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

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63 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
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0answers
104 views

Gradient from Vectors type

I'm working with Vectors type in Mathematica 9. For this purpose I use the following command: ...
0
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0answers
112 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 ...
0
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0answers
199 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 ...
3
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1answer
172 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
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1answer
344 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. ...
4
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2answers
200 views

Cleaning up InverseLaplaceTransforms in Mathematica

I am attempting to use Mathematica to model an electrical circuit in the s domain. The circuit contains capacitances and and inductances. I've written a series of equations using Kirchoff's laws to ...
9
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0answers
207 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
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2answers
197 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
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1answer
146 views

Simplify doesn't simplify HypergeometricPFQ with exact arguments

Consider a series: $$\sum_{t=0}^\infty \frac{8^{-11-2t}(22+4t)!}{t!(11+t)!(11+2t)!(32+t)}$$ ...
4
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2answers
127 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? ...
6
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2answers
117 views

Partial result of aborted evaluation of FullSimplify

When FullSimplify invoked on a large expression, it can run for hours. If I do not have time to wait, and abort the evaluation, I get no result, although, ...
6
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1answer
124 views

Is it possible to disable assumptions used by FullSimplify for zero testing [closed]

Sometimes when I invoke FullSimplify on a large expression, I get a series of messages like this: ...
3
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1answer
100 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 ...
7
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4answers
299 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: ...
1
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1answer
219 views

Why doesn't FullSimplify work properly on this?

I wish to simplify the simple expression fac[n_] := Sum[R^i, {i, 0, n}]; as much as possible for various $n$. FullSimplify or ...
6
votes
1answer
124 views

Is there a version of Together that doesn't cancel common factors?

I'm running code that produces a long combination of rational functions with free constants that need to be tuned such that the combination vanishes. My current method is to put the combination over ...
2
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1answer
160 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
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1answer
65 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 ...
6
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0answers
147 views

Using FunctionExpand to evaluate symbolic derivatives

Some symbolic derivatives of certain special function are not expanded automatically, but FunctionExpand often helps to get a derivative-free closed form ...
8
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1answer
440 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
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2answers
196 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
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2answers
202 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 ...
2
votes
2answers
138 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
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2answers
102 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 ...
0
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0answers
55 views

Reducing a long complex expression to a simplier one by using assumptions

so I have an ugly looking equation that I wish to solve under some specific circumstances. Using DSolve I write; ...
4
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2answers
140 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]]] ...
1
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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
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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
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3answers
218 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 ...
7
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1answer
227 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 ...
8
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2answers
333 views

How can I get $(r^{1/x})^x$ to simplify to $r$?

Simplify and FullSimplify do not simplify this kind of expression: $(r^\frac{1}{x})^x$. Consider ...
1
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1answer
156 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 ...
5
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1answer
323 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 ...
2
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1answer
112 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
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1answer
225 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
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1answer
123 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: ...
1
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1answer
204 views

Function simplification: factoring $f(r,x)$ into $f1(r) \times f2(x)$ [closed]

I have a function of two variables $f(r,x,c)$, where $r$ and $x$ are variables and $c$ is a constant that appears in the function. I would like to write it as a product of two functions $f1(r,c) ...
0
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1answer
176 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
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1answer
162 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 ...
4
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2answers
154 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): ...
0
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1answer
172 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
154 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
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1answer
277 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 ...
6
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1answer
221 views

Forcing Mathematica to use certain simplification rule

I'm trying to force Mathematica to use following transformation function ...
7
votes
2answers
332 views

How to automatically get rid of trig functions in an expression?

I have a large expression containing many terms like this: Sin[1/2 ArcTan[(2 Log[5])/(Log[5]^2 - 2)]] where a trig function is invoked on a rational multiple ...
1
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1answer
204 views

Simplifying with noncommutative multiplication

I am trying to do some quantum algebra computations in Mathematica. Up to now I was able to make the noncommutative multiplication linear and to factorize powers. However, I still have some issues ...
2
votes
1answer
510 views

How to show factorial in expanded form with variables

When evaluating the following (Factorial[n + 1]/Factorial[(n + 1) - (k + 1)]) with Mathematica 9, the result is sent to output as ...
0
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0answers
108 views

How to simplify really complicated symbolic expression?

I have an expression that contains Sinh[x], Cosh[x] and Sin[g], and I want to simplify it ...
1
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1answer
246 views

Simplify vector expression - is there something like “Factor” for vectors, dot products etc.?

I am looking for a way to simplify dot products etc. Here is a minimal example: Lets say I have two vectors a and b: Array[a,2] Array[b,2] Now I evaluate their ...