Report for: Intelligent Computer Mathematics

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Chapter title	Computer certified efficient exact reals in Coq
Chapter number	7
Book title	Intelligent Computer Mathematics
Published in	arXiv, May 2011
DOI	10.1007/978-3-642-22673-1_7
Book ISBNs	978-3-64-222672-4, 978-3-64-222673-1
Authors	Robbert Krebbers, Bas Spitters, Krebbers, Robbert, Spitters, Bas
Abstract	Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. We provide an implementation of the exact real numbers in the Coq proof assistant. This improves on the earlier Coq-implementation by O'Connor in two ways: we use dyadic rationals built from the machine integers and we optimize computation of power series by using approximate division. Moreover, we use type classes for clean mathematical interfaces. This appears to be the first time that type classes are used in heavy computation. We obtain over a 100 times speed up of the basic operations and indications for improving the Coq system.

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Geographical breakdown

Country	Count	As %
United States	2	100%

Demographic breakdown

Type	Count	As %
Members of the public	2	100%

Mendeley readers

The data shown below were compiled from readership statistics for 8 Mendeley readers of this research output. Click here to see the associated Mendeley record.

Geographical breakdown

Country	Count	As %
Austria	1	13%
Unknown	7	88%

Demographic breakdown

Readers by professional status	Count	As %
Student > Ph. D. Student	4	50%
Researcher	2	25%
Student > Master	1	13%
Unknown	1	13%

Readers by discipline	Count	As %
Computer Science	5	63%
Mathematics	2	25%
Unknown	1	13%

Attention Score in Context

This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 21 January 2013.

All research outputs

#13,855,025

of 22,647,730 outputs

Outputs from arXiv

#249,574

of 927,543 outputs

Outputs of similar age

#80,039

of 109,768 outputs

Outputs of similar age from arXiv

#467

of 1,052 outputs

Altmetric has tracked 22,647,730 research outputs across all sources so far. This one is in the 37th percentile – i.e., 37% of other outputs scored the same or lower than it.

So far Altmetric has tracked 927,543 research outputs from this source. They receive a mean Attention Score of 3.9. This one has gotten more attention than average, scoring higher than 70% of its peers.

Older research outputs will score higher simply because they've had more time to accumulate mentions. To account for age we can compare this Altmetric Attention Score to the 109,768 tracked outputs that were published within six weeks on either side of this one in any source. This one is in the 26th percentile – i.e., 26% of its contemporaries scored the same or lower than it.

We're also able to compare this research output to 1,052 others from the same source and published within six weeks on either side of this one. This one has gotten more attention than average, scoring higher than 55% of its contemporaries.

Intelligent Computer Mathematics

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Attention Score in Context