Tagged Questions

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

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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 ...
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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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 ...
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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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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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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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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; ...
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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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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 ...
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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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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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] ...
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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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 ...
Consider $f(x)=x^2+1$ and $g(x)=\sqrt{x-1}$. Note that $(f\circ g)(x)=x$ and this checks in Mathematica. ...