LaTeX

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    E. Rocha
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    Mathdir uses the package QuickLaTeX. This package allows easy inclusion of math formulas and graphics using LaTeX & TikZ. One of the main advantages over similar services is the capability of using native LaTeX syntax directly in the forums, posts, pages and comments without special enclosing tags for every equation.

    Features
    Support of native LaTeX shorthands embedded in the text:

    • $ … $, \[ … \], \( … \), $$ … $$ and environments: equation, align, displaymath, eqnarray, multline, flalign, gather, and alignat.
    • Equation auto-numbering/labeling/referencing by LaTeX rules. Manual equation number setup by \tag{} command, label by \label{} and referencing by \ref{} anywhere in the text.
    • Allows custom LaTeX preamble to use additional \usepackage{} and \newcommand{}.
    • TikZ graphics support. User can write TikZ commands directly in the post using \begin{tikzpicture} … \end{tikzpicture}. QuickLaTeX will render them into image such that text on the picture and on the page will be of the same size.
    • Correct vertical formula positioning relative to baseline of surrounding text. QuickLaTeX calculates correct vertical alignment for the formulas and places them on the text line properly without “jumpy” look.
    • Rendering into vector image format SVG, which means formulas are always crisp and preserve high-resolution quality regardless of zooming factor in the browser. Automatic detection of browser capabilities and silent fall back to raster PNG images for older browsers. This is essential for modern high-dpi screens (Retina, Super Amoled, etc.)
    • Meaningful error messages for mistakes in LaTeX code.
    • Although using native LaTeX syntax is recommended, legacy equations enclosed with (latex) … (\latex), (math) … (\math) are still supported, but replacing in the previous commands “(” and “)” by “[” and “]”, respectively. No need to change existing pages.
      Just use native LaTeX syntax for new pages.

    For further information, please see the QuickLaTeX website.


    The following content should render correctly.

    Example 1:
    At first, we sample f(x) in the N (N is odd) equidistant points around x^*

        \[ f_k=f(x_k), \:\: x_k = x^*+kh, \:\: k=-\frac{N-1}{2},\dots, \frac{N-1}{2}, \]

    where h is some step.
    Then we interpolate points {(x_k, f_k)} by polynomial

    (1)   \begin{equation*}  P_{N-1}=\sum_{j=0}^{N-1} a_j x^j \end{equation*}

    Its coefficients {a_j} are found as a solution of the system of linear equations:

    (2)   \begin{equation*}  \left\{P_{N-1}(x_k)=f_k\right\}, \:\: k=-\frac{N-1}{2},\dots, \frac{N-1}{2}. \end{equation*}

    From (1) and (2) you can deduce… “the rest”.

    Example 2:

    Rendered by QuickLaTeX.com

    • This topic was modified 2 years, 1 month ago by Profile photo of E. Rocha E. Rocha.
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    • This topic was modified 2 years, 1 month ago by Profile photo of E. Rocha E. Rocha.
    • This topic was modified 2 years, 1 month ago by Profile photo of E. Rocha E. Rocha.
    • This topic was modified 2 years, 1 month ago by Profile photo of E. Rocha E. Rocha.
    • This topic was modified 2 years, 1 month ago by Profile photo of E. Rocha E. Rocha.
    • This topic was modified 2 years, 1 month ago by Profile photo of E. Rocha E. Rocha.

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