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

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1answer
48 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 ...
4
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2answers
208 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 ...
1
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1answer
123 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
60 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 ...
5
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2answers
326 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
260 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
112 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
265 views
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0answers
35 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
36 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
147 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 ...
10
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1answer
306 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
74 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
221 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: ...
5
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1answer
153 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
92 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 ...
0
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2answers
73 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 ...
0
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0answers
50 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
239 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
84 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
163 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
338 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 ...
3
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2answers
132 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{ ...
8
votes
2answers
304 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 $$ ...
14
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3answers
277 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
88 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 ...
1
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1answer
90 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
170 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 ...
10
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3answers
937 views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
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1answer
131 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 ...
2
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1answer
159 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 ...
1
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2answers
120 views

eccentric anomaly expansion equation

I try to use this simple algorithm (paper) to calculate the Eccentric Anomaly expansion: ...
0
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1answer
114 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, ...
0
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0answers
55 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
62 views
8
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1answer
216 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
57 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
41 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
68 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 ...
1
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1answer
170 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
187 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
votes
1answer
211 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
votes
2answers
158 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 ...
2
votes
3answers
166 views

Simplify system functions

Consider the code defining two constants: a=Cos[t] b=Sin[t] Suppose that we have another value in terms of Cos[t] and ...
0
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1answer
84 views

FullSimplify with assumptions

Is there a way to write a FullSimplify at the end of the line with some assumptions? That is, if I write a^2+b^2+2 a b //FullSimplify[...] is there any way to ...
0
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0answers
27 views

Simplifying (A+B)* C doesn't work [duplicate]

This is simple, but it doesn't work: In[1]=FullSimplify[(A0 + B0) C0] Out[1]=(A0 + B0) C0 which should be: A0 C0+ B0 C0 It ...
0
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1answer
74 views

How to evaluate Floor[1/2 + Arg[z]/(2π)] with Re[z] > 0

I want to do a series expansion of an expression containing Gamma functions with specific arguments. An example is the following: ...
0
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0answers
34 views

Assumptions for simplifying a long equation

I'm having trouble combining assumptions with the execution of Simplify in a long equation. The idea is to separate imaginary and real parts of a complex equation. ...
0
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0answers
64 views

Simplification of (Co)sine of a sum

I have a huge expression with (Co)Sine of a sum like Cos[[Theta] - 2 [Phi]] (after using \Simplify). I wanted to know if it exists a function which forces Mathematica to express the result in terms of ...