Mathematic equation ------------------- Math mode ~~~~~~~~~ ANGEL also enables expression a variety of mathematical equation in the same manner as TeX and LaTeX. In ANGEL , there is no math mode like LaTeX. Most of the commands described below can only be used in math mode in LaTeX. But, in ANGEL they can be used in normal mode as they are. Noted that, even with ANGEL , there is a math mode that is sandwiched between ``$   $``. In the part between ``$   $``, the alphabetic characters are italicized, and symbols such as ``=,-, +`` are automatically changed to the symbol typeface, making the appearance as a math formula better. Space control ~~~~~~~~~~~~~ In the math mode of ANGEL , as in the normal mode, half-width spaces are treated as actual half-width spaces except for the half-width spaces after the special command that starts with ``\``. However, there are space control commands similar to LaTeX for fine space control. .. list-table:: Commands for space control :name: table-ref-math-spacing :align: center :class: image-table * - .. image:: assets/fon008e.png :width: 483.5pt :class: responsive-figure | :math:`^1` ``\quad`` is to put a 10-point space if you use 10-point characters in the text. Suffix ~~~~~~ The subscript is written after the ``_`` symbol, and the superscript is written after the ``^`` symbol. If the subscript is not a single character, enclose it in ``{   }``. You can also use superscripts and subscripts at the same time. Also, it can be attached in multiple layers. Fraction ~~~~~~~~ The format of the fraction is the same as LaTeX, using ``\``\ ``frac{  }{  }``. Specify the numerator in the first argument and the denominator in the second argument. This command corresponds to a separate fraction expression of LaTeX. In LaTeX text, this fraction is output in small letters. Since ANGEL does not make this distinction, the fractional expression output in small characters is ``\``\ ``fracs{  }{  }``. The input and output of the example are shown below. .. list-table:: Fraction :name: table-ref-fractions :align: center :class: image-table * - .. image:: assets/fon009e.png :width: 483.5pt :class: responsive-figure Square root ~~~~~~~~~~~ Use the command ``\``\ ``sqrt`` to represent the square root. For example, to output :math:`\sqrt{x}`, write ``\sqrt{x}``. Even if you put a long formula in the x part, it will be automatically expanded. However, in the case of ANGEL , unlike LaTeX, the square root symbol does not extend up or down. Therefore, large fractions and subscripts will be out of the square root symbol. .. list-table:: Square root :name: table-ref-square-roots :align: center :class: image-table * - .. image:: assets/fon024e.png :width: 483.5pt :class: responsive-figure Greek alphabet ~~~~~~~~~~~~~~ Greek letters are often used in mathematical formulas. The following Greek letters can be used anywhere in ANGEL . .. list-table:: Greek lowercase :name: table-ref-greek-lowercase :align: center :class: image-table * - .. image:: assets/fon010e.png :width: 483.5pt :class: responsive-figure A variant typeface exists in some Greek lowercase letters. .. list-table:: Variant typeface of Greek lowercase :name: table-ref-greek-variants :align: center :class: image-table * - .. image:: assets/fon011e.png :width: 483.5pt :class: responsive-figure The command to output the uppercase Greek letter is the capitalized English name following ``\``. .. list-table:: Uppercase Greek :name: table-ref-greek-uppercase :align: center :class: image-table * - .. image:: assets/fon012e.png :width: 483.5pt :class: responsive-figure Math accent ~~~~~~~~~~~ ANGEL does not have the same math mode as LaTeX, so you can use regular accent command as well. You can also use the following LaTeX math accents. Here is an example of accenting :math:`a`. .. list-table:: Math accent :name: table-ref-math-accents :align: center :class: image-table * - .. image:: assets/fon013e.png :width: 483.5pt :class: responsive-figure There are also large math accents such as: .. list-table:: Large math accents :name: table-ref-wide-math-accents :align: center :class: image-table * - .. image:: assets/fon014e.png :width: 483.5pt :class: responsive-figure Math ruby ~~~~~~~~~ | You can put a variable name above the arrow and a symbol below the equal sign. The format and function are almost the same as the Chinese character ruby. .. container:: minipage angel-doublebox | 　``\mathop{ 1st argument }``\ ``^``\ ``{ 2nd argument }`` | 　``\mathop{ 1st argument }``\ ``_``\ ``{ 2nd argument }`` | If using ``^``, the second argument is placed in the upper center of the first argument. Meanwhile when using ``_``, the second argument is placed in the lower center of the first argument. An example is shown below. .. list-table:: Math ruby :name: table-ref-math-ruby :align: center :class: image-table * - .. image:: assets/fon025e.png :width: 483.5pt :class: responsive-figure Binary operator ~~~~~~~~~~~~~~~ It is a companion to the operators for addition and subtraction. .. list-table:: Binary operator :name: table-ref-binary-operators :align: center :class: image-table * - .. image:: assets/fon015e.png :width: 483.5pt :class: responsive-figure Relational operator ~~~~~~~~~~~~~~~~~~~ It is a companion to the equal sign :math:`=` and the inequality sign :math:`<, >`. .. list-table:: Relational operator :name: table-ref-relations :align: center :class: image-table * - .. image:: assets/fon016e.png :width: 483.5pt :class: responsive-figure Mathematical symbols ~~~~~~~~~~~~~~~~~~~~ They are mathematical symbols such as Planck’s constant :math:`\hbar`, infinity :math:`\infty`, and empty set :math:`\emptyset`. .. list-table:: Mathematical symbols :name: table-ref-math-symbols :align: center :class: image-table * - .. image:: assets/fon017e.png :width: 483.5pt :class: responsive-figure Arrows ~~~~~~ .. list-table:: Arrows :name: table-ref-arrows :align: center :class: image-table * - .. image:: assets/fon018e.png :width: 483.5pt :class: responsive-figure Mathematical function ~~~~~~~~~~~~~~~~~~~~~ If you write ``$log x$`` with the intention of outputting :math:`\log x`, you can get an unsightly output like :math:`log x`. Correctly write ``$\log x$`` using the command ``\log``. Mathematical functions in the following are available. .. list-table:: Mathematical function :name: table-ref-math-functions :align: center :class: image-table * - .. image:: assets/fon019e.png :width: 483.5pt :class: responsive-figure Large math symbol ~~~~~~~~~~~~~~~~~ For large mathematical symbols such as the sum symbols, there may be subscripts above and below the symbol. The following are the ones in which the subscripts fit neatly up and down. Each command with ``s`` at the end corresponds to when used inside the text line of LaTeX. .. list-table:: Large math symbol :name: table-ref-large-symbols :align: center :class: image-table * - .. image:: assets/fon020e.png :width: 483.5pt :class: responsive-figure Integral symbol ~~~~~~~~~~~~~~~ Integral symbols come in three sizes. .. list-table:: Integral symbol :name: table-ref-integrals :align: center :class: image-table * - .. image:: assets/fon021e.png :width: 483.5pt :class: responsive-figure Parentheses and delimiters ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. list-table:: Parentheses and delimiters :name: table-ref-delimiters :align: center :class: image-table * - .. image:: assets/fon022e.png :width: 483.5pt :class: responsive-figure The following parentheses come in three sizes. .. list-table:: Large parentheses :name: table-ref-large-delimiters :align: center :class: image-table * - .. image:: assets/fon023e.png :width: 483.5pt :class: responsive-figure