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

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4
votes
1answer
262 views

Simplifying numerical expressions involving special functions

I've encountered the following problem. There is the identity that the special functions EllipticK[x] and EllipticE[x] satisfy: ...
4
votes
1answer
161 views

Simplifying expressions using rules that span nonconsecutive terms

Suppose there is some function with the property f[x,y] f[y,x^2] / f[x^3,y] == f[2x,y] How can I simplify an arbitrary expression that contains the lhs of the ...
4
votes
2answers
166 views

Assumptions with patterns

I want that Mathematica assumes every symbol like Subscript[s,i] to be evaluate as a real and positive number. I have tried ...
4
votes
1answer
48 views

Simplify complex answer given by DSolve[]

I tried the technique in this question, but that did not work for the solution given by the MWE: DSolve[{f'[t] + f[t]*g[t] == h[t], f[0] == f0}, {f[t]}, t] How ...
4
votes
1answer
69 views

Problem with Simplify, Sqrt, and Set: What's going on?

I am having some trouble getting Mathematica to simplify an expression of the form Sqrt[x]*Sqrt[1/x], where x>0. The problem is that x is assigned to some complicated form by the time Mathematica ...
4
votes
1answer
68 views

TensorReduce not simplifying transpose for symmetric matrix?

I know Mathematica is not very good with symbolic manipulation of matrix expressions, but I was surprised to find that it can't reduce the following expression: ...
4
votes
3answers
77 views

Expand just first level of an expression

Is there a way to build a function to expand just the first level of powers and products of an expression? Edit: ...
4
votes
1answer
225 views

How to find the most compact form of an equation

I would like to know whether there is any general approach to obtain the most compact form of an equation with Mathematica. I used to believe that the ...
4
votes
2answers
113 views

ArcTan[x,y] problems

I need an ArcTan[x,y] function that is continuous in (0,2 π) For the standard ArcTan function: ...
4
votes
2answers
117 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...
4
votes
1answer
166 views

Mathematica rule to express exponentials as multiplication

I'm sorry if this has been asked before, but it is a very simple question and I would imagine it shouldn't be terribly hard for someone that knows to answer. I'm essentially trying to tell ...
4
votes
2answers
130 views

Can one use Map during Expand?

Can one Map a simplifying function to the summands of an Expand before fully expanding the expression in question first? ...
4
votes
1answer
138 views

How can I prevent a polynomial from being simplified?

I'm having a problem with polynomials. Let's say I have a polynomial "2x^2 - 5x + 6 - 3x^2" .. How can I check that this expression is not simplified ? Additionally, I would like to locate the ...
4
votes
2answers
171 views

How to simplify only the lowest level of a nested expression

I have a large expression that takes forever to simplify if I apply FullSimplify[...]. The expression has lots and lots of brackets that luckily already groups ...
4
votes
0answers
116 views

How to get mathematica to simplify a result

I have the following output $\text{Li}_2\left(3-2 \sqrt{2}\right)-4 \text{Li}_2\left(-1+\sqrt{2}\right)$. This turns out to be equivalent to $\displaystyle\log^2(1+\sqrt{2})-\frac{\pi^2}{4}$. How ...
4
votes
0answers
90 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
0answers
90 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
3
votes
3answers
499 views

How to simplify the following trigonometry expression such that the number of used characters is minimal?

How to simplify the following trigonometry expression such that the number of used characters is minimal? (13*Cos[t] - 5*Cos[2*t] - 2*Cos[3*t] - Cos[4*t])/4 The ...
3
votes
2answers
765 views

Eliminate doesn't work in Mathematica

Hello Mathematica users, I have problems trying to eliminate variable $Q(x,y)$ froma PDE, but Mathematica output is just True. The problem is that I already found ...
3
votes
2answers
252 views

Mathematica does not understand (R^3)^(1/3) is the same as R [closed]

In the output from a calculation in mathematica stands a/((R^3*c)^(1/3)), with c and a ...
3
votes
1answer
208 views

Is this a bug in FunctionDomain (V.10)?

I used FunctionDomain[1/(x^3 + 1), x, Complexes] and got 1 + x^3 != 0 Is this a bug in FunctionDomain (V.10)? Can I receive $x \neq -1$, $x \neq ...
3
votes
2answers
239 views

Fullsimplify does not simplify Abs'[1.-a]

I have to simplyfy an expression involving Abs' This works: FullSimplify[Abs'[1 - a], a ∈ Reals] Sign[1 - a] but this ...
3
votes
2answers
133 views

Replace expression, but only “outside” of a function [duplicate]

I have a horrid expression, which is basically a sum of exponents with coefficients. Here's a taste: What I want to do is to replace ks with another expression, ...
3
votes
1answer
668 views

Don't simplify an expression

I have an expression that I want Mathematica to fully expand without any simplification afterwards. I want the output to look like the following example. ...
3
votes
2answers
233 views

What would be the inverse function for the following condition?

I tried the problem but i couldn't take above condition in question in terms of f(x)
3
votes
2answers
117 views

Trying to solve simultaneous equations based on format found on official website [closed]

$\def\1{x_1}\def\2{x_2}\def\3{x_3}\def\f{f(\1,\2,\3)}\def\bs{\bigskip}\def\b{\begin{pmatrix}}\def\e{ ...
3
votes
1answer
174 views

FullSimplify yielding different results in mathematica 8 and 9

I have been experiencing some problems running a certain mathematica file in version 9. I've tracked the problem to a particular sum that I perform. Running the same code in version 8 and 9 I get two ...
3
votes
1answer
641 views

Trace of FullSimplify

I have a symbolic function and I used FullSimplify command to simplify the equation given below. I am calculating it by hand but I couldn't reach the same solution. ...
3
votes
2answers
482 views

Combining and separating sums

How can I combine or separate sums in Mathematica in the way that Together or Expand work for rational expressions? For ...
3
votes
4answers
165 views

Simplify binary expressions

Is it possible for Mathematica to do simplifications for expressions where the variables are binary, such as: a + b = 1 + 2*c => a + b = 1 Here c must be 0 because if it is 1, the RHS is 3 but ...
3
votes
2answers
794 views

Mathematica won't simplify the expression with obvious common factor of a fraction

I have an expression obtain from an integral, which is: Integrate[ϵ^2/Sqrt[(ϵ - u)^2 + Δ^2], ϵ] // FullSimplify The denominator and numerator of the result have ...
3
votes
2answers
104 views

Assumptions within Simplify

I am using the ratio between two error probabilities in various functions. I want Mathematica to display this ratio in the most simple manner. How do I let Mathematica know that, in this case, the ...
3
votes
2answers
147 views

Exploiting a relation among constants

Say I have two arbitrary real constants $p,q$ that satisfy $p^2+q^2=1$. Is there any way to easily declare this relation in Mathematica? Edit More specifically I have this (among others) expression: ...
3
votes
1answer
120 views

Decomposing a complex numbers equation into its real and imaginary part

I have an equation such as: a*z^2 + b*(z - c)^2 == d where z is a complex variable and ...
3
votes
2answers
309 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. Particularly, I define a sum via ...
3
votes
2answers
90 views

Detecting operator Set in Assumptions

Here is a typical issue: Simplify[x + y, x = y] produces 2 True. Is there a way to detect operator ...
3
votes
2answers
320 views

integral, explicit form

I want to estimate the ratio of integrals: $$ \frac{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_1 \left(\frac{4}{T^3}+1\right)}}{\int \frac{4 a T^3}{\frac{4 a T^4}{3}+\Lambda_0 ...
3
votes
3answers
821 views

Non Commutative sorting in Mathematica

I have been trying to do some oscillator algebra in Mathematica and having troubles with sorting and simplifying expressions. I am using the NCAlgebra package which helps to improve the properties of ...
3
votes
2answers
515 views

a problem about simplifing conjugate

the situation is as follows ...
3
votes
2answers
282 views
3
votes
1answer
191 views

Strange behavior of Reduce with a cubic equation

This equation: $(\frac{-a}{x})^2=\sqrt{\frac{1}{x}}$ at $a > 0$ and $x > 0$ has a clear solution $x=a^{4/3}$, doesn't it? However, ...
3
votes
1answer
470 views

How to get rid of all complex numbers and functions?

For almost esthetical reasons, I always have been fascinated by infinite sums of series and I always wonder if theyhave a closed form. A couple of days ago, I found on MSE a question related to the ...
3
votes
1answer
370 views

How to implement Condition programmatically?

I am writing my own symbolic functions with custom symbolic properties. So often I wish to introduce some automatic simplifications or evaluations, which return the same head as it's argument. This ...
3
votes
1answer
330 views

What's the correct method to simplify exponentials?

I have a sum of exponentials that I'd like to simplify. The issue is when I use Simplify, Mathematica loves to factor out one exponential factor. See below: $$e^{-i ...
3
votes
1answer
66 views

Merge Roots of Polynomial

How can I make mathematica "merge" solutions of a polynomial by using $\pm$ instead of listing the two solutions fully with only one sign difference? In particular, I am looking to "compactify" the ...
3
votes
1answer
120 views

Write Integer powers as products

I need to wirte all occasions of (a+b)^3,Ftp^2, Sin[th]^2, ...etc as (a+b)*(a+b)*(a+b), Ftp*Ftp, Sin[th]*Sin[th], ...etc ...
3
votes
2answers
156 views

Mathematica not recognising closed forms as specific values

I have a Mathematica program that outputs a piecewise function, and some parts of the expression are not being recognised as specific numbers when using ...
3
votes
1answer
200 views

Simplify doesn't simplify HypergeometricPFQ with exact arguments

Consider a series: $$\sum_{t=0}^\infty \frac{8^{-11-2t}(22+4t)!}{t!(11+t)!(11+2t)!(32+t)}$$ ...
3
votes
1answer
105 views

Check that a relational expression is true for all complex numbers

How can I use Mathematica to check if a statement like $$\left| \frac{\sqrt{1+2z}-2}{2z-3} \right| \le 1$$ is true for all complex numbers $z$? Also, how can I use Mathematica to check such a ...
3
votes
2answers
376 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 ...