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

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1answer
33 views

Simplifying x Conjugate[x]

I am trying to simplify a big expression containing many times terms of the form x Conjugate[x]. While this works for a single term: ...
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18 views

How to resolve this issue related to Conjugate?

When I perform the vector multiplication given below FullSimplify[{a,b}.Conjugate[{a,b}]] I am getting the result as I expect ...
2
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1answer
66 views

difference between FullSimplify and Simplify

I have a problem to dinstinguish the following two mathematica codes, the only difference is the first use FullSimplify and the second is Simplify. but the results are totally different. what is wrong,...
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0answers
38 views

Simplify: Why does it miss this simple one?

I got a result with the expression ...
7
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2answers
252 views
+100

Symbolically prove that two expressions are identical

I encountered this problem when trying to reproduce the result of this paper. (The relevant parts are all included in the preview i.e. the 1st page of the article. This link is just given as ...
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2answers
76 views

Problem with simplification of $\sqrt{1+\frac{y^2}{x^2}}$

When I evaluate my Mathematica code I get out a term of the following form: $\sqrt{1+\frac{y^2}{x^2}}$. However, I also have $\sqrt{x^2+y^2}$ terms that I would like it to cancel with. For example, ...
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0answers
44 views

Simplify a complex trigonometric equation resulting from constraint solving

In the solving of mechanical constraints, I often meet complex trigonometric equation that I have to simplify. Here the equation I would like to simplify : Mathematica notebook presenting the ...
2
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1answer
52 views

Simplifying integer inequalities to equality

I try (in Mathematica 10) FullSimplify[l >= l1 + l2, {l <= l1 + l2, Element[l | l1 | l2, Integers]}] But that gives back ...
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0answers
37 views

Expectation of summation with symbolic indices

I am working on symbolic computations with mathematica. I faced an issue with taking expectation of a large expression involving summations with symbolic indices. Is it possible to take expectation ...
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0answers
31 views

How to solve a quadratic inequality containing parameters?

I have the following inequality to solve for $R$ in terms of $\delta$ and $n$, with assumption that $n \geq 3$ and $\delta>0$: $$-2 < 2 -\frac{16n\delta^{2}}{R^{2}\sin^{2}\frac{\pi}{n}} \left(...
2
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1answer
233 views

Simplifying square root of exponential

Very simple question: Why doesn't Mathematica simplify this square root expression? Refine[Sqrt[Exp[I p]], p > 0] // FullSimplify It should give ...
0
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1answer
27 views

Making multi-linear polynomial change of variables (simplifications) by updating `replacementFunction`

This is an evolution of one of my previous questions; I've got a partial answer to that question and now have a much cleaner question to ask: Question: What changes to ...
6
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3answers
217 views

Why doesn't Lambert function (ProductLog) simplify?

I have Simplify[ProductLog[x*Exp[x]]] By the definition of the Lambert function, this should be simply x. But Mathematica outputs this: ...
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2answers
108 views

Factor out imaginary unit of root of obviously negative term

Suppose I have the term $t=\sqrt{-a^2-b^2}$, where $a,b\in\mathbb R$. Of course, we know that it holds $$ t = \mathbb i \sqrt{a^2+b^2} $$ which is (in my opinion) more convenient. How can I get ...
1
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1answer
129 views

Residue failed to reproduce this residue in a paper

This problem is a more clearly state of my original problem which is off topic, so I reconsider my problem carefully based on previous discussions, and gives the following valid code to reproduce my ...
1
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0answers
144 views

Problem of calculating the residue of a expression (to confirm the result from a paper) [duplicate]

I use Mathematica to confirm a result from a paper which is to calculate the residue of a expression at zero. The code and result are given below. Is this residue too complicated for Matheamtia or ...
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2answers
85 views
1
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1answer
84 views

A simplification of a complex expression

I use mathematica to confirm a result from a paper ("...
3
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1answer
73 views

Replacing patterns (determinants) in a rational multivariate function and/or getting `replacementFunction` to work on a multi-linear expression

Given a rational multivariate function known to contain determinants, what is the best way to rewrite the function in terms of the determinants? A simple example: ...
0
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0answers
46 views

NCAlgebra: define a scalar variable

I have a linear operator L and a scalar h, and would like to expand L[f + h phi] to ...
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0answers
36 views

Evaluating a function after simplifying to avoid infinite expressions

My Poly[j_, s_] function simplifies to a polynomial for all j. So I defined a PolySim[j_, s_] = Simplify[Poly[j,s]] function. However, if I try to evaluate PolySim[j,0], since this is PolySim[j,0] = ...
3
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0answers
80 views

Bringing rational functions to canonical form

I have a complicated expression, which among other things has stuff like functions of rational functions: expr = f[x/(-x^2 + y)] + f[-(x/(x^2 - y))] (* + ...*) ...
0
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0answers
66 views

Avoiding divide by zero to simplify an expression enough to solve

I have a very complicated expression that I'm trying to set to zero and solve. I simplify by substituting in variables, but Mathematica isn't fully simplifying it -- my guess is because it thinks it ...
3
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0answers
78 views

Why isn't Mathematica listening to my assumptions?

I'm trying to simplify the expression ωplus := 1/2 c (I f V + Sqrt[4 k^2 - f (f + 8 I k) V^2]) so that I can get it in the form $a+i b$. I am using the global ...
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1answer
64 views

Need help on simplifying the integral of a square root of a polynomial

I have the following expression a = 4 Cos[af / 2]^2; b = 1 - 5 Cos[af / 2]^2; c = Cos[af / 2]^2; s = Sqrt[a*x^4 + b*x^2 + c] and I need the integration of $s$ in ...
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0answers
4 views

Simplifying using identies [migrated]

Simplify tanxcos^2x/(sinx-sin^3x) I tried to turn all terms into sin and cos and i got secx as the answer. Then I tried to changed the cos^2x into 1-sin^2x and ended up with tanx/cosx. Why am i ...
2
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1answer
74 views

Weird behavior of `HypergeometricPFQ`

Consider the following function: fun = HypergeometricPFQ[{1, x1-y1, 1-x1-y1-2u}, {x2-y1, 3-x2-y1-2u}, 1]; Let us try and evaluate this function on the following ...
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0answers
33 views

Mathematica can't simplify disguised expression [duplicate]

When I simplify the following quartic polynomial with a linear constraint; Simplify[x y z a + x y z b , a + b + c == 0] // Expand I get what to me seems like the ...
2
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1answer
82 views

Way to simplify an inequality with many variables

my problem is the following: I have three inequalities in five variables $x,u,a,b,c\in \mathbb{R},x>0 $: ...
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0answers
41 views

`QPochhammer` function simplification?

Consider the function which in Mathematica is denoted as QPochhammer[a,q,n], and its infinite product cousine: which in Mathematica reads ...
8
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1answer
105 views

Adding irrelevant assumptions changes the result of Simplify

I've run into this problem a number of times. A typical example is Simplify[Sign[k], {0 < A, 0 < B, A*Exp[2*y] < k, y > 1}] which evaluates to $1$, ...
4
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1answer
88 views

How to tell Mathematica to avoid simplification of product of exponentials with the same base?

There has been a similar question, but it doesn't solve my problem. I have this input: var = Exp[a] Exp[b] And the output is ...
0
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0answers
29 views

Finding results using qualifiers?

I have set of recursive function definitions and assumptions $\forall n.t1(n+1)=t1(n)-Y*S(n)$ $\forall n.t2(n+1)=t2(n)+S(n)$ and assumption $\forall n.n<K\rightarrow L1=L2*t2(n)+t1(n)$ I want ...
0
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1answer
53 views

Not simplify an easy equation with “Simplify”

I've a problem with the function Simplify. I've this equations x^2 + 2 x + 1 == 0 and 4 x^2 == 0. If I use Simplify, it returns <...
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2answers
32 views

Simplifying polynomials with conditions on variables

I'm working with polynomials of 5 variables $a,b,p,q,r$ which have a condition $a+b=p+q+r$. I'd like to minimize the number of variables in the answer. However, FullSimplify can't handle even simple ...
1
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1answer
52 views

FullSimplify fail with general assumption

Assume I want to simplify this: -a^(-1) ** b^(-1) + (b ** a)^(-1) given assumption: $\frac{1}{b\_\text{**}a\_}=\frac{1}{a\_}\text{**}\frac{1}{b\_}$ Then it ...
3
votes
3answers
130 views

How to obtain this expression in terms of real functions

I know that this expression (2 (ArcCot[E^(-((I ϕ)/2)) r] + ArcCot[E^((I ϕ)/2) r]))/π is real, because is the sum of a real series, in particular: ...
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0answers
53 views

Handling Inequality with condition

I have verifying inequality using Mathematica using Simplify command For Example I want to check whether inequality a<f ...
0
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1answer
34 views

Complex number simplifications

My Mathematica notebook is not simplifying some expressions which do look trivial. I mean that one of my outputs contains: ...
3
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3answers
441 views

Simplify big numbers in a second order equation

How can I simplify big exponents like $10^{39}$ in the solution of a second order equation: ...
0
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1answer
36 views

Option for Simplify command in mathematica

What does Simplify[%[[1]], %[[2]]] mean in following code? I mean [[1]] and [[2]] exactly what does refer to? ...
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2answers
80 views

Double sum in mathematica

It may look like a stupid question, but I was really confused by how double sums works in mathematica: After simplification, the function actually has nothing to do with n2? Also, when I manually ...
2
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1answer
104 views

Complicated implicit plotting

I'm quite new to Mathematica and have already spent tons of time on problems of this type, browsing through tutorials and topics here. I'm now coming to conclusion that it cannot be done and am about ...
0
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1answer
53 views

Simplify assuming $x$ is small [closed]

I would like to assume that $x$ is small so that values of the order $x^2$ (and higher orders) are negligible. For example, I would like Mathematica to return $1-2m$ when I ask it to simplify $(1-x)^...
0
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1answer
53 views

Metric Simplify & grouping

I'm changing a basis from one metric to another. When simplifying the result Mathematica doesn't seem to grasp all the possible simplification: ...
0
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3answers
59 views

how to take complex conjugate of a real variable

I have a function defined as follows: g[θ_] := 1/k (Exp[-I δ0] Sin[δ0] + 3 Exp[I δ1] Sin[δ1 Cos[θ] + 5/2 Exp[I δ2 (3 (Cos[θ])^2 - 1)) and I compute ...
1
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2answers
48 views

Simplify Expressions used to define Region

For example, RegionPlot[{x + y > 1, x - y > 1, y - x > 1, -x - y > 1}, {x, -2, 2}, {y, -2, 2}] can be somehow written as: ...
2
votes
1answer
98 views

Mathematica doesn't know about the absorption identity? [closed]

The well-known binomial absorption identity states that $$n\binom{n-1}{k-1} = k \binom{n}{k}$$ However, Mathematica gives ...
0
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1answer
50 views

Inverse of a Fourier matrix [closed]

I am trying to find the inverse of a Fourier matrix but I am getting confusing results. If R is a Fourier matrix, then ...
0
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2answers
99 views

Solving recursion relation from power series

I am interested in solving differential equations in the form of power series. Let's say we have following equation: $$f^{\prime \prime} (\rho) + \left( \frac{2 e^{-k \rho}}{\rho} - \varepsilon \...