ANU-NQ(1)

🎀 NAME 🎀

anu-nq — the nq command line interface 💅 (yes bestie, this whole page is the man page for the ANU nq program, manual section 1, and I am so excited to walk you through it)

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✨ SYNOPSIS ✨

anu-nq [-a] [-M] [-d] [-g] [-v] [-s] [-f] [-c] [-m] [-t <n>] [-l <n>] [-r <n>] [-n <n>] [-e <n>] [-y] [-o] [-p] [-E] [presentation] [class]

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🌸 DESCRIPTION 🌸

okay so 🫶 this is the man page for the ANU nq program, and ngl it only briefly documents the parameters — it's giving little teaser trailer energy. The real, main documentation lives inside the GAP nq documentation, which you can get in html and pdf format. So if you want the full lore, go there, bestie.

The options -l, -r and -e are the ones that can be used to enforce Engel conditions on the nilpotent quotient that's about to be calculated. All three of these options have to be followed by a positive integer <n>. Their meaning is:

• -n <k> — this option forces the first k generators to be a left or right Engel element, but only if the option -l or -r (or both, queen, why not) is also present. If neither of those is hanging around, it is ignored. 💀
• -l <n> — this forces the first k generators g_1,...,g_k of the nilpotent quotient Q to be left n-Engel elements, i.e., they satisfy [x,...,x,g_i] = 1 (with x occurring n-times) for all x in Q and 1 <= i <= k. If the option -n is not used, then k = 1. simple as that ✨
• -r <n> — this forces the first k generators g_1,...,g_k of the nilpotent quotient Q to be right n-Engel elements, i.e., they satisfy [g_i,x,..,x] = 1 (with x occurring n-times) for all x in Q and 1 <= i <= k. If the option -n is not used, then k = 1. mirror image, still iconic 💖
• -e <n> — this enforces the n-th Engel law on Q, i.e., [x,y,..,y] = 1 (with y occurring n-times) for all x,y in Q. whole-quotient behaviour, no cap.
• -t <n> — this option specifies how much CPU time the program is allowed to use 🕐. It will terminate after <n> seconds of CPU time. And if <n> is followed (without space!) by one of the letters m, h or d, then <n> specifies the time in minutes, hours or days, respectively. cute little shorthand, obsessed.

The other options have the following meaning. Now — care has to be taken when the options -s or -c are used, because the resulting nilpotent quotient need NOT satisfy the required Engel condition 😭. The reason for this is that a smaller set of test words is used if one of these two options is present. And like, although this smaller set of test words seems to be sufficient to enforce the required Engel condition, that fact has not been proven. so, y'know. proceed accordingly, bestie.

• -a — for each factor of the lower central series, a file is created in the current directory that contains an integer matrix describing the factor as an abelian group. The first number in that file is the number of columns of the matrix, and then the matrix follows in row major order. The matrix for the i-th factor is put into the file presentation.abinv.<i>. 📁
• -p — toggles printing of the pc presentation for the nilpotent quotient at the end of a calculation. lil toggle, big vibes.
• -s — this option causes the program to check only semigroup words in the generating set of the nilpotent quotient when an Engel condition is enforced. If none of the options -l, -r or -e are present, it is ignored.
• -f — this option causes the program to check semiwords in the generating set of the nilpotent quotient first and then all other words that need to be checked. It is ignored if the option -s is used, or if none of the options -l, -r or -e are present.
• -c — this option stops checking the Engel law at each class if all the checks of a certain weight did not yield any non-trivial instances of the law. early exit queen 👑
• -d — switch on debug mode and perform checks during the computation. Not yet implemented. 🙈
• -o — in checking Engel identities, instances are processed in the order of increased weight. This flag reverses the order. 🔄
• -y — enforce the identities x^8 and [ [x1,x2,x3], [x4,x5,x6] ] on the nilpotent quotient.
• -v — switch on verbose mode. she talks a lot 💬
• -g — produce GAP output. Presently the GAP output consists only of a sequence of integer matrices whose rows are relations of the factors of the lower central series as abelian groups. This will change as soon as GAP can handle infinite polycyclic groups. ⏳
• -E — the last n generators are Engel generators. This works in conjunction with option -n.
• -m — output the relation matrix for each factor of the lower central series. The matrices are written to files with the names matrix.cl where cl is replaced by the number of the factor in the lower central series. Each file contains first the number of columns of the matrix and then the rows of the matrix. The matrix is written as each relation is produced and is not in upper triangular form. 🫣
• -M — output the relation matrix before and after relations have been enforced. This results in two groups of files with names pres.nilp.cl and pres.mult.cl where pres is the name of the input files and cl is the class. The matrices are in upper triangular form. ✨ tidy!

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💜 COPYRIGHT 💜

The ANU nq program is Copyright (C) by Werner Nickel. respect the author, bestie 🫶

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🦋 SEE ALSO 🦋

The GAP nq manual /usr/share/gap/pkg/nq/doc/manual.pdf — go read it, it's the main character of documentation fr fr 📖

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and that's the whole thing! this page is straight out of the General Commands Manual, dated January 2026, and it's ANU-NQ(1) — slay, periodt 💅✨🎀