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

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1answer
62 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: ...
-1
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0answers
54 views

Why is result from evaluation not simpler? [on hold]

How do I define variables $\qquad u(x_m , y_n)\qquad m,n=1,2,\dots,4$ in Mathematica? $x_m, y_n$ are known and $u$ is unknown. The result I am getting is: ...
1
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1answer
78 views

Substutution of Ansatz of an ODE [duplicate]

I am only beginning to learn to use Mathematica, and got stuck while trying to implement what is apparently a simple substitution rule. So I have a second order ODE in f, and I want to put in the ...
0
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0answers
56 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 ...
5
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1answer
101 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 ...
2
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1answer
32 views

Replacing expressions with variables [closed]

I have a large matrix where the entries are rational in Jacobi elliptic functions e.g. I'd like to replace the elliptic functions by variables, e.g. ...
1
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1answer
68 views

Efficient method to calculate green's function between points

I am working on an analytical model for sound radiation from a cylinder. As part of this work I am using the boundary element method to predict the sound pressure at a particular location away from a ...
5
votes
1answer
102 views

Trouble factoring an expression

I've got the term $-1 + 2b^2 + 2b\sqrt {b^2-1}$ appearing several times within several larger expressions. It is easy to see that this expression factors into ${(b+\sqrt{b^2-1})^2}$, but when I use <...
3
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1answer
67 views

Simplification of Gamma functions

I am having some trouble simplifying some Gamma functions. I have a large expression in which some combinations of Gamma functions appear, that can be simplified, but applying ...
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2answers
94 views

Verifying inequality in Mathematica

I am trying to verify the following inequality Mathematica. This I wrote the fillowing code: ...
3
votes
1answer
90 views

Factor a polynomial Root into Roots of smallest possible degree

Suppose I have a polynomial Root representing an algebraic number. I want to represent it (if possible) as a product of several polynomial ...
1
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2answers
37 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 ...
4
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1answer
144 views

Simplify sum of complex logs to single real log

Sometimes, mathematica likes to give me complex results when, e.g, integrating a real valued function. The result might be something like ...
1
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1answer
64 views

Collect partial derivatives and rewrite them with delta/nabla

Ultimately, I wish to get the higher generalized product rule for Laplacian. That is, we have $\Delta(fg)=f\Delta g+2\nabla f\cdot\nabla g+g\Delta f$ but what is $\Delta^n(fg)$? I am tying to guess ...
0
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0answers
49 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 ...
2
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2answers
315 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 ...
2
votes
1answer
95 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,...
1
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1answer
49 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: ...
2
votes
1answer
109 views

Complicated implicit plotting [closed]

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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0answers
41 views
2
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1answer
55 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 ...
9
votes
2answers
290 views

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 ...
0
votes
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, ...
0
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0answers
33 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
votes
1answer
242 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
votes
3answers
220 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: ...
1
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0answers
145 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 ...
2
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1answer
135 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 ...
0
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0answers
48 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 ...
3
votes
1answer
74 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: ...
1
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2answers
110 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
87 views

A simplification of a complex expression

I use mathematica to confirm a result from a paper ("...
0
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0answers
39 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
votes
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
votes
0answers
79 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 ...
1
vote
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 ...
2
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1answer
79 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 ...
9
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1answer
521 views

RootSum result manipulation/simplification

Consider the sum sum1 = Sum[ k/( k^7 - 2 k + 3), {k, Infinity}] ...
1
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2answers
71 views

Simplifying expressions containing unit of zero magnitude

I have obtained the following form as a part of a computation: k (Quantity[0, "Kilohertz"]) + Quantity[1/500, "Kilohertz"] This is typeset as Here, ...
0
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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
votes
1answer
86 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 $: ...
8
votes
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 $1$, ...
1
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0answers
44 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 ...
3
votes
4answers
417 views

Mathematica not able to confirm its own solution to differential equation

I type the following into Mathematica: DSolve[q''[x] + 2 x/(x^2 - 1) q'[x] - 4*q[x]/(x^2 - 1) == 0, q[x], x] It gives me the result ...
1
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2answers
126 views

Simplifying ArcTan[Cos[u], Sin[u]]

I am trying to evaluate the following expression in Mathematica: $$ \bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2 $$ Here $z$ is the complex ...
0
votes
0answers
30 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
votes
1answer
54 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 <...