\begin{algorithm}[H]
    \begin{enumerate}
        \item Fix a degree $d$, starting from $d=1$.
        \item Find all curves at degree $d$, and form the set $\mathcal{S}:=\{\mathcal{C}\in \mathcal{M}_X|\text{deg}(\mathcal{C})=d\}$. Since at linear order $\psi^{\vec{n}}=q^{\vec{n}}$, the GW or GV invariants can be read off from the coefficient of the corresponding monomial in $\mathcal{F}_a^{\text{inst.}}$, cf.~\eqref{eq:rerepeatperturbative_GV_formula}.  Thus, we extract all invariants from the curves in $S$.
        \item Compute either $q^{\vec{n}}$ or $\text{Li}_2(q^{\vec{n}})$ for all curves in $\mathcal{S}$ in parallel. This is the most expensive step in the entire algorithm, as it involves many polynomial multiplications. To improve efficiency, we keep some intermediate results, so that subsequent computations require fewer polynomial multiplications.
        \item Subtract the computed terms, multiplied by the appropriate factor, so as to eliminate the corresponding monomials in $\mathcal{F}_a^{\text{inst.}}$.
        \item Increment $d$ by one, and repeat from the first step, until the maximum degree is reached.
    \end{enumerate}
    \caption{Find enumerative invariants iteratively.}
\end{algorithm}

\begin{algorithm}
[H]
\begin{enumerate}
\item Fix a degree $d$, starting from $d=1$.
\item Find all curves at degree $d$, and form the set $\mathcal{S}:=\{\mathcal{C}\in \mathcal{M}_X|\text{deg}(\mathcal{C})=d\}$. Since at linear order $\psi^{\vec{n}}=q^{\vec{n}}$, the GW or GV invariants can be read off from the coefficient of the corresponding monomial in $\mathcal{F}_a^{\text{inst.}}$, cf.~\eqref{eq:rerepeatperturbative_GV_formula}. Thus, we extract all invariants from the curves in $S$.
\item Compute either $q^{\vec{n}}$ or $\text{Li}_2(q^{\vec{n}})$ for all curves in $\mathcal{S}$ in parallel. This is the most expensive step in the entire algorithm, as it involves many polynomial multiplications. To improve efficiency, we keep some intermediate results, so that subsequent computations require fewer polynomial multiplications.
\item Subtract the computed terms, multiplied by the appropriate factor, so as to eliminate the corresponding monomials in $\mathcal{F}_a^{\text{inst.}}$.
\item Increment $d$ by one, and repeat from the first step, until the maximum degree is reached.
\end{enumerate}
\caption{Find enumerative invariants iteratively.}
\end{algorithm}
{
    "title": "computational mirror symmetry",
    "id": "2303.00757",
    "abstract": "we present an efficient algorithm for computing the prepotential in compactifications of type ii string theory on mirror pairs of calabi-yau threefolds in toric varieties. applying this method, we exhibit the first systematic computation of genus-zero gopakumar-vafa invariants in compact threefolds with many moduli, including examples with up to 491 vector multiplets.",
    "categories": "hep-th",
    "doi": "",
    "created": "2023-03-01",
    "updated": "2024-01-19",
    "authors": [
        "mehmet demirtas",
        "manki kim",
        "liam mcallister",
        "jakob moritz",
        "andres rios-tascon"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2303.00757"
}
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