# 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 ...
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### 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. ...
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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', ...
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### 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 ...
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1 vote
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### 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, <...
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### 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 ...
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### 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 ...
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### How to factorize high-order polynomials that have only complex roots?

I have polynomials like this: ...
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 $x4c + x^26c$ .
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 ...
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### 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, ...
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1 vote
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### Simplify argument of Logs

I have the following expression ...
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### 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, ...
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### 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 ...
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### 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 ...
• 215
1 vote
161 views

### Converting expression to quadratic formula

I want to manipulate and represent the following expression in a more presentable way. ...
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130 views

### Kernel Crash Using Solve

The following code crashes the Kernel with no error message. ...
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### On MacOs, I cannot use Needs["QDENSITYQdensity"]

I am trying to get Needs["QDENSITYQdensity"] from (https://library.wolfram.com/infocenter/MathSource/5715/), however, it failed and I get this error: ...
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 ...
• 17.5k
1 vote
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 ...
• 17.5k
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 ...