LibreOffice Math: Integral, Sum, and Product Formatting

LibreOffice Math provides a comprehensive set of markup commands to render and format integral, summation, and product symbols. This guide covers the syntax options for single and multiple integrals, contour integrals, standard summations, products, coproducts, and the methods used to position their upper and lower limits.

Integrals

LibreOffice Math supports various types of standard and contour integrals. You can create indefinite, definite, double, and line integrals using distinct keyword commands.

Basic Syntax and Multiple Integrals

• Single Integral: int
• Double Integral: iint
• Triple Integral: iiint

Contour and Closed-Path Integrals

• Single Contour Integral: lint
• Double Contour Integral: llint
• Triple Contour Integral: lllint

Adding Limits to Integrals

Limits can be positioned using the from and to operators, or by using subscript (_) and superscript (^) syntax: * Using from and to: int from {a} to {b} f(x) dx * Using sub/superscripts: int_{a}^{b} f(x) dx * Lower limit only: int from {0} f(x) dx or int_{0} f(x) dx * Upper limit only: int to {infinity} f(x) dx or int^{infinity} f(x) dx

Summations

The summation symbol (\(\sum\)) is rendered using the sum keyword.

Standard Formatting

• Full Summation with Range: sum from {i=1} to {n} {a_i}
• Condition-based Lower Limit: sum from {i in S} {x_i}
• Subscript/Superscript Alternative: sum_{i=1}^{n} {a_i}

Products and Coproducts

LibreOffice Math provides commands for both the standard capital Pi product operator (\(\prod\)) and the coproduct operator (\(\coprod\)).

Product Operator

• Standard Product: prod from {k=1} to {m} {x_k}
• Using Subscripts: prod_{k=1}^{m} {x_k}

Coproduct Operator

• Standard Coproduct: coprod from {i=1} to {n} {A_i}
• Using Subscripts: coprod_{i=1}^{n} {A_i}

Limit Positioning and Layout Adjustments

The placement and appearance of limits can be adjusted using specific formatting techniques:

from/to vs. Subscript/Superscript

• Using from {lower} to {upper} places limits centered directly above and below the operator in standalone display equations, and shifts them to the side when nested inside compact or inline text blocks.
• Using _{lower}^{upper} places limits as standard sub/superscripts to the right of the symbol.

Grouping Complex Limits

When upper or lower bounds contain multiple terms, spaces, or operations, wrap the expressions inside curly braces {} to ensure correct parsing: * Correct: sum from {i = 0, j = 0} to {infinity} {a_{i,j}} * Incorrect: sum from i = 0, j = 0 to infinity {a_{i,j}}

Size Scaling

To manually resize operators along with their limits, prefix the command with the size modifier: * Example: size +4 {int from {0} to {1} f(x) dx}