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

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0
votes
1answer
104 views

How to re-express solution to system of equations after truncating the solution at a given order to give an exact answer

I have a simple enough system of two equations that need to be inverted: ...
3
votes
1answer
125 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
4
votes
0answers
117 views

Better way to compute triple (or higher order) convolution

I have an identity that I want to verify: $$\sum_{i+j+k\ge ...
23
votes
1answer
2k views

A one line proof that one is zero using Mathematica 10

a = (Sqrt[2] + 1) (Sqrt[2] - 1) - 1; {a/a, Simplify[a]/a, b/b == Simplify[b]/b} {1, 0, True} This one line "proof" that ...
3
votes
1answer
81 views

Integrate[] does not work when the function has an antiderivative function

This function (1 + (1 + 1/(2*Sqrt[x]))/(2*Sqrt[Sqrt[x] + x]))/(2*Sqrt[x + Sqrt[Sqrt[x] + x]]) has the antiderivative function, since ...
2
votes
2answers
99 views

Parabola plotting tangential to x = const, and y= const

ContourPlot[ pm Sqrt[x - a] + pm Sqrt[y - b] == Sqrt[c], {x, 0, 2 a}, {y, 0,2 b}] plots a parabola, but only a part between points of tangency (a, 0) and (0, ...
1
vote
2answers
131 views

Simplifying an expression given a known variable relation

I am wondering if there is a way to simplify an algebraic expression given a known variable equation using Mathematica. For instance, I wish to simplify an expression for the heat change in a process: ...
0
votes
1answer
103 views

What does the expression “Total[funca[a,#] & /@ #] & /@ {x,y}” possibly mean?

Can the expression be simplified as "Total[funca[a,#]] & /@ {x,y}"? What does the double of "& /@" mean? Where can I find some reference? Updated According to Mr.Wizard's answer, I now know ...
0
votes
0answers
61 views

How to control factor gathering in Simplify

To make my results more readable, I need to make MMA gather terms differently. In this example, Simplify gathers terms by common z[]: ...
1
vote
1answer
144 views

Why Abs[Infinity] is an element of the real numbers

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
5
votes
3answers
106 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: ...
0
votes
1answer
165 views
0
votes
0answers
66 views

Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
4
votes
2answers
150 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 ...
0
votes
1answer
50 views

Why don't these assumptions result in further simplification?

I'm trying to simplify an expression, which has a factor of $\lambda(\lambda-1)$, where $\lambda$ may be either $1$, or $0$. So I try: ...
2
votes
1answer
58 views

Is there a simple function identify the sign of an expression given constraints

I'm looking to find a simple function that can identify the sign of an expression given a set of constraints. I have looked around and do see that there is a few threads on this but I'm not sure I ...
2
votes
1answer
135 views

How can I simplify this implicit equation to an explicit equation

How can I simplify this implicit equation to an explicit equation: Tan[5 y/12] - (7 y/((x)^2 + (y)^2 - (3.5)^2)) == 0 i.e: $y=f(x)$ where $y$ is a explicit ...
1
vote
2answers
85 views

Convert imaginary exponentials to goniometric expressions?

Can I force Mathematica to re-express something like $$\left\{\frac{1}{2}i\left(\frac{1}{16} e^{-2 i (\alpha (1)+4 \alpha (2))} \left(-1+e^{8 i \alpha (2)}\right) \text{d$\alpha $}(1) \left(2 \left(2 ...
0
votes
1answer
46 views

Simplifying a fraction with bringing in new variables

Let's say I have a fraction like this: (a b x^2 + a^3 x) / (a^2 b x) and I would like to simplify it by multiplying both the numerator and the denominator with ...
1
vote
2answers
272 views

How do I check to see if two expressions are equal?

This is what I am trying: (2 x - 2 Sqrt[x (x - v)] - v)/(2 x + 2 Sqrt[x (x - v)] - v) == (Sqrt[x] - Sqrt[x - v])^4/v^2 but it's not working. Can someone tell me ...
1
vote
1answer
51 views

simplifying the range of two definite integrals

Today, I tried to obtain the solution of the following equation, sol = DSolve[ {m v'[t] + \[Gamma] v[t] == \[Xi][t] , v[0] == v0}, v[t], t] The solution, of ...
4
votes
2answers
335 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 ...
1
vote
1answer
194 views

Rationalize complex numbers

What is the best way to rationalize complex numbers, if not both the real and imaginary part are actually rational? According to the documentation, Rationalize ...
1
vote
2answers
66 views

Simplification assumptions strange behavior

I am trying to cancel common factors under square roots in some expression with all positive real variables: $$\text{Simplify}\left[\frac{\left(3+\sqrt{6}\right) \sqrt{g} \text{nn}^4}{2 ...
5
votes
2answers
415 views

Simplifying general solutions of differential equations (driven harmonic oscillator)

Solving general differential equations in Mathematica usually leads to somewhat unsightly results. As an example, consider the solution of the driven, damped harmonic oscillator: ...
5
votes
2answers
162 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: ...
4
votes
1answer
290 views

Mathematica doesn't simplify a simple expression

The question is simple as that. I have: ...
3
votes
0answers
58 views

Derive logistic choice probabilities symbolically

More generally, I am interested in learning what the current limitations of Mathematica are when using it for doing pure mathematics. A recent blog post by Stephen Wolfram (see: ...
11
votes
1answer
350 views

Mathematica 10 unable to Simplify[Cos[2 ArcCos[A]]]

Mathematica 10 evaluates Simplify[Cos[2 ArcCos[A]]] as Cos[2 ArcCos[A]], instead of the desired ...
2
votes
1answer
170 views

How to simplify an expression using a differential equation as an assumption?

I have a fluid dynamics flow described by a 3D velocity field such as u = {ux[x, y, z], uy[x, y, z], uz[x, y, z]} I want to calculate ...
1
vote
1answer
83 views

How to set products of small variables to zero

Say I have an expression which contains different product combination of very small variables, say, δA, δB, δC. I want to set all the products and all the ...
5
votes
1answer
193 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.: ...
0
votes
1answer
105 views

Expand a rational function in a one degree partial fraction, but not include a two degree expression?

How can I expand a rational function into a one degree partial fraction, and not include a two degree expression? For example, for Apart[] will get but I want the following result: What ...
6
votes
2answers
240 views

Simplify 2D polyhedral Regions like Interval

I don't think there's a built in "RegionSimplify" for polyhedral Regions and derived akin to how Interval automatically simplifies its argument expression: ...
0
votes
0answers
54 views

Custom simplification of symbolic definite integral with regards to bounds

I would like to rewrite symbolic definite integrals such that the bounds are always positive. For example : $\int_{-\infty}^\infty f(x) \mathrm{d} x \rightarrow \int_0^\infty \left[ f(x) + f(-x) ...
3
votes
2answers
218 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 ...
3
votes
1answer
182 views

Why do I get Floor and Ceiling in my output despite my assumptions

I am trying to simplify the following expression. ...
5
votes
1answer
211 views

Why does Mathematica not simplify this expression?

Consider this simple example: ...
1
vote
1answer
89 views

Guiding Mathematica to perform specific simplifications

I would like Mathematica to cancel out a specific term as much as possible. One of my computations simplify to ...
3
votes
1answer
194 views

Simplify product of square roots

What assumption is needed to make both outputs equal to Sqrt[P^2]/2 ...
3
votes
2answers
251 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)
4
votes
1answer
418 views

Can I check if an expression is positive using assumptions?

I have the following notebook: ...
8
votes
2answers
332 views

FullSimplify giving unexpected result

When I perform a FullSimplify on the list $$ \left\{-\sqrt{5-2 \sqrt{6}},\sqrt{5-2 \sqrt{6}},-\sqrt{5+2 \sqrt{6}},\sqrt{5+2 \sqrt{6}}\right\} $$ I get $$ ...
15
votes
3answers
315 views

Why does Mathematica simplify $x/x\to1$?

If I enter x/x, I get 1. Such behavior leads to this: Simplify[D[Sqrt[x^2], x, x]] 0 ...
2
votes
1answer
175 views

FullSimplify ratio of two gamma functions

I have the following input m = 2; Gamma[n + m]/Gamma[n + 1]; FullSimplify[%] It gives me 1+n For ...
5
votes
1answer
173 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 ...
2
votes
1answer
207 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
1
vote
2answers
142 views

eccentric anomaly expansion equation

I try to use this simple algorithm (paper) to calculate the Eccentric Anomaly expansion: ...
0
votes
1answer
149 views

Simplifying a symbolic product of rational powers

I'm trying to symbolically evaluate a lot of equations that can consist of up to 10 parameters. The form of these expressions is a product/quotient of rational powers of the mentioned parameters, ...
1
vote
1answer
64 views

Some question on “Reduce”

Is this my mistake? I am trying to solve ...