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

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1answer
31 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 ...
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2answers
92 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 ...
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1answer
46 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 ...
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2answers
49 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 ...
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2answers
159 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: ...
4
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2answers
199 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 ...
5
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2answers
54 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
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1answer
220 views

Mathematica doesn't simplify a simple expression

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

Simplify results further

I have an extremely long result in polynomial form following some matrix operations. However, given the symmetry of the problem, I can safely say that the solution will reduce much further than is ...
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1answer
22 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 ...
2
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1answer
98 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 ...
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1answer
96 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 ...
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1answer
108 views
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1answer
254 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 ...
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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 ...
6
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2answers
182 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: ...
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1answer
118 views
4
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1answer
92 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
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1answer
65 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 ...
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2answers
53 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 ...
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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) ...
3
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2answers
218 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)
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1answer
73 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
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1answer
111 views

Simplify product of square roots

What assumption is needed to make both outputs equal to Sqrt[P^2]/2 ...
2
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1answer
57 views

Want Wolfram|Alpha to assume $n$ is an integer [closed]

I would rather use Wolfram|Alpha on my iPad then Mathematica, so I need your answer to be applicable to W|A. I want to input a function or an expression in a way that Wolfram|Alpha will understand ...
4
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1answer
177 views
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2answers
91 views

Trying to solve simultaneous equations based on format found on official website [closed]

$\def\1{x_1}\def\2{x_2}\def\3{x_3}\def\f{f(\1,\2,\3)}\def\bs{\bigskip}\def\b{\begin{pmatrix}}\def\e{ ...
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2answers
255 views

FullSimplify giving unexpected result

When I perform a FullSimplify on the list $$ \left\{-\sqrt{5-2 \sqrt{6}},\sqrt{5-2 \sqrt{6}},-\sqrt{5+2 \sqrt{6}},\sqrt{5+2 \sqrt{6}}\right\} $$ I get $$ ...
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3answers
220 views

Why does Mathematica simplify $x/x\to1$?

If I enter x/x, I get 1. Such behavior leads to this: Simplify[D[Sqrt[x^2], x, x]] 0 ...
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3answers
85 views

Place symbols from small to big

I am wondering how to compare the different values of ω I derived in this code, and place them in order as follows. (use Print ...
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1answer
37 views

FullSimplify ratio of two gamma functions

I have the following input m = 2; Gamma[n + m]/Gamma[n + 1]; FullSimplify[%] It gives me 1+n For ...
5
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1answer
165 views

Restrict Mathematica command to what is inside parentheses

I have a bunch of expressions like this one: $\frac{e^{-\frac{7 J}{2 k T}} \left(2 e^{-\frac{2 g H \mu _B}{k T}}+e^{-\frac{g H \mu _B}{k T}}-e^{\frac{g H \mu _B}{k T}}-2 e^{\frac{2 g H \mu _B}{k ...
7
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1answer
276 views

Why does Simplify with TimeConstraint return Removed[$$Failure]?

Bug existed in version 7 and is fixed in version 10.0.0 I have a rather ugly Mathematica expression (edit: shown below) that I would like to simplify with a time constraint; simplifying without a ...
9
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3answers
443 views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
1
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1answer
124 views

Format Preservation of FullSimplify on Indexed System of Autonomous Equations

I currently have a large system autonomous differential equations. I've indexed a more managable dummy system of identical form, using Part to reference each ...
1
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1answer
131 views

Check for holomorphy of a function

Given a (rather complicated) function H(z), what is the best approach to check symbolically whether it is holomorphic? What I tried is checking explicitly the ...
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2answers
88 views

eccentric anomaly expansion equation

I try to use this simple algorithm (paper) to calculate the Eccentric Anomaly expansion: ...
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1answer
60 views

Simplifying a symbolic product of rational powers

I'm trying to symbolically evaluate a lot of equations that can consist of up to 10 parameters. The form of these expressions is a product/quotient of rational powers of the mentioned parameters, ...
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0answers
49 views

What is taking so long in this simplification?

I killed this after 48 hours, it did not seem to be getting anywhere. In the best of all possible worlds it would spit out n!. If I put the summation in a function it does compute factorials ...
1
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1answer
56 views

Some question on “Reduce”

Is this my mistake? I am trying to solve ...
8
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1answer
105 views

Expanding derivatives of hypergeometric functions

Sometimes Mathematica expresses results of integration or summation in terms of symbolic derivatives of Hypergeometric2F1 function, and cannot further simplify ...
1
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1answer
53 views

Can someone please help me to state assumption?

I am currently trying to solve under what condition does the following term will be zero? ...
0
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2answers
38 views

Taking inverse powers of an expression to that power [closed]

I'm finding a curious behavior for Mathematica 8. The code (x^3)^(1/3) does not want to Simplify or FullSimplify. I'd prefer not to make a rule for this, because ...
0
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2answers
59 views

How to combine the sum of two rational polynomials into a single rational polynomial [closed]

I have browsed the web and found no information. I have two rational polynomials $f1(x,y)$ and $f2(x,y)$. When I perform f1 + f2, I always get two separate ...
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0answers
60 views

Inconsistent behavior of Assuming[] in combination with Simplify[]

The following integral gives the correct result ...
1
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1answer
159 views

Efficient way to give symbolic elements symmetry

I have a symbolic expression that represents a set of operators. These operators have quite a bit of symmetry to simplify expressions: ...
4
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1answer
111 views

Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
3
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1answer
195 views

Is this a bug in FunctionDomain (V.10)?

I used FunctionDomain[1/(x^3 + 1), x, Complexes] and got 1 + x^3 != 0 Is this a bug in FunctionDomain (V.10)? Can I receive $x \neq -1$, $x \neq ...
0
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2answers
120 views

Expand 2f[x] to f[x]+f[x] (Simplify sums of ArcTan)

I'm trying to simplify an expression with sums of ArcTan, for which I've written a transformation rule that works for simple sums, so that ...