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

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0
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2answers
85 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
289 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
1answer
121 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 ...
0
votes
0answers
81 views

Writing polynomials in standard form in a matrix

A symbolic matrix with two parameters, say $x,y$, shows up in my calculation. The entries of the matrix are homogeneous polynomials. I want the entries to be written in some standard format, e.g. in ...
2
votes
2answers
98 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 ...
1
vote
1answer
79 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 ...
0
votes
1answer
105 views

Why isn't Simplify completely simplifying my expression when it has all the necessary info?

I have a complex variable, and I'm trying to multiply it by its Conjugate[], which should give me a real number. So, I'm currently doing: ...
0
votes
1answer
148 views

Reduce Cannot Solve Complicated Function

As per the answer to this question: SolveAlways rejects inequality, I tried the following commands: ...
0
votes
1answer
74 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 ...
9
votes
2answers
462 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 ...
3
votes
2answers
242 views

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

Can you explain me about the result of Integrate. ...
1
vote
0answers
57 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
82 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
62 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
votes
0answers
158 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
votes
1answer
124 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
224 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. ...
1
vote
1answer
112 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
votes
0answers
150 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
132 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
81 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
votes
2answers
122 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
votes
2answers
95 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
votes
1answer
114 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
votes
1answer
95 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
votes
4answers
246 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
vote
1answer
173 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
110 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
votes
1answer
110 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
62 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
votes
0answers
112 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
votes
1answer
240 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
168 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
170 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
129 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
97 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
votes
0answers
48 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
votes
2answers
123 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
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
30 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
195 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
votes
1answer
208 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
votes
2answers
297 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
vote
1answer
133 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 ...
4
votes
1answer
248 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
votes
1answer
97 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
121 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
111 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
vote
1answer
198 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
votes
1answer
125 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: ...