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

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5
votes
2answers
113 views

Rewriting expression in terms of factor

I have two expressions: expr = (a - R)^2 (a + 2 R)/(2 R^3); factor = 1 - a^2/R^2; I would like to write expr in terms of <...
5
votes
1answer
205 views

Simplifying a b = 1 in non-commutative products?

Yesterday, I try to define some rules for non-communicative multiplication, here. I find some quite helpful rules, but things still do not work properly; the distributive rule can't be applied (e.g.: <...
5
votes
2answers
177 views

FullSimplify inconsistent

I'm having problems using FullSimplify to simplify a differential equation. The expression is simplifying just as I would like when I express a variable ...
5
votes
1answer
224 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...
5
votes
2answers
238 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 ...
5
votes
1answer
182 views

Restrict Mathematica command to what is inside parentheses

I have a bunch of expressions like this one: $\frac{e^{-\frac{7 J}{2 k T}} \left(2 e^{-\frac{2 g H \mu _B}{k T}}+e^{-\frac{g H \mu _B}{k T}}-e^{\frac{g H \mu _B}{k T}}-2 e^{\frac{2 g H \mu _B}{k T}...
5
votes
1answer
253 views

Is there a way to track the Simplify process?

Is there any way to track how Mathematica actually performs Simplify, so that we can see what those "Automatic" transformation functions it applies are and how it ...
5
votes
3answers
458 views

Running out of variables

I am running symbolic calculations with Mathematica. Simplification of algebraic expressions is an important part of them as very often final results can be simplified considerably. Typically my ...
5
votes
1answer
94 views

Simplify with a condition

I have an expression, $-a (u + a v)$, and I would like to simplify it using the fact that $a^2 = 1$. I have tried Simplify[Expand[-a (u + a v)], a^2 == 1] but ...
5
votes
3answers
123 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: $$\text{ExpandUpToLevel}\left[\left(\left(x^2+1\right)^2+1\right)^2,1\right]=\left(x^...
5
votes
1answer
363 views

Using Hold correctly with Simplify and ComplexityFunction

It seems like Mathematica immediately evaluates the expression Sqrt@I to (-1)^(1/4). I'm trying to use ...
5
votes
1answer
68 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 ...
5
votes
1answer
102 views

Trouble factoring an expression

I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
5
votes
1answer
216 views

Why does Mathematica not simplify this expression?

Consider this simple example: ...
5
votes
1answer
158 views

How to apply tags to expression terms?

I often see on this site and at the mathgroup the repeated questions on how to rearrange expression that Mathematica "likes" to keep in one form, but the user prefers in another. Consider this trivial ...
5
votes
1answer
101 views

How to tell Mathematica to avoid simplification of product of exponentials with the same base?

There has been a similar question, but it doesn't solve my problem. I have this input: var = Exp[a] Exp[b] And the output is ...
5
votes
0answers
53 views

External and internal Assumptions on `PiecewiseExpand` and `Mod`

After this question I'm intrigued about the different behaviors depending where and how the assumptions are given. ...
5
votes
0answers
149 views

Better way to compute triple (or higher order) convolution

I have an identity that I want to verify: $$\sum_{i+j+k\ge 2}\binom{n}{i,j,k}{B_{N,i}B_{N,j}B_{N,k}}=\left(\frac{2N^2+n^2-3nN}{2N^2}\right)B_{N,n}+\left(\frac{3n^2-2n-4nN}{2N^2}\right)B_{N,n-1}+\...
5
votes
2answers
192 views

Simplification due to recognition of dummy indices in sums?

Today I noticed something weird concerning implicit sums. Apparently, Mathematica cannot recognize dummy indices as such and simplify accordingly. Consider: ...
5
votes
0answers
163 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
2answers
425 views

How can I simplify $\log(512)$ to $9\log(2)$?

Can you explain me about the result of Integrate. ...
4
votes
3answers
197 views

Output to preserve dot product

I am fairly new to Mathematica and I am faced with a problem. I tried to search for the solution but it seems that I don't know how to formulate the short search request. I need to perform a matrix ...
4
votes
4answers
604 views

Simplifying just parts of an expression

I'm having trouble with the simplifications of certain expressions. A typical example of this is the following (all my variables are positive real numbers): ...
4
votes
4answers
1k views

Simplifying a trigonometric expression

I'm sure this has been addressed before, but I can't find it! I want Mathematica to simplify Sqrt[1 - Sin[π/6 - θ]^2] to ...
4
votes
3answers
413 views

How to transform power of -1 into exponential [duplicate]

After FullSimplify, Mathematica usally gives some coefficients like ((-1)^(1/5)) But I don't want this form, I want ...
4
votes
2answers
268 views

Simplifying If statements

How can I get Mathematica to simplify the true and false clauses for If[] statements? For example: bar[a_] := a FullSimplify[If[a > b, bar[a], bar[b]]] ...
4
votes
1answer
89 views

Simplify $\tan(\arctan(a) - \arctan(b))$

I want to simplify the expression $\tan(\arctan(a) - \arctan(b))$ to $\tfrac{a-b}{1+a\cdot b}$ (if $b \neq - \tfrac{1}{a}$). Right now, the output of ...
4
votes
2answers
482 views

Force a negative square root to be interpreted as an I

I have expressions like $$\sqrt{-\sqrt{1+x^2}} $$ how can I force mathematica to systematically rewrite this as $$i(1+x^2)^{1/4} \quad ? $$
4
votes
2answers
185 views

HornerForm of polynomials in terms of E^(i x)

I want to know how to get the HornerForm of the following expression in terms of E^(I x): ...
4
votes
2answers
367 views

How to expand all portions of an expression?

Consider a toy expression: expr = Sin[x (a + b)]/(y (z + c)) I would like to expand all parentheses to get something like: ...
4
votes
1answer
144 views

Simplify sum of complex logs to single real log

Sometimes, mathematica likes to give me complex results when, e.g, integrating a real valued function. The result might be something like ...
4
votes
1answer
425 views
4
votes
2answers
441 views

Why doesn't FullSimplify simplify expressions with DiracDelta?

I want to simplify a complicated expression with some Dirac delta distributions, but FullSimplify does not do what I want. Specifically, I want ...
4
votes
1answer
789 views

Does the Im function work with symbolic arguments?

Does the Im function work with symbolic arguments? ...
4
votes
2answers
87 views
4
votes
1answer
561 views

Can I check if an expression is positive using assumptions?

I have the following notebook: ...
4
votes
2answers
1k 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 ...
4
votes
2answers
193 views

Why Refine does not simplify Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] to $(-1)^{i+j+k}$?

I am obtaining in Mathematica: Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] We know that for $i, j, k$ being positive integers this expression after simplification ...
4
votes
1answer
237 views

Can't simplify Abs[a*Cos[x]]^2

Why doesn't FullSimplify[ Abs[a*Cos[x]]^2, Assumptions -> {{a, x} ∈ Reals}] simplify to (a*Cos[x])^2 but this query <...
4
votes
2answers
599 views

Simplifying expressions involving Sum

I am trying to use Mathematica to simplify a symbolic expression involving Sum. The expression is defined as follows: ...
4
votes
4answers
228 views

Another confusion with simplify

After reading some of the questions concerning Simplify, I still didn't find a solution to my confusion. I want Mathematica to simplify ...
4
votes
1answer
290 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
4
votes
1answer
349 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 ...
4
votes
2answers
140 views

Symmetrise a complicated expression

I am calculating the derivatives of a symmetric function $F(a_1, a_2)$ and got very complicated expressions, which I'd like to write in a symmetric form with respect to $1 \leftrightarrow 2$ (clearly ...
4
votes
1answer
93 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 ...
4
votes
1answer
222 views

Simplifying conditional expressions using assumptions does not work

I have a conditional expression f[x_] := x /; x ∈ Reals This works fine for normal numbers and symbols, e.g. ...
4
votes
1answer
314 views

Mathematica doesn't simplify a simple expression

The question is simple as that. I have: ...
4
votes
2answers
195 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 FullSimplify...
4
votes
2answers
176 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: ...
4
votes
1answer
397 views

Simplify doesn't simplify HypergeometricPFQ with exact arguments

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