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Questions tagged [algebraic-manipulation]

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

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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
111 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
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0 votes
1 answer
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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
435 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
31 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
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2 votes
0 answers
58 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
99 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
247 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
173 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
197 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
  • 1,667
7 votes
4 answers
362 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
40 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
67 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
106 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
  • 1,846
4 votes
3 answers
182 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
86 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
43 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
  • 533
5 votes
1 answer
436 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
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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
161 views

Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
Dotman's user avatar
  • 424
0 votes
1 answer
130 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
48 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
337 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
  • 17.5k
1 vote
3 answers
121 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
  • 17.5k
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
72 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
240 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
156 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
  • 725
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
  • 144k
1 vote
1 answer
32 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
103 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
234 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
150 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
0 votes
1 answer
56 views

What's a good way to do specific algebraic operations on an expression?

This is the first time I've submitted a question so please forgive my inexperience. I want to simplify the following expression Cos[ArcTan[Xt/Rt]] which is ...
Pat Lane's user avatar
1 vote
1 answer
91 views

How can I solve/verify the following matrix?

Given $ZFZ’ = C$, I have the following set of symbolic matrices: $Z$ of order $m\times q$ $Z’$ is the transpose of matrix $Z$ of order $q\times m$ $F$ of order $q\times q$ $C$ of order $m\times m$ ...
EVC's user avatar
  • 13
12 votes
5 answers
431 views

How to make an expression manifestly invariant under a symmetry?

Context I would like to have a function which symmetrizes and simplifies a symbolic expression to highlight its internal symmetries. I believe such a function would be extremely useful for post ...
chris's user avatar
  • 23k
2 votes
1 answer
49 views

Replace coefficients with RootApproximant of themselves

I have an expression, not necessarily a polynomial, and want to take all the coefficients on whatever terms there are and replace them with the RootApproximant ...
D. Brown's user avatar
  • 304
2 votes
2 answers
308 views

Is there a Mathematica function that puts a list of numbers in a normalized [1, 10[ scale

I have the following list: ...
Granger Obliviate's user avatar
0 votes
1 answer
91 views

Simplifying expression and arranging terms in power of exponent

I have lots of expressions like below which I want to simplify but I am not sure how to do it in Mathematica. I am looking to simplify them in the form of $\Sigma _i A_i e^{y_i}$ where $A_i$ will be ...
Navneet M's user avatar

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