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Questions on manipulating complicated expressions and making them look simpler using Simplify, FullSimplify and Reduce.

0
votes
1answer
49 views

FullSimplify not simplifying expression containing the form Sin[n] where n is an integer

I have a function f[n] which give 0 for integer input, but FullSimplify doesn't work for it, why? ...
1
vote
2answers
61 views

Simplify product of complex numbers

I am trying to take product of a complex number with its conjugate. When I take A*Conjugate[A] // FullSimplify The output is as desired ...
0
votes
0answers
25 views

cTensor (xCoba) doesn't simplify my expressions [closed]

As you see below, the final output of the defined covector isn't simplified (the grey box). Anyone familiar with this problem?
1
vote
3answers
36 views

Eliminating radicals from denominator or numerator of an expression

I need to find the limit when r2 tends to r1 of the following expression: ...
4
votes
0answers
69 views

Integrate under assumptions

I am trying to solve the following integral: $$\int_0^\infty u^{\sigma-1} \exp\left[-c u^\sigma\right] \mathrm{d}u$$ under the assumptions $\sigma \in (0,1)$ and $c>0$. I know the result is $$\...
3
votes
4answers
223 views

Alternative form of ArcSin[Sin[x]]

Is it possible to get the following result in Mathematica by using only built-in functions: $$\arcsin( \sin(x)) = x $$ if $x \in [-\pi /2 , \pi/2]$ $$\arcsin ( \sin(x)) = \pi - x $$ if $x \in [\pi /...
0
votes
1answer
55 views

Sum was simplified and I don't know how it was done

I want to compute the sum $\qquad \sum_{i=1}^{n+r}(i+1)n^{i-1}(n+1)^{n+r-i}$ However, when I input the expression ...
1
vote
1answer
48 views

Simplifying elliptic functions

I am working with (long) elliptic functions, which are rational functions in WeierstrassP and WeierstrassPPrime. As expressed in ...
2
votes
0answers
43 views

Simplify (or Reduce) a system of inequalities intelligently

I have the following system of inequalities of 4 real variables 3 (a + b) + 4 (d + c) > 0 && 2 (a - d) + 3 (b - c) > 0 The system can be written as ...
7
votes
2answers
159 views

Issue with Upvalues

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: ...
10
votes
2answers
777 views

Mathematica can't simplify some logarithmic expressions

When I simplify some logarithmic expressions in Mathematica, it just returns the expression ...
0
votes
0answers
36 views

How can I simplify expressions correctly?

the final output of my code gives this expression which i call ttt: ...
0
votes
1answer
60 views

Rewrite $x\sqrt{1-y^2/x^2} = \text{sgn}(x)\sqrt{x^2-y^2}$

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 ...
0
votes
2answers
39 views

Calculate value of expressions based on solution of given linear equations

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: ...
1
vote
1answer
51 views

Simplifying a Sum of Fractions by Removing Fractions in Denominators

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 ...
1
vote
0answers
36 views

How to force the output to be in terms of a specific function?

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}) $:- ...
0
votes
1answer
34 views

How to assume lexicographical ordering

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: ...
0
votes
0answers
55 views

For Fourier Transform with $ x(t) $, how to obtain result in terms of $ X(f) $?

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-...
1
vote
0answers
38 views

Help Simplifying Expressions [closed]

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$} \cosh (\text{$\...
1
vote
0answers
38 views

Simplyfing a quotient of polynomials [closed]

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 ...
0
votes
4answers
66 views

help with simplifying function

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}}+\...
10
votes
3answers
433 views

Remove Abs from Norms of Vectors

I have the following norm Norm[{a, b*c}] (* Sqrt[Abs[a]^2 + Abs[b c]^2] *) How do I remove the Abs from it? ...
1
vote
2answers
60 views
2
votes
3answers
84 views

How can I find the rules I need to simplify my expression?

In a previous post, I simplified 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]) $\...
1
vote
2answers
71 views

FullSimplify of equation that contains Log has no effect (and I think it should)

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 ...
1
vote
1answer
45 views

Eliminating Gamma from result of integration

I think the following integration result can be shown without Gamma. Can anyone explain Why Mathematica Uses Gamma. How to ...
0
votes
0answers
49 views

FullSimplify of Dirac Delta Function failed

I have t1 and t2 whose difference should be 0. But ...
4
votes
1answer
40 views

Simplify behavior: assumption as Interval versus assumption as bounds

I am using MMA V11.2 under Linux I am surprised by this: ...
0
votes
0answers
29 views

Preferences for simplifying

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 ...
7
votes
2answers
69 views

Finding sub-expressions that simplify larger formula

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 ...
8
votes
2answers
153 views

How to simplify this huge expression to get a known smaller expression?

I have the following massive expression ...
0
votes
1answer
62 views

Incorrect results in trig table

I have a table given by Table[ Evaluate[ Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]], {r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0 The ...
6
votes
2answers
80 views

Simplifying boolean algebra without using certain operations

when I use Simplify or FullSimplify in Mathematica it often simplifies it using all the existing boolean operations. For example,...
3
votes
1answer
60 views

Determining the absence of Truth value of an inequality given assumptions

I have a set of assumptions, say, $x > 0$ and $y > 0$. So I specified the $Assumptions = x > 0 && y > 0 Now the inequality $x - y/2 > 0$ ...
5
votes
2answers
58 views
1
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2answers
125 views

Why Mathematica does nothing with the expression Gamma[2 z]? [closed]

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(...
0
votes
1answer
44 views

Simplifying a solution of an equation

I have a linear system, this way: ...
1
vote
1answer
44 views

Make a term appear in my solution

There is a solution for a linear system: ...
0
votes
2answers
115 views

Is $\frac{\log \left(\frac{1}{a}-1\right)+\log \left(-\frac{a}{a-1}\right)}{\log (10)} = 0$? [closed]

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 ...
4
votes
2answers
155 views

Recursively turn expression into nested list

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: ...
1
vote
1answer
38 views

Modify the function `Simplify`

When I use Simplify with equations, the function simplifies both sides of the equation, for example: ...
7
votes
2answers
93 views

Mathematica Not Interpreting Free Parameters Correctly

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 ...
6
votes
1answer
148 views

How to speed up evaluation of expression (multiple variables) to gain speed? Compile?

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. ...
1
vote
0answers
89 views

Simplify rational function with removable singularity

In this example I consider a rational function f ( {n \[Element] Integers, n > 0, v \[Element] Reals, 0 < v < 1} ) ...
0
votes
0answers
29 views

Recurring simplification of a complicated algebraic expression

I intend to simplify the first eigenvalue of a particular matrix since it's an extremely ugly expression. I begin with the following 3x3 matrix ...
0
votes
0answers
70 views

Simplify closed formula for distance-preserving great circle spherical coordinate parametrization

Short version: can the function paramLonLat defined below be simplified given the conditions conds below? Note that the return ...
1
vote
3answers
61 views

Elimination of terms not containing at least one variable from a set

I have an expression with each term therein either containing at least one $n_i \in \left\{ n_1 , n_2 \dots , n_{5} \right\}$ or no $n_i$ at all. I would like to easily eliminate all the terms that ...
1
vote
4answers
68 views

Problem with particular simplification of complex function under assumptions

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 ...
2
votes
0answers
41 views

What is the acceptable error in numerical calculations? [closed]

I am doing a calculation where I try to simplify a very complicated complex function. I did this step by step and I checked that the numerical values that the function gets for certain values of the ...