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The class number of a number field is by definition the order of the ideal class group of its ring of integers. Thus, a number field has class number 1 if and only if its ring of integers is a principal ideal domain (and thus a unique factorization domain). The fundamental theorem of arithmetic says that Q has class number 1.
JPXDecode, a lossy or lossless filter based on the JPEG 2000 standard, introduced in PDF 1.5. Normally all image content in a PDF is embedded in the file. But PDF allows image data to be stored in external files by the use of external streams or Alternate Images. Standardized subsets of PDF, including PDF/A and PDF/X, prohibit these features.
Google Classroom is a free blended learning platform developed by Google for educational institutions that aims to simplify creating, distributing, and grading assignments. . The primary purpose of Google Classroom is to streamline the process of sharing files between teachers and students.
Google Code Search was a free beta product from Google which debuted in Google Labs on October 5, 2006, allowing web users to search for open-source code on the Internet. Features included the ability to search using operators, namely lang: , package: , license: , and file: .
For given low class number (such as 1, 2, and 3), Gauss gives lists of imaginary quadratic fields with the given class number and believes them to be complete. Infinitely many real quadratic fields with class number one Gauss conjectures that there are infinitely many real quadratic fields with class number one.
In object-oriented programming, a class defines the shared aspects of objects created from the class. The capabilities of a class differ between programming languages, but generally the shared aspects consist of state and behavior that are each either associated with a particular object or with all objects of that class. [1] [2]
Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.