**1.324 simplifying-expressions questions.**

I want to introduce two variables (I call them EXt and EXtC, where "C" stands for complex conjugate) which would mimic the behavior of a phase of a complex number. For that, I use the following tags:
...

When I simplify some logarithmic expressions in Mathematica, it just returns the expression
...

In a previous post, I simplified the following equationf =
(P ((2 - ϵ) Log[1 - ϵ] + (2 + ϵ) Log[1 + ϵ])) /
((-1 + ϵ) Log[1 - ϵ] - (1 + ϵ) Log[1 + ϵ])$\...

The following equation,f =
(P ((2 - ϵ) Log[1 - ϵ] + (2 + ϵ) Log[1 + ϵ])) /
((-1 + ϵ) Log[1 - ϵ] - (1 + ϵ) Log[1 + ϵ])when fully simplified as
...

I have an integral inte1 as below:
...

the final output of my code gives this expression which i call ttt:
...

I'm trying to coax Mathematica into rewriting $x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2}$ for $x$ and $y$ real. I have tried all combinations of FullSimplify and Refine with the appropriate ...

I have the following problem. Consider expressionf=Sqrt[(x-2y)^2]There is an obvious ambiguity in the definition of f ...

I have these three equations:1/X + 1/Y == 1/15;
1/Y + 1/Z == 1/20;
1/Z + 1/X == 1/25;I want to calculate the value of expression:
...

RSolve yields a large (multi-page) solution (LeafCount=25891) containing a number of 7F6 (and higher) hypergeometric functions when applied to
...

I have a rectangular function rect[t], which is a window function with values of $ 1 $ in the interval $ (-\frac{1}{2},\frac{1}{2}) $:-
...

I have a sum of fractions of the form $x1 - \frac{(x2 + x3)}{(x4 + x5)} - \frac{(x6 + \frac{x7}{x13})}{(x8 - x9 - \frac{x10}{(x11 + x12)})}.$
How might I simplify it to remove fractions from the ...

I have a function $ x(t) $ and I denoted its Fourier transformation as $ X(f) $. I want to get the Fourier transformation of $ x(t)\mathrm e^{2\mathrm i \pi f_0 t} $, and I know the result is $ X(f-...

Suppose I have functions which depends on the symbols $c[I]$, where $I$ is some subset of $\{1,2,...,n\}$.
For example, $$f = c[1] + c[1,2,3] + c[1,2],$$ $$g = c[2] + c[2,1],$$
Code:
...

I have three complicated vectors u, v and w as well as three simple prefactors ...

I'm trying to take a (-1) from a power to 3/2 as this:Simplify[(-(a))^(3/2) - ((-1)^(3/2) (a)^(3/2)), a > 0]I get as a result as expected 0. But when I try ...

In the following expression, how can I group apart the terms in the exponential with a and b coefficients so that I can express ...

I have the following set of equations:
1)
$\text{$b_1$} \cos (\text{$\beta_1$} u)-\text{$b_1$} \cosh (\text{$\beta_1$} u)-\text{$b2$} \cos (\text{$\beta_1$} \theta y)-\text{$d_2$} \cosh (\text{$\...

MMa gave me a complicated result involving Hypergeometric0F1's. It was much less complicated after I discovered this identity:
...

I am computing the 4th order talyor approximation of this function
$$\big(\frac{b}{g-x}\big)^{0.25}$$
The analytic textbook result is:
$$b^{0.25} \big(\frac{1}{g^{0.25}}+\frac{0.25 x}{g^{1.25}}+\...

I am trying to simplify some quotient of polynomials. In this case, they are really easy but I will have to deal with way harder expression and I wanna know how to do it in full generality. An example ...

I have the following massive expression
...

I'm on 11.3.0 for macOS (64-bit).
On a recent CAS-enabled exam question a few weeks ago I was required to evaluate the following integral:
$$
\int_0^5\left(\sqrt[3]{125-x^3}\right)^2\,dx
$$
In ...

I have the following normNorm[{a, b*c}]
(* Sqrt[Abs[a]^2 + Abs[b c]^2] *)How do I remove the Abs from it?
...

I think the following integration result can be shown without Gamma.
Can anyone explain
Why Mathematica Uses Gamma.
How to ...

I have an equation namely
...

I am using MMA V11.2 under Linux
I am surprised by this:
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If I use FullSimplify on a large formula it will consequently return a much smaller expression. However, suppose I notice the simplified expression can benefit from ...

I have a set of assumptions, say, $x > 0$ and $y > 0$.
So I specified the $Assumptions = x > 0 && y > 0Now the inequality $x - y/2 > 0$ ...

I often (always?) find that Mathematica prefers to express $(a-1)^2$ as $(-1+a)^2$, thus "wasting" a character. Moreover, for me, the expression $(a-1)^2$ is more attractive since it doesn't have the ...

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 ...

I have a function that outputs a large expression containing dot products of vectors. None of the vector components are known, so all dot products are symbolic. For instance, part of the output may ...

Following my previous question I have this issue using TensorExpand:KroneckerProduct[x, y].(KroneckerProduct[2 z, w]) // TensorExpandresults in:
...

Any suggestion on how to bring a nested KroneckerProduct form into just one?
I mean some way of converting:
...

when I use Simplify or FullSimplify in Mathematica it often simplifies it using all the existing boolean operations. For example,...

I have a table given byTable[
Evaluate[
Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]],
{r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0The ...

I'm trying to solve the following problem:
...

Could someone tell me why Mathematica just returns the input with this expression:Gamma[2z] Gamma[2 z]
?
I expected this result:
$Γ(2z)=\frac{2^{2z-1}Γ(z)Γ(...

I have a linear system, this way:
...

Forgive me if this has an obvious answer, but I've run into seemingly the same problem in a few different contexts now. When I evaluate expressions using different variables, all of which show up as ...

I have the following function, which for all values of $a$ is exceedlingly close to 0:(Log[-1 + 1/a] + Log[-(a/(-1 + a))])/Log[10] However, it does not ...

I've been trying to write a simple function that turns an expression into a nested list. So for example, a+2b+3c becomes {a,{2,b},{3,c}}. This is what I wrote:
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When I use Simplify with equations, the function simplifies both sides of the equation, for example:
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I obtained some long expression and need to use them with a lot of different parameters inside a simulation. However, evaluation of the expressions is pretty slow, so that I would like to speed it up. ...

I have proven that $expr=(1 - i)(\dfrac{1+z}{1-z})^{1/4}\dfrac{\sqrt{ 1-z^2+i z\sqrt{1 - z^2}}}{1+z-i\sqrt{1 - z^2}}=1$ when it is assumed that $z\in R$ and $|z|<1$ and when I also plot the real ...

- assumptions
- equation-solving
- symbolic
- complex
- trigonometry
- expression-manipulation
- calculus-and-analysis
- algebraic-manipulation
- special-functions
- replacement
- functions
- summation
- series-expansion
- evaluation
- factorization
- differential-equations
- matrix
- polynomials
- bugs
- performance-tuning
- inequalities
- pattern-matching
- linear-algebra
- tensors
- list-manipulation

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