Update LaTeX style guide to deal with brackets (#6069)

packages/gollm/common/prompts/latex_style_guide.py

@@ -6,13 +6,14 @@
 3) All variables that have time "t" dependence should be written with an explicit "(t)" (for example, "X" should be written as "X(t)")
 4) Rewrite superscripts and LaTeX superscripts "^" that denote indices to subscripts using LaTeX "_"
 5) Replace any unicode subscripts with LaTeX subscripts using "_". Ensure that all characters used in the subscript are surrounded by a pair of curly brackets "{{...}}"
-6) Avoid parentheses
-7) Avoid capital sigma and pi notations for summation and product
-8) Avoid non-ASCII characters when possible
-9) Avoid using homoglyphs
-10) Avoid words or multi-character names for variables and names. Use camel case to express multi-word or multi-character names
-11) Use " * " to denote multiplication between scalar quantities
-12) Replace any variant form of Greek letters to their main form when representing a variable or parameter; "\\varepsilon" -> "\\epsilon", "\\vartheta" -> "\\theta", "\\varpi" -> "\\pi", "\\varrho" -> "\\rho",  "\\varsigma" -> "\\sigma", "\\varphi" -> "\\phi"
-13) If equations are separated by punctuation (like comma, period, semicolon), do not include the punctuation in the LaTeX code.
-14) Expand all algebraic expressions with parentheses according to distributivity property of multiplication (for example, "S(t) * (a * I(t) + b * D(t) + c * A(t))" -> "a * S(t) * I(t) + b * S(t) * D(t) + c * A(t) * S(t)")
+6) Do not use square brackets "[ ]", curly braces "{ }", and angle brackets "< >" when grouping algebraic expressions; use parentheses "( )" when necessary
+7) Expand time-dependent algebraic expressions grouped by parentheses according to distributivity property of multiplication (for example, "S(t) * (a * I(t) + b * D(t) + c * A(t))" -> "a * S(t) * I(t) + b * S(t) * D(t) + c * A(t) * S(t)")
+8) Do not expand constant algebraic expressions grouped by parentheses; for example, "a * b * (1 - c)" should not be expanded since "a", "b", "c" are constants
+9) Avoid capital sigma and pi notations for summation and product
+10) Avoid non-ASCII characters when possible
+11) Avoid using homoglyphs
+12) Avoid words or multi-character names for variables and names. Use camel case to express multi-word or multi-character names
+13) Use " * " to denote multiplication; for example, "b S(t) I(t)" -> "b * S(t) * I(t)"
+14) Replace any variant form of Greek letters to their main form when representing a variable or parameter; "\\varepsilon" -> "\\epsilon", "\\vartheta" -> "\\theta", "\\varpi" -> "\\pi", "\\varrho" -> "\\rho",  "\\varsigma" -> "\\sigma", "\\varphi" -> "\\phi"
+15) If equations are separated by punctuation (like comma, period, semicolon), do not include the punctuation in the LaTeX code.
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