The utilization of advanced computing technology in mathematical research: new mathematical results discovered partly or entirely with the aid of computer-based tools.

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2answers
18 views

Partial fraction decomposition of 1/(e^x-1)

This link has discussion on finding partial fraction decomposition of $1/(e^x-1)$, so I experimented with Mathematica to see if M can do it, but looks like not. Similar is the case with one more CAS I ...
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0answers
48 views

How can I view piecewise cases considered by Reduce?

Caution: Run before removing comments from the commented-out code. If you have $MaxPiecewiseCases set to it's default, you will get an error message about the ...
3
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2answers
110 views

Getting the Cumulative Distribution Function of f(x) from a dataset of x

I've a data set $\mathcal{X}$ which consists of randomly generated numbers. Let's say for example data = RandomVariate[ExponentialDistribution[1], 10^4]; My aim ...
2
votes
3answers
111 views

Can you compute more terms in this sequence?

I am trying to identify a sequence related to the von Mangoldt function matrix. Since I believe/conjecture that the columns in the matrix have period lengths as in this sequence b: ...
2
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2answers
100 views

Making a conjecture concerning a certain upper-triangular matrix

I have searched for commands which will let me to create matrices and do matrix operations, but I don't know how to apply Mathematica to the following exercise. Make a conjecture for the result of ...
1
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2answers
75 views

factorization of integer into two parts with specific prime factors

I would like to write a Mathematica code to decompose an integer into two or more parts with primes in special intervals. For instance, I want to decompose $m=\binom{n}{k}$ into two parts U and V ...
3
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0answers
53 views

Does it help to do any preprocessing before `FindSequenceFunction`?

I am always amazed how smart FindSequenceFunction can be in discovering general term formula for a sequence of rational numbers. The documentation says it can work ...
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0answers
82 views

How to mathematically represent MMA 9 Spikey?

I am trying to figure out how to mathematically represent the MMA 9 Spikey in order to send to a 3D printer. According to this page, " In particular, spikeys for version 2 and up are based on a ...
0
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1answer
105 views

Integration of DiracDelta

I just came across the following curiosity and I'm not sure whether it's a bug or just me missing something. Here's a minimal example: I defined the following "function" ...
7
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1answer
174 views

Least Square Data Fit /Design Matrix

I am trying to learn how to use the DesignMatrix function in Mathematica and how to perform a LeastSquares fit. I am at end of ...
39
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10answers
2k views

Can Mathematica propose an exact value based on an approximate one?

Sometimes, I use Mathematica to do some hypothesis on homeworks to make the question easier. For instance, when I have to compute big sums when $n\to\infty$ and Mathematica can't give the exact ...