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
How to force an expression to be shown in terms of a specific function?
I have an integral inte1 as below:
...
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
How do I separate 2 variables to be independent from each other in the equation?
I have an equation namely
...
0
votes
0answers
49 views
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
How to force DSolve to return ODE solution in terms of BesselK instead of BesselY
I'm trying to solve the following problem:
...
1
vote
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
1
vote
1answer
44 views
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 ...
