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Then the word problem in is solvable: given two words , in the generators of , write them as words in and compare them using the solution to the word problem in . It is easy to think that this demonstrates a uniform solution of the word problem for the class K {\displaystyle K} (say) of finitely generated groups that can be embedded in G ...
This operation is known as reduction, and it does not change the group element represented by the word. Reductions can be thought of as relations (defined below) that follow from the group axioms. A reduced word is a word that contains no redundant pairs. Any word can be simplified to a reduced word by performing a sequence of reductions:
Microsoft Math Solver (formerly Microsoft Mathematics and Microsoft Math) is an entry-level educational app that solves math and science problems. Developed and maintained by Microsoft , it is primarily targeted at students as a learning tool.
Microsoft is a developer of personal computer software. It is best known for its Windows operating system , the Internet Explorer and subsequent Microsoft Edge web browsers, the Microsoft Office family of productivity software plus services, and the Visual Studio IDE.
Microsoft Word is a word processing program developed by Microsoft.It was first released on October 25, 1983, [13] under the name Multi-Tool Word for Xenix systems. [14] [15] [16] Subsequent versions were later written for several other platforms including: IBM PCs running DOS (1983), Apple Macintosh running the Classic Mac OS (1985), AT&T UNIX PC (1985), Atari ST (1988), OS/2 (1989 ...
Microsoft 365 is a family of productivity software, collaboration and cloud-based services, encompassing online services, products formerly marketed under Microsoft Office, and enterprise products and services. This list contains all the programs that are, or have been, in Microsoft Office since it was released for classic Mac OS in 1989, and ...
The word problem for an algebra is then to determine, given two expressions (words) involving the generators and operations, whether they represent the same element of the algebra modulo the identities. The word problems for groups and semigroups can be phrased as word problems for algebras. [1]
Microsoft Graph (originally known as Microsoft Chart) is an OLE application deployed by Microsoft Office programs such as Excel and Access to create charts and graphs. The program is available as an OLE application object in Visual Basic. Microsoft Graph supports many different types of charts, but its output is dated.