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List of matrices; List of numbers; List of relativistic equations; List of small groups; Mathematical constants; Sporadic group; Table of Clebsch-Gordan coefficients; Table of derivatives; Table of divisors; Table of integrals; Table of mathematical symbols; Table of prime factors; Taylor series; Timeline of mathematics; Trigonometric ...
Here, the list [0..] represents , x^2>3 represents the predicate, and 2*x represents the output expression.. List comprehensions give results in a defined order (unlike the members of sets); and list comprehensions may generate the members of a list in order, rather than produce the entirety of the list thus allowing, for example, the previous Haskell definition of the members of an infinite list.
An infinite series of any rational function of can be reduced to a finite series of polygamma functions, by use of partial fraction decomposition, [8] as explained here. This fact can also be applied to finite series of rational functions, allowing the result to be computed in constant time even when the series contains a large number of terms.
Another method of grouping the data is to use some qualitative characteristics instead of numerical intervals. For example, suppose in the above example, there are three types of students: 1) Below normal, if the response time is 5 to 14 seconds, 2) normal if it is between 15 and 24 seconds, and 3) above normal if it is 25 seconds or more, then the grouped data looks like:
Before version 3.0, Python had two kinds of classes (both using the same syntax): old-style and new-style; [113] current Python versions only support the semantics of the new style. Python supports optional type annotations. [4] [114] These annotations are not enforced by the language, but may be used by external tools such as mypy to catch errors.
gretl is an example of an open-source statistical package. ADaMSoft – a generalized statistical software with data mining algorithms and methods for data management; ADMB – a software suite for non-linear statistical modeling based on C++ which uses automatic differentiation; Chronux – for neurobiological time series data; DAP – free ...
The Cayley table tells us whether a group is abelian. Because the group operation of an abelian group is commutative, a group is abelian if and only if its Cayley table's values are symmetric along its diagonal axis. The group {1, −1} above and the cyclic group of order 3 under ordinary multiplication are both examples of abelian groups, and ...
Subgroup series can simplify the study of a group to the study of simpler subgroups and their relations, and several subgroup series can be invariantly defined and are important invariants of groups. A subgroup series is used in the subgroup method. Subgroup series are a special example of the use of filtrations in abstract algebra.