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

learn more… | top users | synonyms (3)

10
votes
1answer
228 views

Cancellation of common terms

Can someone explain why the term A in case 2 does not get canceled out when case 1 does? I use "9.0 for Microsoft Windows (64-bit) (January 25, 2013)" ...
0
votes
1answer
243 views

Normalization of eigenvectors

I am trying to normalize the following vector in Mathematica with the Normalize command. $$(-1+2\cot[x]\csc[x]+2\csc[x]^2,\;2^\frac{1}{2} (1+\cos[x])\csc[x],\; ...
0
votes
2answers
103 views

Simplify an expression under certain condition

I have a variable A = g / (1 + g R) Actually, if the quantity (g R) >> 1 it is possible to write A as A ≈ 1/R. How can I do this in Mathematica? I tried with Assumptions, Refine, Simplify, but i can ...
4
votes
4answers
414 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): ...
1
vote
0answers
120 views

How can I say that all quantities need to be positive (and real)? [duplicate]

Can you say at the beginning of a script in Mathematica that you want all the quantities to be positive (and real)? So that in all calculations, only the real values of these quantities will be ...
2
votes
2answers
114 views

Simplification with assumptions

I'm trying to make Mathematica do some simplifications for me. I have the expression ((1 + s[1]) (-1 + s[2]) )/(-1 + s[1] s[2]) and want to simplify this with ...
4
votes
1answer
192 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 ...
1
vote
1answer
94 views

Simplifying using assumptions

Is there a way to simplify the following equation (-p(a-x)((a-b)P(b-x)+Q(b+x)(a-b+2x))+q(a+x)(-(a-b)Q(b+x)+P(b-x)(-a +b+2x)))/((b-x)(-a + x)(a+x)(b+x)) assuming ...
9
votes
2answers
521 views

Memory leak issues

I am working with noncommuting objects and basically I am using Mathematica to sort large expressions by normal ordering and simplifying them. To this end, I first create an object called ...
4
votes
2answers
129 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? ...
0
votes
1answer
90 views

How to convert the expression '{a->a0, b->b0}' to the expression 'a=a0; b=b0'? [duplicate]

How to convert the expression '{a->a0, b->b0}' to the expression 'a=a0; b=b0'? I think this is a common question and do not know if someone has asked it before. Any help or suggestion will be ...
0
votes
0answers
205 views

Solving for equilibrium distribution (symbolic) by matrix multiplication

I have a huge transition matrix (81x81). The matrix is too huge to paste here, so I store it in this notebook. (There are constraints on the symbols: $0<p_b<1$ and $0<p_g<1$. If further ...
4
votes
2answers
325 views
1
vote
0answers
67 views

How to simplify expressions

I read several similar posts but I have not found a solution yet. However, I think that my problem should be quite easy. So here we are. Relations ...
0
votes
0answers
106 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
0
votes
0answers
124 views

Alternate method of conjugation using replaceall

Mathematica really struggles to simplify complex conjugates of complicated expressions - even given assumptions for every symbol in the expression being real. Often times I've found that I can ...
3
votes
1answer
205 views

How to simplify to form without imaginary unit

I have an integral that I compute with Mathematica and as a result I get a seemingly complex expression (i.e. the expression contains the imaginary unit, $i$, at some places). However, if I try to ...
9
votes
1answer
402 views

What is the proper way to verify that two expressions are equivalent?

First of all, it appears to me that $$\left|\frac{1}{x} + x^2\right| \Leftrightarrow \frac{|1 + x^3|}{|x|}$$ is true. I don't know why, but my attempt to verify it in Mathematica failed. ...
7
votes
4answers
358 views

Counting multiplications (complexity function)

I'm trying to count the number of times multiplication appears in an expression (for the purpose of constructing a ComplexityFunction that would help me simplify a terrible algebraic expression for ...
9
votes
0answers
217 views

Simplify and Sqrt, inconsistent behavior?

I have encountered some problems when using Simplify with expressions containing a square root and isolated a following test case ...
2
votes
2answers
236 views

Pulling out common terms when simplifying complicated equations

I have a complicated expression where common terms are apparent but Simplify[] and FullSimplify[] don't appear able, even with plenty of assumptions added, to reduce down to a simpler form with common ...
3
votes
1answer
157 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
101 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 ...
8
votes
4answers
310 views

How to make Mathematica simplify $\cos[(i + j + k)\pi]$ to $(-1)^{i+j+k}$?

We know that: $$ \cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k} $$ for $i, j, k$ being positive integers. In Mathematica I've tried: ...
2
votes
1answer
181 views

Why FullSimplify doesn't work here?

Since the emphasis of this question is on finding a workaround, I decided to post this question with an emphasis on the explanation of the behavior of Mathematica. The Bessel function satisfies the ...
5
votes
1answer
67 views

How to bail out from a non-applicable transformation function?

I provide a custom function in TransformationFunctions options of FullSimplify that can do a transformation only for some values ...
8
votes
1answer
488 views

how to simplify large expression with lots of special functions in it (BesselY, Hypergeometric, MeijerG etc…)

I saw this DE in Maple forum. When solving it using Mathematica 9.01, even though the result was correct (both solutions gave the same numerical answer for some random values), Mathematica's answer ...
1
vote
2answers
208 views

How to simplify an expression with square roots?

The expression $\sqrt{L^2 M+\sqrt{L^2 (-J^2 + L^2 M^2)}}/\sqrt{2}$,can be simplified into $\sqrt{L}(\sqrt{LM + J}+\sqrt{LM - J})/2$, but how can I obtain this result with Mathematica? That is, how ...
2
votes
2answers
211 views

Calculate information entropy integral in infinite square well problem

In the context of information theory, entropy is a measure of uncertainty of a random variable. In quantum mechanics, the uncertainty principle states that $\Delta x\Delta k \ge 1/2$. The same can be ...
6
votes
1answer
962 views

Simplify $\cos(n \pi)$ and $\sin(n \pi)$ when n is an integer

I was trying to calculate this integral in Mathematica 9: 2/π Integrate[ Cosh[a x] Cos[n x], {x, 0, π}, Assumptions -> n ∈ Integers] I got as a result : ...
2
votes
2answers
142 views

FullSimplify used with Assuming giving unexpected results

Can someone shed some light on why Assuming[{x ∈ Reals}, x (Sign[x]^2 - 1)] // FullSimplify returns x (-1 + Sign[x]^2) ...
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 ...
7
votes
4answers
2k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
4
votes
2answers
151 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]]] ...
5
votes
1answer
347 views

How to express an expression with only ArcTan and ArcTanh?

I have an expression which is simply (j/k) x^(j/k) LerchPhi[x,1,j/k)] where 0 < j < k. Manually I have been able ...
4
votes
2answers
160 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): ...
7
votes
1answer
239 views

Limit for Matrix expression

Let's assume that $Q_0$ is $3\times 3$ matrix with $\det Q_0\neq0 $ and $$ Q_{i+1} = \frac{1}{2}\left[ Q_i+(Q_i^{-1})^T \right] $$ I need to find next limit: $\lim _{i \to +\infty}$$Q_i$. In other ...
1
vote
0answers
79 views

Introducing new variables implicitly [duplicate]

I have a calculation expr111 = cs[giso, xiso, 1, 1, 1] that gives the result -((k x)/(2 (1 + 1/4 k (x^2 + y^2 + z^2)))) ...
0
votes
0answers
31 views

Find repeated groups in a long algebraic expression [duplicate]

I have an algebraic output (a solution to a de) similar to, but far longer than: {y->(x+3)^2/sin(7*(x+3))+(x+3)^3/7} I'd like to get Mathematica to notice that the group x+3 appears repeatedly, ...
7
votes
3answers
222 views

Why does Mathematica not seem to know that $i^x$ cannot be equal to $0$?

I am experiencing a curious behaviour of Simplify when handling expressions involving powers of $\mathbf{i}$, such as $\mathbf{i}^x$ where $x$ is unknown. For ...
1
vote
1answer
164 views

Mathematica won't simplify multiplication by zero

I'm getting a huge output, but it appears that almost every term should actually be zero, unless I'm misunderstanding the expression. For example, part of the output reads ...
2
votes
1answer
118 views

Evaluating Abs'[2 x] gives different results than evaluating D[Abs[2 x], x]

I noticed the following difference Assuming[x ∈ Reals, FullSimplify[D[Abs[2 x], x]]] (* 2 Sign[x] *) Assuming[x ∈ Reals, FullSimplify[Abs'[2 x]]] (* Sign[x] *) ...
0
votes
1answer
255 views

Convert expression to C-form and simplifying

I have an expression which is the sum of many terms of the form $$ \frac{0.00000000274341}{(0.000363856+(0.611425+z)^2)^{3/2}} $$ My problem is that I need to include this long expression in a ...
1
vote
1answer
128 views

Assumptions in mathematica when Symplify on Log[Exp[a/b]]

In mathematica 9.0: This: Assuming[b > 0 || b < 0, Simplify[Log[Exp[a/b]]]] yields: a/b However, this: ...
0
votes
1answer
189 views

Simplify expression after substitution

I tried to substitue variable x of one equation with another variable z (z=nx/(nx+m)). See as follow: ...
3
votes
1answer
167 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 ...
7
votes
2answers
2k views

Fourier Transform of a Step Function

I'm trying to obtain the form of a sinc function that I know I'm supposed to get in Mathematica. I'm doing this because I intend to do a lot with Fourier transforms (FT) and I'd like to know I'm not ...
0
votes
1answer
185 views

Why does Mathematica find a form for this general sum, but not for some special cases?

Today I found a Sum which Mathematica will simplify for a general parameter value $\nu$, but which will not simplify fully for special cases $\nu = 1, 3, ...$ despite the fact that the general answer ...
2
votes
2answers
169 views

Transform Piecewise[] into sum of indicators

I'm interested in transforming a piecewise defined function into a sum of indicator functions, ultimately with the aim to be better able to integrate them. As an example I would like to transform the ...
12
votes
1answer
287 views

How to enlarge $\it{Mathematica}$'s knowledge about certain functions?

I'm often troubled with the following task. I need to carry out symbolical computations involving certain special functions. Let me take as an example Barnes gamma-function. It is included in ...