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

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0
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1answer
150 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: ...
4
votes
0answers
89 views

Simplifying expressions involving Divisible

FullSimplify[ Divisible[p^2 - 1, 24] , Element[p, Primes] && p > 3] Should evaluate to True, but I get ...
1
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1answer
103 views

Behaviour of Simplify when used with ArcTan and ComplexExpand along with assumptions

I am trying to simplify the slope of vectors with symbolic coordinates {x,y} using ArcTan[x,y] I am working with real X and Y I tried the following : ...
4
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0answers
87 views

Transform an expression to remove the singularity

I have the expression Sin[c x]/c. Clearly it is undefined at $c=0$, but that is merely a removable singularity, since $$\frac{\sin(cx)}c=x\frac{\sin(cx)}{cx}= ...
4
votes
1answer
159 views

Mathematica rule to express exponentials as multiplication

I'm sorry if this has been asked before, but it is a very simple question and I would imagine it shouldn't be terribly hard for someone that knows to answer. I'm essentially trying to tell ...
0
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0answers
72 views

Preventing numeric constants from being pulled out of square roots

If I input Sqrt[2 g], Mathematica automatically pulls out the 2 and returns Sqrt[2] Sqrt[g]. ...
3
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1answer
435 views

How to get rid of all complex numbers and functions?

For almost esthetical reasons, I always have been fascinated by infinite sums of series and I always wonder if theyhave a closed form. A couple of days ago, I found on MSE a question related to the ...
1
vote
1answer
100 views

Use Simplify option Trig->False when 3rd argument to Collect is Simplify

I would like to simplify the following expression AAA (4 Sin[x]^2 Cos[x]^2) + AAA 4 Sin[x] Cos[x] + AAA with the ...
-1
votes
2answers
84 views

Can I tell Simplify to prefer nested polynomials?

I need to export expressions for numerical evaluations in a C codebase. Simplify often does a good job for this, and polynomial factorisation goes a long way. However, occasionally I would come ...
0
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0answers
83 views

Recognizing a generalized function as zero

Consider the following expression: HeavisideTheta[x]HeavisideTheta[-x] Mathematica will not simplify it further. But $\Theta(x)\Theta(-x)$ is zero if considered ...
3
votes
4answers
154 views

How do I prevent exponents from being expanded when displaying text

I have a power of 2 in a list, and I want it to show as $2^{31}$ (2 with exponent 31), not 2147483648. I've tried this: ...
5
votes
1answer
198 views

Simplification of integrals depending on a parameter [duplicate]

Assuming[Element[n, Integers], Integrate[Sin[x]*Sin[n*x],{x,0,Pi}]] returns 0, which is obviously wrong for n=1. ...
1
vote
1answer
247 views

Latest Mathematica 9.0 can't use Format.m to generate optimized Fortran code [closed]

Before updating to Mathematica 9.0, I have successfully generated beautiful Fortran code using Mark Sofroniou's Format.m package, which is posted on MathSource. ...
0
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1answer
183 views

Reduce Cannot Solve Complicated Function

As per the answer to this question: SolveAlways rejects inequality, I tried the following commands: ...
4
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2answers
163 views

Why Refine does not simplify Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] to $(-1)^{i+j+k}$?

I am obtaining in Mathematica: Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] We know that for $i, j, k$ being positive integers this expression after simplification ...
3
votes
2answers
145 views

Exploiting a relation among constants

Say I have two arbitrary real constants $p,q$ that satisfy $p^2+q^2=1$. Is there any way to easily declare this relation in Mathematica? Edit More specifically I have this (among others) expression: ...
0
votes
1answer
95 views

Binomial sum identities

How do you persuade Mathematica to give simple identities involving binomial sums. For example Sum[Binomial[a,i]*Binomial[b,i],{i,0,n}] where n is bigger than ...
7
votes
2answers
224 views

Behavior of Reduce with variables as domain

When using Reduce, I accidentally put a set of variables as the domain. To my surprise, it not only seems that Reduce expects ...
5
votes
3answers
636 views

How to prevent Mathematica combining similar terms?

For example, given: x + 2 x y - x y + y I need to put it in this form: x (1 + 2 y) - y (x - 1). But Mathematica will simplify ...
10
votes
1answer
244 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
270 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
105 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
449 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
122 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
119 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
211 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
105 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
536 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
95 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
219 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
344 views
1
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0answers
70 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
111 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
153 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
235 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 ...
11
votes
1answer
533 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
418 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
242 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
264 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
186 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
103 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
336 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
205 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
70 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
577 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
221 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
222 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
1k 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
149 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) ...