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

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28 views

Pulling out an exponential function from the a general equation

How can I pull out an equation from the general equation of motion of a system in Mathematica ? Actually, I am trying to solve the equation of motion of a spherical shell, therefore, I am trying to ...
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0answers
35 views

How to change the output form of result

If you use Mathematica to do this integral: Integrate[1/(x^2 - a^2), x] you will get a uncommon function form like ...
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1answer
47 views

solve equation with integer maximum [closed]

how to solve with Mathematica a)$ \left [\kern-0.10em\left[ 5 x \right]\kern-0.15em\right] = 2x+1$ b) $ \left [\kern-0.10em\left[1/ 5 x \right]\kern-0.15em\right] > 2x+1$ EDIT = double ...
5
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1answer
102 views

Trouble factoring an expression

I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
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0answers
65 views

Interpretation of a function

I know this is not great, as far as a question, but I came across this function, ...
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6answers
405 views

Rewrite a real polynomial in real (but only linear and quadratic) factors

According to my calculus book: "Every real polynomial can be factored into a product of real (possibly repeated) linear factors and real (also possibly repeated) quadratic factors having no real zeros....
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1answer
165 views

How to extract all the coefficients of a homogeneous polynomial [duplicate]

Suppose p is a homogeneous polynomial in four variables, say p = x^10 y^10 z^5 w^5 + 3 a x^10 w^20; ...
2
votes
3answers
100 views

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 ...
2
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2answers
76 views

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 ...
3
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1answer
90 views

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 ...
5
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1answer
264 views

Finding an analytic solution of a cubic equation

I have been trying to solve a cubic equation $$y=zy^3 + z$$ in $y$ – that is, my desired result is a function $y(z)$ satisfying the equation. Now, there are three solutions of this equation and ...
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0answers
35 views

collect does not work with fraction

The third line in the following code does what I want, the second simply does nothing. Why is that? Is there an option I am missing to make a simple collect behave like the third line or - even better ...
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1answer
62 views

How do you collect trigonometric functions in a polynomial?

I have an expression that has various forms of Sin and Cos and I want to collect them specifically so that I can make substitutions. As you can see I cannot figure out how to separate i Cos[theta] ...
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2answers
172 views

Conjugate[a/b + c/d]

Trying to obtain the result of Conjugate[a/b+c/d] only gives the same result. As such, I use Refine as: ...
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0answers
33 views

How to solve a quadratic inequality containing parameters?

I have the following inequality to solve for $R$ in terms of $\delta$ and $n$, with assumption that $n \geq 3$ and $\delta>0$: $$-2 < 2 -\frac{16n\delta^{2}}{R^{2}\sin^{2}\frac{\pi}{n}} \left(...
0
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1answer
128 views

Unexpected result from InverseFunction [closed]

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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1answer
27 views

Making multi-linear polynomial change of variables (simplifications) by updating `replacementFunction`

This is an evolution of one of my previous questions; I've got a partial answer to that question and now have a much cleaner question to ask: Question: What changes to ...
3
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1answer
74 views

Replacing patterns (determinants) in a rational multivariate function and/or getting `replacementFunction` to work on a multi-linear expression

Given a rational multivariate function known to contain determinants, what is the best way to rewrite the function in terms of the determinants? A simple example: ...
4
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1answer
197 views

How do I use “Factor” to get this form

Here is the default answer. However, I want to get the result which looks like this Here is the Mathematica code: ...
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1answer
54 views

how to use Expand command efficiently

Recently I got in a problem and I will try to explain with a simple example. I have an expression which reads : y = (10 + 2*x )/x; Now I want to substitute 1/x ->...
2
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3answers
924 views

Partial fraction decomposition of $1/(e^x-1)$

This link has discussion on finding partial fraction decomposition of $1/(e^x-1)$, so I experimented with Mathematica to see if M can do it, but looks like not. Similar is the case with one more CAS I ...
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1answer
69 views

generating random algebraic matrix using elementary operations

I generate several algebraic matrices of 12x12 where each element is a combination no repeat of the variables x, y, z and operations +, -, *, /, power, establishment (square root), any of them or any ...
9
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1answer
521 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
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1answer
22 views

build absolute value equations know solution [closed]

We have absolute value equations with unknown coefficients: |x + a| = b and we know solutions: x = 11 and x = 5 We need ...
8
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2answers
334 views

Lagrangian to Hamiltonian

I want to go from Lagrangian description to Hamiltonian one. Using the example given by Mathematica I do something like: ...
4
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1answer
134 views

Expand power of a polynomial

I'm very new to Mathematica, so excuse my innocence. I have the following expression: $$ \left( \sum_{n=0}^r \frac{(-1)^n}{n!} y^n \right)^f $$ I would like Mathematica to expand out the expression ...
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5answers
139 views

How find constant term of quadratic with square already completed?

Suppose I have a quadratic polynomial in two variables x and y in which the squares with respect to ...
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0answers
34 views

ApartSquareFree function

I have a doubt concerning the ApartSquareFree function in Mathematica. Roughly speaking, it is supposed to compute the partial fraction decomposition of a rational function $h/g$ with the denominators ...
4
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1answer
86 views
3
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1answer
80 views

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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1answer
46 views

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 $\...
2
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0answers
45 views

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? $$...
3
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1answer
55 views

Collecting the Log Problem

I have been having tremendous success with my students due to the following idea: ...
1
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1answer
79 views

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 ...
1
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1answer
62 views

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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1answer
42 views

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 $f(x,y,...
3
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0answers
89 views

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 ...
7
votes
5answers
279 views

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 me....
14
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4answers
3k views

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 ...
10
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1answer
203 views

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 ...
3
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1answer
58 views

How to gather terms into Elementary Symmetric Polynomials?

I would like to gather the terms of this polynomial (and much higher order ones): $$q = 1-3 c+c^2+p[1]-2 c p[1]+p[2]-2 c p[2]+p[1] p[2]-c p[1] p[2]+p[3]-2 c p[3]+p[1] p[3]-c p[1] p[3]+p[2] p[3]-c p[2]...
0
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1answer
51 views

Simple grouping equations [closed]

I'm new in the Mathematica world. A very basic question. I have been using the command Eliminate on a set of equations as follow: ...
0
votes
1answer
59 views

Eliminate variable on multiple equations [closed]

I'm pretty new with Mathematica. I have to perform a really simple operation, but I'm really struggling with that. I have a set of 4 equations, for example (they can also be more complex): $ AA = 2 ...
4
votes
1answer
92 views

Pertubation series of given equations

I would like to define a function that does the following. If I have an equation, for example: $$f(x)+[1-f^2(x)]+f^{\prime\prime}(x)+f(x)\ f^\prime(x)=0$$ and I am given a value for $f$ to expand ...
0
votes
1answer
57 views

Dividing out any constant factor from expression [closed]

How do I divide out any constants from an expression? Let's say: $2A+4B+2C+6 \rightarrow A+2B+C+3$ What's the right command for this? I have been using ...
4
votes
2answers
162 views

Find condition under which variables fall away

I have a somewhat lengthy expression, looking like expr = 1 + x + b + Pi + 2*a Is there some way of generating a relationship between ...
6
votes
4answers
129 views

Forcing Mathematica to Output $1/\sqrt2$ as $\sqrt2/2$

I am trying to force Mathematica to output $\frac{1}{\sqrt2}$ as $\frac{\sqrt2}{2}$. I tried: {1, Sqrt[2]}*Sqrt[2] Which outputs: ...
5
votes
4answers
126 views

Solving an equation with rational expressions (step by step) [duplicate]

Consider the following equation with rational expressions: $$\frac{5}{x+4}=4+\frac{3}{x-2}$$ We will look at the plot. We will use the Solve command to check our answer. ...