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

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4
votes
1answer
91 views

What options need to be set for Simplify to perform a certain manipulations similar to FullSimplify?

Simplify performs algebraic transformations and is fast, while FullSimplify tries a wide range of transformations involving ...
8
votes
2answers
872 views
0
votes
1answer
222 views

Simplifying square root expressions

I have read lots of questions on square root simplification on MMA, but I haven't really seen my problem posted (or understood a clear way to deal with this issue). I am simplifying some expressions ...
0
votes
1answer
61 views

How can I manipulate a long expression to order it by factors/derivatives of a particular function?

I have a Mathematica notebook that generates a linear expression involving derivatives of a given variable. Expanded (and simplified for our purposes), it looks something like this: \begin{equation} ...
1
vote
0answers
72 views

Inverse Laplace computation Mathematica [closed]

I have a transfer function such as following, which I would like to find its inverse: F=(a*s^2)/(b*s^3+c*s^2+d*s+e) I have a numeric value for a b c d and e but ...
2
votes
1answer
176 views

Simplification of exponential

I would like to understand why FullSimplify doesn't entirely simplify this expression ...
1
vote
0answers
110 views

Summing the probability distribution to 1 to convince myself

I have worked out a probability distribution and want to check its sum which is necessarily 1. First we write $$ r \triangleq \frac{(2 \lambda + \mu)^2}{2(\mu + \lambda)^2}, \quad s \triangleq ...
6
votes
4answers
210 views

Minimizing a function with a constant $l > 0$

I'm VERY new to Mathematica and would like some help with minimizing a function. $$f(x) = \frac{1}{2} \sqrt{\frac{\left(l^4+x^4\right)^2}{l^4 x^2}}$$ I want to find which $x-value$ (probably ...
24
votes
1answer
582 views

A better simplification function

I am creating this question and posting an answer to it as a help for those who have problems with Mathematica simplification oddities that appear in other questions on the site. First of all, there ...
0
votes
0answers
94 views

PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
3
votes
1answer
367 views

Simplify doesn't simplify HypergeometricPFQ with exact arguments

Consider a series: $$\sum_{t=0}^\infty \frac{8^{-11-2t}(22+4t)!}{t!(11+t)!(11+2t)!(32+t)}$$ ...
1
vote
1answer
66 views

What am I missing on this part of the documentation?

In the documentation for FullSimplify, under Options > Assumptions it is stated that: When assumptions are given as an argument, $Assumptions is used as well: ...
2
votes
3answers
131 views

Simplifying Logs assuming arbitrary arguments real and positive

I have some expressions involving Logs which I would like to simplify. Unfortunately FullSimplify doesn't work because it assuming the arguments are general. I have no way of knowing a priori what the ...
4
votes
1answer
135 views

Collect without grouping terms

The built-in function Collect, when applied to more than one variable, will group expressions by the first variable, as here: ...
0
votes
0answers
18 views

Not Simplify automatic some expression(values)

I try to calculate $$\text{res}\left(h(z) (\psi ^{(0)}(z)+\gamma )^2,\{z,-4\}\right)$$ the result is $$\frac{1}{6} \left(6 h'(-4)-25 h(-4)\right)$$ the result it is possible to write as $$2 \left(6 ...
1
vote
1answer
159 views

Is there an easy way to let mathematica print out every Erfc and InverseErfc as F and F^{-1}

Mathematica uses complementary error function and its inverse as functions for example when integral of a Gaussian is taken. Therefore, all output expressions of Mathematica involve Erfc and ...
0
votes
0answers
26 views

Create Linear System from derivatives of variables and solve it [duplicate]

I have the following simply function: f[x_, y_, z_] = (x - A)^2 + (y - B)^2 + (2*z - C)^2 + (5 + z + x - D)^2 + (y - 2 + 2*x)^2 + (y - z + F)^2 I am ...
2
votes
1answer
80 views

Wrong result after Simplify of a complex variable with assumptions satisfying an inequality

Using Mathematica 10,Simplify[a\[Conjugate], Assumptions -> {(a + a\[Conjugate]) > 0}] returns a, i.e. treats ...
4
votes
1answer
336 views

Simplifying numerical expressions involving special functions

I've encountered the following problem. There is the identity (Legendre's relation) that the special functions EllipticK[x] and ...
3
votes
0answers
74 views

simplify expressions into sum function

Is there a way to have Mathematica simplify long expressions involving sums of variables into expressions using a sum function? Suppose I have something like this: ...
2
votes
1answer
80 views

Failure in the use of FullSimplify

My question is about an apparent failure of the function "FullSimplify" to simplify an easy algebraic expression. This is the expression that I ask Mathematica to evaluate: ...
0
votes
0answers
25 views

PolynomialGCD in complex numbers for vector simplification

I wanted to define a function $f(t,\vec{r})=e^{i\omega t-i\vec{k}\cdot\vec{r}}$, and take gradient of it. With, ...
7
votes
4answers
271 views

How do I invoke the default complexity function?

Documentation on ComplexityFunction says: With the default setting ComplexityFunction->Automatic, forms are ranked ...
2
votes
2answers
100 views

Common subexpression elemination of complicated function by nesting using HornerForm and Experimental`OptimizeExpression

I want to have common subexpression elimination of comlicated functions where the elimination is done by factoring out the expressions. The result is not to be digested by a compiler, it should remain ...
27
votes
1answer
3k views

Simplify matrix algebra

I'm trying to simplify some matrix linear algebra, for example, simplify $$\big(a1\times(A1\cdot A2)\big)\cdot\Big(a2\times A3\cdot A4+(a3\times A5)\cdot(a4\times A6)\Big)^{T}$$ where lower case ...
0
votes
2answers
165 views

Simplify large sum of fractions to shortest representation

I appear not to be able to find a way to simplify the sums of fractions like the following example to their shortest representation. For me shorteste representation means, to have as few as possible ...
3
votes
1answer
112 views

How to control cancellations with Simplify functions?

FullSimplify only simplifies the result of the following calculation halfway, leaving a lot of $e^{x^2/v}$ and $e^{m^2/v}$ terms that could have been cancelled: ...
4
votes
2answers
571 views

Replacing gamma at half integers by double factorial

It is well-known that for any positive integer $n$ the equality $\Gamma(n+\frac12)=\sqrt\pi\,(2n-1)!!/2^n$ holds, where $!!$ stands for the double factorial. I am using ...
0
votes
0answers
185 views

Is there a function equivalent to rewrite function in Sympy

Sympy provide rewrite function to rewrite expression in terms of other functions. ...
2
votes
4answers
109 views

how to cancel arbitrary term in fractional formula

I often encounter this kind of problem that I want the fractional formula to be looked like the way I want it to be. For example, this one $$\frac{R^2 \left(g m_1-g m_2\right)}{J+m_1 R^2+m_2 R^2}$$ ...
13
votes
2answers
294 views

Transform an expression to remove the singularity

I have the expression Sin[c x]/c. Clearly it is undefined at $c=0$, but that is merely a removable singularity, since $$\frac{\sin(cx)}c=x\frac{\sin(cx)}{cx}= ...
4
votes
3answers
86 views

Automatically split an expression and use TrigFactor to solve the parts

I want to simplify the following expression: 1/2*(Sqrt[3]*Cos[x]*la - Sin[x]*la - lb + Sqrt[3]*Cos[x+y]*lf - Sin[x+y]*lf) I used ...
5
votes
2answers
222 views

Trigonometric simplification

How can I simplify 1/2 (Sqrt[3] Cos[x] - Sin[x]) in order to get Cos[x + Pi/6] on Mathematica? I saw that Wolfram|Alpha lists ...
0
votes
0answers
54 views

FullSimplify cascades too much/groups variables too eagerly

This is something FullSimplify will give: $$\frac{n (s+\text{s2})-\text{a1} g}{\text{a1} (g-\text{a2} s)+s (s+\text{s1}) (s+\text{s2})}$$ I could find better examples where FullSimplify cascades ...
14
votes
2answers
482 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
0
votes
1answer
82 views

How to shorten/simplify my plotting code

Is there a way to simplify and shorten my code? ...
1
vote
0answers
96 views

Simplification with absolute value

I have a long expression that has absolute values in the exponent. Some parts of the expression would clearly simplify if one assumes that the power is an odd or even integer. When I give one of this ...
3
votes
2answers
244 views

How can Mathematica help me to find a real radical expression for roots of this polynomial?‎

The polynomial $P(x)=x^‎‏4‏‎-‎‏4‏x^‎‏2‏‎-‎‏2‏x+‎‏1$‏‎ has ‎‏4‏‎ real roots (this can be clearly checked by plotting). But solving $P(x)=‎‏0‏‎$, using ...
2
votes
0answers
210 views

Factor out a constant from a matrix [closed]

I've got a matrix in which every entry is of the form x/4. I cant find out how to factor out the 1/4 so that the actual matrix is clearer. Thanks for your help!
2
votes
1answer
167 views

Inverse Laplace Transform difficulty

I am asked to find the inverse Laplace transform of: $$F(s)=\frac{2s^2+s+13}{(s-1)((s+1)^2+4)}$$ I did the partial fraction decomposition by hand and got: $$F(s)=\frac{2}{s-1}-\frac{3}{(s+1)^2+4}$$ ...
1
vote
1answer
383 views

Solving a complex logarithmic equation

I am trying to solve the following equation for $x$, with integer $n$. (1 - ((-1 + x)^E x^(1 - x) Log[x]^-E)^(1/(-1 + E)))/(-1 + x) == n
0
votes
2answers
84 views

How can I put the results of TrigFactor function into a more convenient form?

a1 D11 Cos[n x] + a0 a1 D11 Cos[n x] + 1/2 a1 a3 D11 Cos[n x] + 1/2 a2 a4 D11 Cos[n x] I have a large trigonometric expression. Can I factor out different ...
2
votes
1answer
112 views

Dealing with functional equations

I have the specific function $G$ of $x$ satisfying the functional equation $G^3x=-1+G(1-x)+G^2x$. By using Mathematica, I would like to simplify the following polynomial of $G$ and $x$. $2 G^2 + 6 ...
1
vote
2answers
98 views

How to stop FullSimplify from returning Root objects

I have several expressions in a series, such as 1/4 (-(1/4) + Sqrt[5]/4 + I Sqrt[5/8 + Sqrt[5]/8]) (-1 - Sqrt[5] + 2 Sqrt[7/2 + (5 Sqrt[5])/2]) If I run ...
0
votes
0answers
40 views

How can I put the results of TrigReduce function into a more convenient form? [duplicate]

a1 D11 Cos[n x] + a0 a1 D11 Cos[n x] + 1/2 a1 a3 D11 Cos[n x] + 1/2 a2 a4 D11 Cos[n x] .......for example this expression can be written like ('expression') * ...
0
votes
0answers
65 views

Pulling out terms from an expression

I have an expression that is in a really complicated form but I know can be written like this: F[X,Y] = AX^2+BY^2+CXY where A,B, and C are complicated terms, but split up F[x,y] into a more ...
3
votes
2answers
158 views

How to simplify exponents of the form $\exp\left(i\frac{2\pi}{N}(N+1)\right)$ inside a function

I'm really annoyed with Mathematica and I need your help. I defined a discrete Fourier-Transformation(I use II instead of N, because Mathematica wont let me-.-): ...
-2
votes
1answer
342 views

I don't want Erf[x]

I would much rather have the expression remain as an integral rather than have Mathematica convert it into $\mathrm{erf}$. Is this possible? I always end up differentiating the $\mathrm{erf}$ ...