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

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1answer
139 views
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54 views

Handling Accuracy and Simplifying

I have the following problem. I have a system of non-linear equations that I log-linearize around a certain point, let's call it point A, using a function that I ...
4
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2answers
134 views

Remove redundant parameters from equation

I have random expressions like (b1 x + b2 x)/(b3 + b4/b5 x) + Sin[b6 x] where $x$ is a variable and {b1, ..., b6} are parameters to be fitted. This expression is ...
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1answer
49 views

Why don't these assumptions result in further simplification?

I'm trying to simplify an expression, which has a factor of $\lambda(\lambda-1)$, where $\lambda$ may be either $1$, or $0$. So I try: ...
2
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1answer
51 views

Is there a simple function identify the sign of an expression given constraints

I'm looking to find a simple function that can identify the sign of an expression given a set of constraints. I have looked around and do see that there is a few threads on this but I'm not sure I ...
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1answer
104 views

How can I simplify this implicit equation to an explicit equation

How can I simplify this implicit equation to an explicit equation: Tan[5 y/12] - (7 y/((x)^2 + (y)^2 - (3.5)^2)) == 0 i.e: $y=f(x)$ where $y$ is a explicit ...
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2answers
70 views

Convert imaginary exponentials to goniometric expressions?

Can I force Mathematica to re-express something like $$\left\{\frac{1}{2}i\left(\frac{1}{16} e^{-2 i (\alpha (1)+4 \alpha (2))} \left(-1+e^{8 i \alpha (2)}\right) \text{d$\alpha $}(1) \left(2 \left(2 ...
-2
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1answer
178 views

Why is it so complicated to simplify a complex conjugate? [closed]

My question is very simple. I would like to multiply a complex number by its conjugate. Unfortunately, this seems to be extremely complicated in Mathematica. Consider the very basic example: ...
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0answers
28 views

Expanding Function Based on Congruence Classes

I'm trying to get Mathematica to expand $\quad \quad \beta_n=\sum_{r=0}^{n}\frac{\alpha_r}{(q^4;q^4)_{n-r}(q^4;q^4)_{n+r}},$ where $\alpha_r$ is an integer valued sequence that is given by ...
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1answer
44 views

Simplifying a fraction with bringing in new variables

Let's say I have a fraction like this: (a b x^2 + a^3 x) / (a^2 b x) and I would like to simplify it by multiplying both the numerator and the denominator with ...
0
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0answers
50 views

Simplification of a complex-valued expression with purely real components

(I'm including all the information here, as I'm not sure how much of it is necessary to solve the problem. For a tl;dr skip to the bottom) I've been working on a problem involving calculating ...
1
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2answers
198 views

How do I check to see if two expressions are equal?

This is what I am trying: (2 x - 2 Sqrt[x (x - v)] - v)/(2 x + 2 Sqrt[x (x - v)] - v) == (Sqrt[x] - Sqrt[x - v])^4/v^2 but it's not working. Can someone tell me ...
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1answer
50 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
242 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
140 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 ...
1
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2answers
63 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
350 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: ...
5
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2answers
123 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
271 views

Mathematica doesn't simplify a simple expression

The question is simple as that. I have: ...
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0answers
40 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
38 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 ...
10
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1answer
313 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 ...
2
votes
1answer
152 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
75 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 ...
5
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1answer
168 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
95 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 ...
6
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2answers
227 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: ...
0
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2answers
74 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
51 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) ...
2
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2answers
177 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 $P(x)=‎‏0‏‎$, using ...
3
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1answer
161 views

Why do I get Floor and Ceiling in my output despite my assumptions

I am trying to simplify the following expression. ...
5
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1answer
202 views

Why does Mathematica not simplify this expression?

Consider this simple example: ...
1
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1answer
88 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
170 views

Simplify product of square roots

What assumption is needed to make both outputs equal to Sqrt[P^2]/2 ...
3
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2answers
242 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)
2
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1answer
393 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 ...