\begin{algorithm}[!ht]
\caption{3d Subspace Intersects Box} 
\begin{algorithmic}
	\Require
		\State \hspace{5mm}Boundary $\mathcal{S} = [-B,B[\times[-B,B[\times[-B,B[\times[-B,B[$
		\State \hspace{5mm}4d normal $N=(n_x,n_y,n_z,n_t)$ to 3d subspace $\mathcal{S_N}$
		\State \hspace{5mm}Point $V=(x,y,z,t)$ contained in $\mathcal{S_N}$
	\Ensure
		True if $\mathcal{S_N} \cap \mathcal{S} \neq \emptyset$, False otherwise
	\vspace{1mm}
\Procedure{}{}
    \vspace{1mm}
    \State $d \gets n_xx + n_yy + n_zz + n_tt$
    \State $nxB0 \gets -n_xB$
    \State $nyB0 \gets -n_yB$
    \State $nzB0 \gets -n_zB$
    \State $ntB0 \gets -n_tB$
    \State $nxB1 \gets n_x(B-1)$
    \State $nyB1 \gets n_y(B-1)$
    \State $nzB1 \gets n_z(B-1)$
    \State $ntB1 \gets n_t(B-1)$
    \State $s_0 \gets nxB0 + nyB0 + nzB0 + ntB0 - d$
    \State $s_1 \gets nxB1 + nyB0 + nzB0 + ntB0 - d$
    \State $s_2 \gets nxB0 + nyB1 + nzB0 + ntB0 - d$
    \State $s_3 \gets nxB1 + nyB1 + nzB0 + ntB0 - d$
    \State $s_4 \gets nxB0 + nyB0 + nzB1 + ntB0 - d$
    \State $s_5 \gets nxB1 + nyB0 + nzB1 + ntB0 - d$
    \State $s_6 \gets nxB0 + nyB1 + nzB1 + ntB0 - d$
    \State $s_7 \gets nxB1 + nyB1 + nzB1 + ntB0 - d$
    \State $s_8 \gets nxB0 + nyB0 + nzB0 + ntB1 - d$
    \State $s_9 \gets nxB1 + nyB0 + nzB0 + ntB1 - d$
    \State $s_a \gets nxB0 + nyB1 + nzB0 + ntB1 - d$
    \State $s_b \gets nxB1 + nyB1 + nzB0 + ntB1 - d$
    \State $s_c \gets nxB0 + nyB0 + nzB1 + ntB1 - d$
    \State $s_d \gets nxB1 + nyB0 + nzB1 + ntB1 - d$
    \State $s_e \gets nxB0 + nyB1 + nzB1 + ntB1 - d$
    \State $s_f \gets nxB1 + nyB1 + nzB1 + ntB1 - d$
	\State If all of $s_0,\dots,s_f$ have the same sign, return False, otherwise return True
\EndProcedure
\end{algorithmic}\label{alg1}
\end{algorithm}

\begin{algorithm}
[!ht]
\caption{3d Subspace Intersects Box}
\begin{algorithmic}
\Require
\State \hspace{5mm}Boundary $\mathcal{S} = [-B,B[\times[-B,B[\times[-B,B[\times[-B,B[$
\State \hspace{5mm}4d normal $N=(n_x,n_y,n_z,n_t)$ to 3d subspace $\mathcal{S_N}$
\State \hspace{5mm}Point $V=(x,y,z,t)$ contained in $\mathcal{S_N}$
\Ensure
True if $\mathcal{S_N} \cap \mathcal{S} \neq \emptyset$, False otherwise
\vspace{1mm}
\Procedure{}{}
\vspace{1mm}
\State $d \gets n_xx + n_yy + n_zz + n_tt$
\State $nxB0 \gets -n_xB$
\State $nyB0 \gets -n_yB$
\State $nzB0 \gets -n_zB$
\State $ntB0 \gets -n_tB$
\State $nxB1 \gets n_x(B-1)$
\State $nyB1 \gets n_y(B-1)$
\State $nzB1 \gets n_z(B-1)$
\State $ntB1 \gets n_t(B-1)$
\State $s_0 \gets nxB0 + nyB0 + nzB0 + ntB0 - d$
\State $s_1 \gets nxB1 + nyB0 + nzB0 + ntB0 - d$
\State $s_2 \gets nxB0 + nyB1 + nzB0 + ntB0 - d$
\State $s_3 \gets nxB1 + nyB1 + nzB0 + ntB0 - d$
\State $s_4 \gets nxB0 + nyB0 + nzB1 + ntB0 - d$
\State $s_5 \gets nxB1 + nyB0 + nzB1 + ntB0 - d$
\State $s_6 \gets nxB0 + nyB1 + nzB1 + ntB0 - d$
\State $s_7 \gets nxB1 + nyB1 + nzB1 + ntB0 - d$
\State $s_8 \gets nxB0 + nyB0 + nzB0 + ntB1 - d$
\State $s_9 \gets nxB1 + nyB0 + nzB0 + ntB1 - d$
\State $s_a \gets nxB0 + nyB1 + nzB0 + ntB1 - d$
\State $s_b \gets nxB1 + nyB1 + nzB0 + ntB1 - d$
\State $s_c \gets nxB0 + nyB0 + nzB1 + ntB1 - d$
\State $s_d \gets nxB1 + nyB0 + nzB1 + ntB1 - d$
\State $s_e \gets nxB0 + nyB1 + nzB1 + ntB1 - d$
\State $s_f \gets nxB1 + nyB1 + nzB1 + ntB1 - d$
\State If all of $s_0,\dots,s_f$ have the same sign, return False, otherwise return True
\EndProcedure
\end{algorithmic}\end{algorithm}
{
    "title": "an implementation of the extended tower number field sieve using 4d   sieving in a box and a record computation in fp4",
    "id": "2212.04999",
    "abstract": "we report on an implementation of the extended tower number field sieve (extnfs) and record computation in a medium characteristic finite field $\\mathbb{f}_{p^4}$ of 512 bits size. empirically, we show that sieving in a 4-dimensional box (orthotope) for collecting relations for extnfs in $\\mathbb{f}_{p^4}$ is faster than sieving in a 4-dimensional hypersphere. we also give a new intermediate descent method, `descent using random vectors', without which the descent stage in our extnfs computation would have been difficult/impossible, and analyze its complexity.",
    "categories": "cs.cr",
    "doi": "",
    "created": "2022-12-09",
    "updated": "2024-02-06",
    "authors": [
        "oisin robinson"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2212.04999"
}
{
    "ToxicityFilter": {
        "text_to_toxicity_attributes": {
            "tnfs4d_rev2.bbl": {
                "toxicity_score": 0.011874928,
                "severe_toxicity_score": 0.0011348724,
                "identity_attack_score": 0.003866276,
                "insult_score": 0.0075508766,
                "profanity_score": 0.014532468,
                "threat_score": 0.007521313,
                "sexually_explicit_score": 0.010969753,
                "flirtation_score": 0.2762957
            },
            "tnfs4d_rev2.pgf-plot.gnuplot": {
                "toxicity_score": 0.021314176,
                "severe_toxicity_score": 0.0015068054,
                "identity_attack_score": 0.0029228306,
                "insult_score": 0.008975885,
                "profanity_score": 0.018119188,
                "threat_score": 0.0083886795,
                "sexually_explicit_score": 0.014331453,
                "flirtation_score": 0.42694536
            },
            "tnfs4d_rev2.pgf-plot.table": {
                "toxicity_score": 0.02308189,
                "severe_toxicity_score": 0.0019264221,
                "identity_attack_score": 0.0048837173,
                "insult_score": 0.00971689,
                "profanity_score": 0.017709278,
                "threat_score": 0.008893564,
                "sexually_explicit_score": 0.013387818,
                "flirtation_score": 0.19838828
            },
            "refs.bib": {
                "toxicity_score": 0.0068799187,
                "severe_toxicity_score": 0.0012874603,
                "identity_attack_score": 0.0010035669,
                "insult_score": 0.0069238725,
                "profanity_score": 0.013166099,
                "threat_score": 0.005738034,
                "sexually_explicit_score": 0.011736456,
                "flirtation_score": 0.28735408
            },
            "tnfs4d_rev2.tex": {
                "toxicity_score": 0.009927189,
                "severe_toxicity_score": 0.0009918213,
                "identity_attack_score": 0.003089321,
                "insult_score": 0.0072658747,
                "profanity_score": 0.014225035,
                "threat_score": 0.007249452,
                "sexually_explicit_score": 0.011677479,
                "flirtation_score": 0.2910117
            }
        },
        "reason": null
    }
}
{
    "num_done": {
        "figure": 0,
        "algorithm": 3,
        "plot": 0
    }
}
{
    "NonTrivialRenderingFilter": {
        "white_pixels_ratio": 92.79844964742128,
        "hash": "030f3f1f87878707",
        "most_frequent_color_ratio": 92.79844964742128
    }
}