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

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5
votes
3answers
1k views

How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
0
votes
1answer
51 views

Expanding a function with trigonometric expressions in a controlled manner by excluding addition identities

I want to simplify a nonlinear equation with trigonometric terms. After I've expanded I don't want to loose open terms to Trigonometric Addition Formulas ...
7
votes
2answers
110 views

Simplify expression to Integer

I have the following function: f[n_]:=(n-1) E Gamma[n,1]; I know that this expression always evaluates to an Integer, but Mathematica doesn't always output the ...
1
vote
0answers
59 views

How to remove parts of an expression

I have an expression where terms Transpose[R].R appear. R is a matrix with the property Transpose[R].R=IdentityMatrix[3]. How ...
3
votes
1answer
110 views

Simplify a huge expression with limited memory

I would like to perform some analytical sums such as the following ...
0
votes
1answer
64 views

How to simplify a quotient with exponents (using power rules)

I'm trying to simplify the following expression (b (1 - x)^n (-1 + x)^-n (-1 + x - w x)^n)/(n (-1 + w) (1 - x + w x)). All parameters and the variable x should ...
-2
votes
1answer
42 views

How can I simplify this simple formula? [closed]

:) If we have x+(x*l), is it possible to simplify this, on having only one single x?
0
votes
0answers
40 views

How to print intermediate steps of simplifying a power formula? [duplicate]

To answer the question of proving Fibonacci sequence is periodic mod 5 without using induction., I came across Mathematica to prove $$F_{n}\equiv F_{n+20}\pmod 5$$ for all $n \geq 2$ I defined: ...
2
votes
3answers
159 views

Question on alternate forms of polynomial output

EDIT: Would it be possible to do something like let $y=ax+b$ then use Collect[] or Apart[] on the new expression? How would I go about this. I've tried using Collect[%,ax+b], Collect[%,{ax+b}], and ...
14
votes
1answer
298 views

What's wrong with Simplify and FullSimplify?

I have a quite complex list of equations and inequalities I combine to a boundary condition for my cost function. After investigation of two days I found the bug (I really name it a bug!). One of my ...
4
votes
1answer
92 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 ...
0
votes
1answer
62 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 ...
12
votes
1answer
219 views

Using Simplify on a consistent system returns False

Bug introduced in 8.0 and fixed in 10.3. It's late, but am I missing something here? Why should two independent equations, which together are consistent, ...
2
votes
1answer
178 views

Simplification of exponential

I would like to understand why FullSimplify doesn't entirely simplify this expression ...
0
votes
0answers
95 views

PolyLog does not simplify

How come mathematica can not simplify a simple expression involving the PolyLog function? An example is: You know that ...
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
146 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 ...
0
votes
0answers
19 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 ...
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 ...
4
votes
1answer
140 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: ...
2
votes
1answer
81 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 ...
3
votes
0answers
76 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
81 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
26 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, ...
3
votes
1answer
113 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: ...
0
votes
0answers
194 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
2answers
101 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 ...
0
votes
2answers
170 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 ...
1
vote
1answer
90 views

Equation simplification

Given that: ...
1
vote
1answer
82 views

How to reduce trigonometric expressions under special conditions

For the following problems I used "FullSimplify" and "TrigReduce" but I manage to reduce more by hand. ...
4
votes
3answers
87 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
229 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 ...
1
vote
0answers
100 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 ...
0
votes
1answer
82 views

How to shorten/simplify my plotting code

Is there a way to simplify and shorten my code? ...
24
votes
1answer
588 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 ...
2
votes
0answers
227 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!
1
vote
1answer
396 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
6
votes
1answer
86 views

How to simplify expressions by closing open inequalities?

Recently I have often acquired results which consist of combinations of 0, 1 and 2-dimensional (in)equalities. For instance, consider a very simple case with ineq1 ...
2
votes
4answers
114 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 $$\frac{R^2 \left(g m_1-g m_2\right)}{J+m_1 R^2+m_2 R^2}$$ ...
2
votes
1answer
121 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 ...
25
votes
4answers
410 views

FullSimplify wrongly reduces expression to zero

Bug introduced in 9.0 and persisting through 10.4 I get the following output with a fresh Mathematica (ver 10.0.2.0 on Mac) session ...
1
vote
2answers
100 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
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 ...
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') * ...
3
votes
2answers
160 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
171 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: $$F(s)=\frac{2}{s-1}-\frac{3}{(s+1)^2+4}$$ ...
-2
votes
1answer
347 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 $\mathrm{erf}$ ...