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

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1answer
59 views

Simplify the following transformed equation [closed]

y=7f(-1/6(x-1))+1 The base function is f(x)=x^2. I just don't understand where the ^2 went and how to simplify this. Any help is much appreciated, thanks.
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0answers
36 views

Factoring rationals from equation based on digit complexity?

Consider an equation of the following type: ( poly = (3 x)/35 + (6 y)/7 ) == 0 If we apply the command Factor to this ...
1
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1answer
102 views

Simplify not working for a real part of a complex expression [closed]

When I try to get the real part of a term, for example: $\qquad \Re\left(\frac{e^{-i k} \left(2 k^2+\pi ^2 \left(-1+e^{i k}\right)\right)}{\pi ^2-k^2}\right)$ Mathematica will output the same thing ...
23
votes
1answer
2k views

A one line proof that one is zero using Mathematica 10

a = (Sqrt[2] + 1) (Sqrt[2] - 1) - 1; {a/a, Simplify[a]/a, b/b == Simplify[b]/b} {1, 0, True} This one line "proof" that ...
4
votes
1answer
48 views

Reliable testing of identities (example: modular functions)

Take, for illustration, the following function (bonus points for anyone who identifies where it comes from!), defined on the upper half plane: ...
0
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0answers
61 views

How to combine similar terms in a density matrix expression? [Ref: Quantum Computing]

I tried the following : Simplify, FullSimplify, and Expand. Due to this problem, I am not ...
1
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0answers
53 views

Running out of memory when doing non-commutative arithmetic

I need to calculate particular coefficients of the composition of two power series in non-commutative variables. The code below which works fine truncates power series in degree $n=5$. For $n=6$ (the ...
9
votes
1answer
82 views

Problem with simplification KroneckerDelta

Bug introduced in 8.0 or earlier and fixed in 9.0 I have: ...
3
votes
3answers
450 views

Fullsimplify does not simplify Abs'[1.-a]

I have to simplyfy an expression involving Abs' This works: FullSimplify[Abs'[1 - a], a ∈ Reals] Sign[1 - a] but this ...
12
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1answer
219 views

Using Simplify on a consistent system returns False

Bug introduced in 8.0 and fixed in 10.3. It's late, but am I missing something here? Why should two independent equations, which together are consistent, ...
1
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0answers
64 views

DiracDelta of a function

If I have, for instance, FunctionExpand[DiracDelta[x^2+x-3]] it evaluates to ...
2
votes
3answers
74 views

Series: two varibles, how to eliminate the (product) higher order

I have a function of $f(x,y)$, where $x,y$ are very small numbers. I want to series expand it to the $3$rd power. However I don't want the terms such that $x^2y^2$, $xy^3$ etc. because I would reckon ...
1
vote
1answer
194 views

Expansion of functions in the real domain

When I try FullSimplify[FunctionExpand[x^(1/12)(1/12) LerchPhi[x,1,1/12]]] I have a nice answer with many complex numbers. Is there any way to have the ...
1
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0answers
39 views

Reduce excess Log[] [closed]

I am trying to solve a differential equation using DSolve: DSolve[y'[t] == t^10 eps^-y[t], y[t], t] And get the following output: ...
7
votes
1answer
146 views

Why don't 1. (0. + a) or (0. + 1. a) simplify?

I'm handling some mixed-numeric-analytic expressions, and I feel I'm missing some subtleties of how Mathematica handles simplification of such expressions. In particular, I was initially puzzled by ...
3
votes
1answer
169 views

Separate variables in equation

I need to know is there a way to separate the desired variables in the equation at one side of the equality. For instance, the following equation ...
1
vote
1answer
50 views

Need help simplifying final expression [closed]

I was carrying out a function and ended up with the desired answer, but for some reason, Mathematica keeps giving me the answer in a strange numerical form. ...
0
votes
1answer
110 views

FactorialPower and Factorial

After some computation, I have obtained a function FactorialPower[1, n, -1]. Clearly, FactorialPower[1, n, -1] equals ...
2
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1answer
80 views
2
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0answers
55 views

Simplifying symbolic expressions using TensorExpand

Following my previous question I have this issue using TensorExpand: KroneckerProduct[x, y].(KroneckerProduct[2 z, w]) // TensorExpand results in ...
3
votes
0answers
121 views

Is it possible to simplify an expression in vector form, which involves crossproduct and dot product?

I often need to simplify expressions involving cross product and dot product, for example: f = Dot[Cross[Cross[p1 - p, e1], Cross[p2 - p, e2]], Cross[p3 - p, e3]] ...
3
votes
2answers
124 views

Simplification of products of KroneckerDelta[]

What is the reason why the following expression does not simplify to True? ...
3
votes
1answer
81 views

Simplifying an expression with complex variables

The other day I was trying to simplify the following expression of $w \in \mathbb{C}$ and $|w| < 1$: $$f(w) = \left|\frac{2}{(\frac{w+1}{1-w}+1)^2}\right|^{-\Delta} \cdot \frac{1}{\left|{\rm ...
4
votes
1answer
91 views

FullSimplify on complex numbers seems inconsistent

FullSimplify[c Conjugate[c]] returns Abs[c]^2 while FullSimplify[2 c Conjugate[c]] ...
5
votes
1answer
87 views

Simplify with a condition

I have an expression, $-a (u + a v)$, and I would like to simplify it using the fact that $a^2 = 1$. I have tried Simplify[Expand[-a (u + a v)], a^2 == 1] but ...
8
votes
1answer
101 views

evaluation of the sum of KroneckerDelta

I need help. I need to know why the next code doesn't simplify in Mathematica 10 but it does in Mathematica 8. I need some similar in version 10. What can I do? ...
2
votes
1answer
76 views

FullSimplify gives wrong answer when operating on HypergeometricPFQ

When I try to simplify this hypergeometric function FullSimplify[HypergeometricPFQ[{1/2 - n/2}, {-(1/2) - n/2}, -a^2]] Mathematica 10.0.1.0 returns ...
1
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1answer
39 views

Why doesn't Simplify use my own TransformationFunction?

I define a simple TransformationFunctions via: tfTest[e_] := e /. {x^2 -> Hold[x*x]} and try to use it with ...
5
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0answers
52 views

External and internal Assumptions on `PiecewiseExpand` and `Mod`

After this question I'm intrigued about the different behaviors depending where and how the assumptions are given. ...
1
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1answer
45 views

Simplify Mod to subtraction when possible

FullSimplify[Mod[t,10], t>101 && t<109] It's a long shot, but can I get Mathematica to return t-100 or something ...
3
votes
2answers
59 views

To simplify an expression further

I have solved the following Eq to get hz: ...
1
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0answers
91 views

General suggestions to accelerate Simplify and FullSimplify

To my understanding, the function Simplify[] and FullSimplify[] work by applying a series of built-in transformation rules to ...
0
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0answers
30 views

Solve for parameters to minimize expression complexity?

I have a set of complicated expressions cf[i] with i=1,...,35 that apart from constants depend on parameters ...
4
votes
0answers
90 views

Simple arithmetic with Irrationals fails [closed]

While solving a simple puzzle that asked for a few calculations in plane geometry, I ended up with this expression: $-\frac{55}{2}+\frac{\sqrt{27233}}{2}+\frac{1}{2}(55-\sqrt{27233})$ Or, in ...
0
votes
2answers
88 views

Simplify square root term by taking variable inside root

I want to simplify expression $\frac{\sqrt{1+b+b^2}}{b}$ to$\sqrt{1+\frac{1}{b^2}+\frac{1}{b}}$. How to achieve this?
0
votes
0answers
76 views

Solve Always with Assumptions

How can I use the Solve Always function imposing some assumption on the parameter space of the symbolic variables? Thanks!
0
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1answer
47 views

Get dominant terms in asymptotic expansion

I'd like to find the dominant terms of an expression given the conditions $x,y >> 1$: $c_0 y+\frac{y^2 \left(4 c_0^2 y - 12 c_1 c_2^2+y^2\right)}{24 x^2 \left(\text{c1}^2+\text{c2}^2+y\right)}$ ...
1
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0answers
66 views

“Reduce” works fine for a non-linear system with 9 equations, but cannot solve it if 10 equations. Any ways to improve the code?

I am trying to solve a class of problems, which are basically about a solution to a system of non-linear equations subject to the constraint that some subset of solutions must be non-decreasing. I ...
2
votes
2answers
176 views

Why doesn't Mathematica pull out common factor when simplifing sums of square roots?

Why can't Mathematica pull out the common factor in the following expression when FullSimplifying, to see that it is zero? ...
3
votes
0answers
33 views

commutative matching

I've been doing some work that results in the creation of hundreds or thousands of equations with the same answer. To prevent them from collapsing to their simple answers, each has been passed through ...
8
votes
4answers
590 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 ...
3
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1answer
44 views

Simplifying nested KroneckerProducts

Any suggestion how to bring a nested KroneckerProduct form into just one? I mean some how converting ...
6
votes
0answers
46 views

Unexpected behaviour of Simplify

I'm evaluating an expression and to me the result should be True but Mathematica is giving me a different result. ...
3
votes
1answer
52 views

How to get Mathematica to make further simplifications to conditional expressions than it has already made?

I have the following Mathematica result under the assumption that {ax, bx, px, ay, by, py} \[Element] Reals, and after refinement by ...
11
votes
1answer
179 views

Why is this evaluation halved when adding units?

Why does this strange behavior occur when dealing with units and quantities? ...
0
votes
1answer
104 views

Why doesn't mathematica replace $\frac{I_0(\kappa)}{I_0(\kappa)}$ by 1 [closed]

I have a matrix of the form: $$\left( \begin{array}{ccc} 1 & \frac{\delta I_1(\kappa )}{I_0(\kappa )} & 0 \\ \frac{I_1(\kappa ) \delta ^*}{I_0(\kappa )} & \frac{\delta (I_1(\kappa ...