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The use of LaTeX in a piped link or in a section heading does not appear in blue in the linked text or the table of content. Moreover, links to section headings containing LaTeX formulas do not always work as expected. Finally, having many LaTeX formulas may significantly increase the processing time of a page.
The algorithm will then find the breakpoints that will minimize the sum of squares of the badness (including penalties) of the resulting lines. If the paragraph contains n {\displaystyle n} possible breakpoints, the number of situations that must be evaluated naively is 2 n {\displaystyle 2^{n}} .
The above formulas lead to an efficient O(log a log b) [3] algorithm for calculating the Jacobi symbol, analogous to the Euclidean algorithm for finding the gcd of two numbers. (This should not be surprising in light of rule 2.) Reduce the "numerator" modulo the "denominator" using rule 2. Extract any even "numerator" using rule 9.
The appearance of this odd number is explained by a still more general result, known as the handshaking lemma: any graph has an even number of vertices of odd degree. [17] Finally, the even number of odd vertices is naturally explained by the degree sum formula. Sperner's lemma is a more advanced application of the same strategy.
LaTeX (/ ˈ l ɑː t ɛ k / ⓘ LAH-tek or / ˈ l eɪ t ɛ k / LAY-tek, [2] [Note 1] often stylized as L a T e X) is a software system for typesetting documents. [3] LaTeX markup describes the content and layout of the document, as opposed to the formatted text found in WYSIWYG word processors like Google Docs, LibreOffice Writer, and Microsoft Word.
The zeta function values listed below include function values at the negative even numbers (s = −2, −4, etc.), for which ζ(s) = 0 and which make up the so-called trivial zeros. The Riemann zeta function article includes a colour plot illustrating how the function varies over a continuous rectangular region of the complex plane.
On paper, write down in one column the numbers you get when you repeatedly halve the multiplier, ignoring the remainder; in a column beside it repeatedly double the multiplicand. Cross out each row in which the last digit of the first number is even, and add the remaining numbers in the second column to obtain the product.
Horner's method can be used to convert between different positional numeral systems – in which case x is the base of the number system, and the a i coefficients are the digits of the base-x representation of a given number – and can also be used if x is a matrix, in which case the gain in computational efficiency is even greater.