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The first rule that applies to a particular part is used; no further rules are tried on that part or on any of its subparts. ReplaceAll applies a particular rule only once to an expression. expr /. rules returns expr if none of the rules apply. ReplaceAll [ rules] [ expr] is equivalent to ReplaceAll [ expr, rules].

Comprehensive documentation for Mathematica and the Wolfram Language. Details and examples for functions, symbols, and workflows. Organized by functionality ...

Widely admired for both its technical prowess and elegant ease of use, Mathematica provides a single integrated, continually expanding system that covers the breadth and depth of technical computing—and is seamlessly available in the cloud through any web browser, as well as natively on all modern desktop systems.

Feb 05, 2013 · $\begingroup$ Note that Mathematica can calculate symbolic results for the roots of any polynomial of order 3 or 4, as well as certain higher-order polynomials; it just doesn't do so by default. Use ToRadicals to get Mathematica to (attempt to) expand these Root objects. $\endgroup$ –

Widely admired for both its technical prowess and elegant ease of use, Mathematica provides a single integrated, continually expanding system that covers the ...

Dec 15, 2021 · Mathematica applies expertise at the intersection of data, methods, policy, and practice to improve well-being around the world. We translate big questions into deep insights that improve programs, refine strategies, and enhance understanding.

04.02.2013 · If you want to define a function, y ( x) = x 2, you just could do: f = #^2 &. The & "pumps in" the expression into the # sign. That is important for pairing & and # when you have nested functions. f [2] (* 4 *) If you have a function operating on two variables, you could do: f …

gives a list of the parts i1, i2, ... of expr. expr[[m ;; n]] gives parts m ... gives the value associated with an arbitrary key k in the association expr.

Parentheses are used in Mathematica only to group arithmetic expressions: 8 / (2 + 3) (4-a) * 6. If you don't keep these straight you will have problems in your programs. Capitalization: Another common syntax mistake is the naming of built-in Mathematica functions. Mathematica functions are always capitalized.

Map[f, expr] or f /@ expr applies f to each element on the first level in expr. Map[f, expr, levelspec] applies f to parts of expr specified by levelspec.

Details. When Function [ body] or body & is applied to a set of arguments, # (or #1) is replaced by the first argument, #2 by the second, and so on. #0 is replaced by the function itself. If there are more arguments supplied than # i in the function, the remaining arguments are ignored. ».

Latest Features in Mathematica 13. Details about featured Mathematica 12 functionality: symbolic & numeric computations, visualization & graphics, geometry & geography, data science & computation, image & audio, machine learning, notebook interface & core language, real-world systems, external & database operations, Wolfram Knowledgebase.

expr /. rules or ReplaceAll[expr, rules] applies a rule or list of rules in an attempt to transform each subpart of an expression expr.

15.12.2021 · Mathematica applies expertise at the intersection of data, methods, policy, and practice to improve well-being around the world. We translate big questions into deep insights that improve programs, refine strategies, and enhance understanding.

The Wolfram Language not only has systemwide support for arbitrary Unicode characters, but also includes nearly a thousand carefully designed characters for ...

Wolfram Mathematica is a software system with built-in libraries for several areas of technical computing that allow machine learning, statistics, symbolic computation, manipulating matrices, plotting functions and various types of data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other programming languages. It was conceived by Stephen Wolfram, and is developed by Wolfram Research of Champaign, Illinois. The Wolfram …

The Wolfram Language has a rich syntax carefully designed for consistency and efficient, readable entry of the Wolfram Language's many language, ...

Mathematica 11 provides integrated tools that yet again vastly expand the scope of cross-domain projects that can routinely be done by users at all levels. Mathematica 11 builds on Wolfram's recent R&D breakthroughs in a host of areas—including neural network computation, audio integration and linguistic computing.

4 PROGRAMMING IN MATHEMATICA, A PROBLEM-CENTRED APPROACH 1. Introduction In this section we give a quick introduction to the very basic things one can perform with Mathematica. 1.1. Mathematica as a calculator. Mathematica can be used as a calculator with the basic arith-metic operations +; ; ;= and ^ for powers. 2682440^4 + 15365639^4 + 18796760^4

The solution given by DSolve is a list of lists of rules. The outermost list encompasses all the solutions available, and each smaller list is a particular solution. If you want to use a solution as a function, first assign the rule to something, in this case, solution: Copy to clipboard. In [2]:=.

or x∈dom asserts that x is an element of the domain dom. Copy to clipboard. ✖. Element[x,reg].

Shorthand notations are a part of the Wolfram Language 's rich syntax system that allows multiple ways to feed arguments to functions.