1 + \gamma q_1 ...
Kazi Abu Rousan's user avatar
1 vote
3 answers
154 views

Expanding a complex number

How does one get Mma to expand (1/2 + I/2)/Sqrt[2] into 1/(2 Sqrt[2]) + I/(2 Sqrt[2]) Even evaluating this second expression ...
Mariano Suárez-Álvarez's user avatar
1 vote
1 answer
49 views

Factoring without need to guess the extension

To provide a simple example (but I need more complicated ones): I want to factor x^2-6x*y+y^2. After solving x^2-6x*y+y^2==0 I ...
მამუკა ჯიბლაძე's user avatar
2 votes
1 answer
110 views

Simplifying expression with many radicals

Are there tools in Mathematica to simplify the following expression further, for $0<x<1$? ...
Yaroslav Bulatov's user avatar

1
2 3 4 5
16