# Tagged Questions

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

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### expressing a rising factorial as a polynomial

I have an equation in $x$ as follows: $f(x)=\prod\limits_{j=0}^{k}(j+x)=x(1+x)(2+x)\cdots(k+x)$ I want to express this as a polynomial in $x$, i.e., as $a_0x^0+a_1x^1+\cdots+a_kx^k$ I tried doing ...
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### Replace pattern for exponentials

Ultimately, I want to replace every Exp[(const) w[i,j]] to T[i,j] and Exp[-(const) w[i,j]] to 1/T[i,j] in the following expression ...
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### Rearrange an expression according to known items

I have this expresion: $\qquad q_{aft}=-i\,f \left(a_2\right){}^{\dagger }+i\,f \left(a_2\right){}^{\dagger }-\left(a_1\right){}^{\dagger }-a_1$ Defining $\qquad q_{0_1}=a_1+(a_1)^\dagger$ and ...
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### Expanding rational functions with minimal denominator

I'm working with rational functions and I want to be able to put them in a specific form and then get a list of terms in which the numerators are monomials. Take for example ...
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### Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
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### Performance of Apart with complex numbers

Consider the following code ...
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### How to remove parentheses from algebraic expression? [closed]

Suppose I have an expression like $x+x+y(x+y(x+y))$. I used Simplify command and get $y^3+x(2+y+y^2)$. How to remove parentheses to get every summand explicitly? ...
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### Collecting the Log Problem

I have been having tremendous success with my students due to the following idea: ...
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### Deriving the Fourier Coefficients Formulas with a Manual Procedure

I already know that there are built-in functions to compute the Fourier coefficients but I want to derive their formulas manually. In fact, I want to obtain the final well-known formulas for the ...
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### Working with Function Domain

Consider $f(x)=x^2+1$ and $g(x)=\sqrt{x-1}$. Note that $(f\circ g)(x)=x$ and this checks in Mathematica. ...
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### Collection prefactors of arbitrary functions

I generated a very lengthy expression in Mathematica which can be written in the form $f(x,y,z)\log(x-y+z) + g(x,y,z)\log(x+y+z) + h(x,y)\log(x+y-z)$ etc. I would like to collect the functions ...
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### How to force Series[] to compute expansions by considering non commutative multiplication?

I wish to compute the Taylor series expansion of the following iteration method $x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$ up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ...
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### Complicated symbolic coefficient slows down equation solving

Here's a simple example for Solve: ...
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### How can I group constants/parameters using Mathematica?

I am trying to solve a problem which may seem quite simple, although I have been unable to find any solution in the documentation or discussion forums. I am not a mathematician, so please bare with ...
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### Is it possible to have Mathematica move all terms to one side of an inequality?

I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ...
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### How does Mathematica calculate $\sin(\pi/5)$?

Consider: Sin[Pi/5] which returns: $$\sqrt{\frac58-\frac{\sqrt5}{8}}$$ Does anyone know how to figure out the trigonometric identities used by Mathematica to ...
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### How to make algebraic substitutions?

I would like to simplify complicated expressions by defining some variable that is a combination of other variables that appear in the expression, but without eliminating the original variables. As a ...
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### How to transform a noncommutative product to a different expression?

I have a (long) sum of the following ** (noncommutative) products: gg**qs**rh (each variable always consists of two letters like in the artificial example ...
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### Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
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### How to reorder and combine terms in a polynomial with multi-variables?

I have a polynomial with the coefficients of {a1, b1, b2} ...
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### “Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
I have a polynomial quotient $$\frac{1-z+z^4}{(1-z)^2}$$ that I want to write in the form $$\frac{g(z)}{(1 - z) (1 - z^4) (1 - z^5) (1 - z^6) (1 - z^7)}.$$ However, every time I try some combination ...