# Tagged Questions

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

46 views

### solve equation with integer maximum [on hold]

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 ...
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 <...
65 views

### Interpretation of a function

I know this is not great, as far as a question, but I came across this function, ...
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....
162 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; ...
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 ...
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 ...
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 ...
263 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 ...
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 ...
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] ...
169 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: ...
33 views

55 views

### Collecting the Log Problem

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

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 $f(x,y,... 0answers 89 views ### How to force Series[] to compute expansions by considering non commutative multiplication? I wish to compute the Taylor series expansion of the following iteration method$x_{k+1}=x_k-f'(x_k)^{-1}f(x_k)$up to four terms of error ($e_k=x_k-\alpha$). When this is a scalar iteration, I very ... 1answer 255 views ### Complicated symbolic coefficient slows down equation solving Here's a simple example for Solve: ... 5answers 278 views ### How can I group constants/parameters using Mathematica? I am trying to solve a problem which may seem quite simple, although I have been unable to find any solution in the documentation or discussion forums. I am not a mathematician, so please bare with me.... 4answers 3k views ### Is it possible to have Mathematica move all terms to one side of an inequality? I have an inequality expression that I would like to express in terms of the relation of the parameters to zero. More simply, I want to have mathematica move all the terms to one side of the ... 1answer 202 views ### How does Mathematica calculate$\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 ...