Tagged Questions

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

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1
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0answers
43 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 ...
0
votes
1answer
61 views

Simplify returns wrong result [duplicate]

For some particular reason, Mathematica makes wrong calculations when using Simplify[]. I need Simplify[] for a fractional decomposition of some fractions of low-order polynomicals. Here is a ...
1
vote
0answers
32 views

Simplifying an inequality inside an answer by parts

I have the following piece of code where I'm evaluating a probability of a variable v being greater than some threshold under a Uniform distribution. ...
0
votes
1answer
50 views
2
votes
1answer
99 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} ...
2
votes
0answers
47 views

Better way to compute triple (or higher order) convolution

I have an identity that I want to verify. $$\sum_{i+j+k\ge ...
3
votes
1answer
70 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
59 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, ...
0
votes
1answer
26 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
84 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
34 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[]: ...
4
votes
2answers
85 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 ...
1
vote
1answer
79 views

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

Element[Abs[Infinity], Complexes] returns False, that's right. But ...
4
votes
3answers
64 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
84 views
0
votes
0answers
43 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 ...
3
votes
1answer
76 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
45 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
42 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 ...
1
vote
1answer
69 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 ...
0
votes
0answers
25 views

Solving/simplifying a trig expression [migrated]

My problem sheet says that $\tan a= 5/12$ and $a \in {\rm Q\,III}$ ($a$'s in quadrant III). Using this information, I am to solve/simplify the expression $\quad \quad \cos\left(\frac{1}{2}a\right)$ ...
0
votes
2answers
44 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 ...
-2
votes
1answer
53 views

Why is it so complicated to simplify a complex conjugate? [closed]

My question is very simple. I would like to multiply a complex number by its conjugate. Unfortunately, this seems to be extremely complicated in Mathematica. Consider the very basic example: ...
0
votes
0answers
23 views

Expanding Function Based on Congruence Classes

I'm trying to get Mathematica to expand $\quad \quad \beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(q^4;q^4)_{n-r}(q^4;q^4)_{n+r}},$ where $\alpha_r$ is an integer valued sequence that is given by ...
0
votes
1answer
35 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 ...
0
votes
0answers
31 views

Simplification of a complex-valued expression with purely real components

(I'm including all the information here, as I'm not sure how much of it is necessary to solve the problem. For a tl;dr skip to the bottom) I've been working on a problem involving calculating ...
1
vote
2answers
162 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
40 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
101 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
58 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
53 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
185 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
60 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
228 views

Mathematica doesn't simplify a simple expression

The question is simple as that. I have: ...
1
vote
0answers
25 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: ...
1
vote
1answer
24 views

Expand Expression with Nested Special Functions [closed]

I am trying to study the following sequence for $a=1$, $n \ge 1$: $$\alpha_n=(1-aq^{2n})\sum_{j=0}^{n}\frac{(aq;q)_{n+j-1}(-1)^{n-j}q^{\binom{n-j}{2}}}{(q;q)_{n-j}(q;q)_j^3}$$ using Mathematica, where ...
9
votes
1answer
268 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
105 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
62 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 ...
4
votes
1answer
97 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
69 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
185 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
2answers
55 views

Write the equation as a polynomial in x and extract the coefficient of x^2 [closed]

I need help solving this problem. Thank you. (a*x^2 + b*x*Sin[y] + c*Sin[y])^2 + (a*Sin[y]^2 + b*x)^3 Write the above as a polynomial in x and extract the ...
0
votes
0answers
35 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) ...
2
votes
1answer
103 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 ...
3
votes
1answer
125 views

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

I am trying to simplify the following expression. ...
3
votes
1answer
130 views

Why does Mathematica not simplify this expression?

Consider this simple example: ...
1
vote
1answer
76 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
122 views

Simplify product of square roots

What assumption is needed to make both outputs equal to Sqrt[P^2]/2 ...
3
votes
2answers
225 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)