# Tagged Questions

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

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### Why is ToRadicals[] not able to handle all cases? Is there a workaround?

The documentation for the function ToRadicals says: ♦ There are some cases in which expressions involving radicals can in principle be given, but ...
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### HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
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### How to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively?

I would like to replace every possible $A+B$ and $AB$ in expansion of $(A+B)^{10}-A^{10}-B^{10}$ with $x$ and $y$, respectively. How to do it with the simplest code in Mathematica? For example, \...
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### Solving an algebraic equation with one or more constraints? [duplicate]

Just as a simple example, say I wanted to solve Sin[x] == a for x with the constraints -1<=a<=1 and 0 < x < Pi. Is there any way to do this?
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### how to permute bit strings and manipulate their elements

I want to write a function(has 2 paremeter, n=range,k=number of 1 digits) which finds all probable combinatorics of arbitrary bit strings and evaluate sum of tensor ...
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### Unexpected result from InverseFunction [on hold]

Given the following two equivalent inverse functions, why does one simplify (using inverse functions that are acceptable to me) and the other doesn't? Is there an assumption or setting I can give ...
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### Rearranging a simple algebraic equation

Suppose I have a simple algebraic equation like: ChebyshevT[4, p] == 0 1 - 8 p^2 + 8 p^4 == 0 and I want to solve for the ...
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### Why do I get a different answer from the use of TrigExpand?

This is an old post but I get two different answers from Mathematica 9.0.1.0 ...
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See this example : ...
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### Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
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### Trigonometry expansion of a product

The following command does what I want: ...
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### How to neglect higher power terms in a polynomial expression [closed]

I have a polynomial expression of order n (say n=20). F(x)=1+x+x^2+x^3++...x^20. I want to approximate the polynomial for order 3 only. So I need to make the ...
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### Solving Det[matrix] == 0 with an 8 x 8 matrix [closed]

I want to solve the equation Det[matrix] == 0 which came from the consistency of solutions of a set of 8 equations. This matrix has two constants λ and μ and two variables $P$ and $q$. I want to get ...
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### What do the hashtags represent in the result of Solve, and how should I use them? [duplicate]

There is a function that I'm trying to get the inverse of. My function is a simple polynomial: Tn[T_] := 4/9 T^3/Tc^2 + 5/9 T Now I tried to find ...
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### Implementing new algebra for list-like objects [duplicate]

I would like to implement an algebra (addition, multiplication, etc.) for what is called "truncated power series" (TPSA) (Differential Algebraic description of beam dynamics). . These 'objects' (sets ...
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### How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
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### How to check an algebraic number for membership in a list

I need to check an algebraic number for membership in a list of algebraic numbers. The numbers can be expressed in different forms (combinations of radicals, Root ...
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### How to get exact roots of this polynomial?

The equation $$64x^7 -112x^5 -8x^4 +56x^3 +8x^2 -7x - 1 = 0$$ has seven solutions $x = 1$, $x = -\dfrac{1}{2}$ and $x = \cos \dfrac{2n\pi}{11}$, where $n$ runs from $1$ to $5$. With ...
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### How can I convert a complex number into an exponent form

When I have an expression such as (1/4 + I/4) ((1 - 2 I) x + Sqrt[3] y) it is hard to get an intuition of the number. So I want to convert it to the complex ...
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### How can I express an algebraic expression as a product?

I have a simply expression that I can see that I can express as a product. ...