# \#algebra **URL:** https://community.wolfram.com/tag/algebra/38.md [Latest](https://community.wolfram.com/latest.md) · [Categories](https://community.wolfram.com/categories.md) · [Tags](https://community.wolfram.com/tags.md) --- ## [FinitelyPresentedGroups: paclet for infinite groups, word problems, and coset enumerations](https://community.wolfram.com/t/finitelypresentedgroups-paclet-for-infinite-groups-word-problems-and-coset-enumerations/28453)
**Author:** [@namantaggar](https://community.wolfram.com/u/namantaggar)\ **Replies:** 1\ **Last updated:** [November 3, 2026, 11:47am UTC](https://community.wolfram.com/t/finitelypresentedgroups-paclet-for-infinite-groups-word-problems-and-coset-enumerations/28453 "2026-11-03T11:47:17Z")
Hi all! As we know Mathematica has a great in-built support for finite group theory in terms of permutation groups and Cycles. Though, support for infinite groups has been missing. One class of infinite groups is covered… --- ## [Finding a and b Given That f(x)=ln|a+1/(1−x)|+b Is Odd](https://community.wolfram.com/t/finding-a-and-b-given-that-f-x-ln-a-1-1-x-b-is-odd/28488)
**Author:** [@camelon](https://community.wolfram.com/u/camelon)\ **Replies:** 1\ **Last updated:** [November 3, 2026, 11:43am UTC](https://community.wolfram.com/t/finding-a-and-b-given-that-f-x-ln-a-1-1-x-b-is-odd/28488 "2026-11-03T11:43:25Z")
Finding a and b Given That f(x)=ln|a+1/(1−x)|+b Is Odd Why doesn’t this code find the values of the parameters, and how should I solve for them? f\[x\_\] := Log\[Abs\[a + 1/(1 - x)\]\] + b Reduce\[ForAll\[x, x != 1 && x != -1 &&… --- ## [Earth-moon Lyapunov orbit construction algorithm](https://community.wolfram.com/t/earth-moon-lyapunov-orbit-construction-algorithm/28474)
**Author:** [@akram2007omar](https://community.wolfram.com/u/akram2007omar)\ **Replies:** 1\ **Last updated:** [November 3, 2026, 11:37am UTC](https://community.wolfram.com/t/earth-moon-lyapunov-orbit-construction-algorithm/28474 "2026-11-03T11:37:44Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (1.3 MB) --- ## [Isoptic curves of an ellipse and isoptic surface of an ellipsoid](https://community.wolfram.com/t/isoptic-curves-of-an-ellipse-and-isoptic-surface-of-an-ellipsoid/28465)
**Author:** [@alatorre](https://community.wolfram.com/u/alatorre)\ **Replies:** 1\ **Last updated:** [November 3, 2026, 11:07am UTC](https://community.wolfram.com/t/isoptic-curves-of-an-ellipse-and-isoptic-surface-of-an-ellipsoid/28465 "2026-11-03T11:07:54Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (159.4 KB) --- ## [On the message "Equations may not give solutions for 'all' variables"](https://community.wolfram.com/t/on-the-message-equations-may-not-give-solutions-for-all-variables/28377)
**Author:** [@HyungKyuKim](https://community.wolfram.com/u/HyungKyuKim)\ **Replies:** 11\ **Last updated:** [November 3, 2026, 4:28am UTC](https://community.wolfram.com/t/on-the-message-equations-may-not-give-solutions-for-all-variables/28377 "2026-11-03T04:28:21Z")
I tried to solve a simultaneous equation consists of numeric coefficients and a paramater (say, ‘xi’). I got the message shown in the title when the matrix size of the coefficient exceeds 6. Up to 5, the “Solve” gave the… --- ## [New special function capabilities in Wolfram language version 15.0](https://community.wolfram.com/t/new-special-function-capabilities-in-wolfram-language-version-15-0/28477)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 0\ **Last updated:** [November 2, 2026, 6:09am UTC](https://community.wolfram.com/t/new-special-function-capabilities-in-wolfram-language-version-15-0/28477 "2026-11-02T06:09:28Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (548.2 KB) --- ## [The Plastic Pentagon - A new tile system](https://community.wolfram.com/t/the-plastic-pentagon-a-new-tile-system/28451)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 2\ **Last updated:** [October 31, 2026, 2:07pm UTC](https://community.wolfram.com/t/the-plastic-pentagon-a-new-tile-system/28451 "2026-10-31T14:07:51Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (5.8 MB) --- ## [Elliptic curves in Weierstrass normal form](https://community.wolfram.com/t/elliptic-curves-in-weierstrass-normal-form/28424)
**Author:** [@p6majo](https://community.wolfram.com/u/p6majo)\ **Replies:** 1\ **Last updated:** [October 27, 2026, 7:14pm UTC](https://community.wolfram.com/t/elliptic-curves-in-weierstrass-normal-form/28424 "2026-10-27T19:14:14Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (1.6 MB) --- ## [Level curves for Zhang's Eta function](https://community.wolfram.com/t/level-curves-for-zhangs-eta-function/28435)
**Author:** [@Stopple](https://community.wolfram.com/u/Stopple)\ **Replies:** 1\ **Last updated:** [October 27, 2026, 6:22pm UTC](https://community.wolfram.com/t/level-curves-for-zhangs-eta-function/28435 "2026-10-27T18:22:12Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (237.0 KB) --- ## [Seeking freelance Wolfram Language developer for interactive fractions / ratio software](https://community.wolfram.com/t/seeking-freelance-wolfram-language-developer-for-interactive-fractions-ratio-software/27120)
**Author:** [@davidcarraher](https://community.wolfram.com/u/davidcarraher)\ **Replies:** 1\ **Last updated:** [October 26, 2026, 9:29pm UTC](https://community.wolfram.com/t/seeking-freelance-wolfram-language-developer-for-interactive-fractions-ratio-software/27120 "2026-10-26T21:29:29Z")
I am developing Extending Fraction Frontiers, an interactive Mathematica / Wolfram Language environment for teaching fractions, ratios, common units, and rational-number reasoning. The project is currently a working pro… --- ## [How does Tesla's Roadster fly? Exploring the physics](https://community.wolfram.com/t/how-does-teslas-roadster-fly-exploring-the-physics/28368)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 2\ **Last updated:** [October 19, 2026, 8:29pm UTC](https://community.wolfram.com/t/how-does-teslas-roadster-fly-exploring-the-physics/28368 "2026-10-19T20:29:48Z")
Open in Wolfram Cloud ↗ FlyingRoadster\_Community.wl (99.6 KB) DOWNLOAD-DESKTOP-NOTEBOOK.nb (1010.8 KB) --- ## [Circular hyperbolic cubic: a geometric envelope construction](https://community.wolfram.com/t/circular-hyperbolic-cubic-a-geometric-envelope-construction/28370)
**Author:** [@alatorre](https://community.wolfram.com/u/alatorre)\ **Replies:** 0\ **Last updated:** [October 19, 2026, 6:48pm UTC](https://community.wolfram.com/t/circular-hyperbolic-cubic-a-geometric-envelope-construction/28370 "2026-10-19T18:48:04Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (91.9 KB) --- ## [One observable is not enough: auditing quantum dynamics on IBM hardware](https://community.wolfram.com/t/one-observable-is-not-enough-auditing-quantum-dynamics-on-ibm-hardware/28353)
**Author:** [@mthiel](https://community.wolfram.com/u/mthiel)\ **Replies:** 1\ **Last updated:** [October 16, 2026, 7:52pm UTC](https://community.wolfram.com/t/one-observable-is-not-enough-auditing-quantum-dynamics-on-ibm-hardware/28353 "2026-10-16T19:52:35Z")
OpenAI-generated conceptual illustration, not measured data or a physical IBM device. Scientific figures are generated by the supplied Wolfram code from archived data and the saved local reference; no IBM or Bahrami d… --- ## [Differential system related to generalised Krawtchouk polynomials: iterated regularisation and Painlevé equation](https://community.wolfram.com/t/differential-system-related-to-generalised-krawtchouk-polynomials-iterated-regularisation-and-painleve-equation/28352)
**Author:** [@gfilipuk](https://community.wolfram.com/u/gfilipuk)\ **Replies:** 1\ **Last updated:** [October 16, 2026, 6:55pm UTC](https://community.wolfram.com/t/differential-system-related-to-generalised-krawtchouk-polynomials-iterated-regularisation-and-painleve-equation/28352 "2026-10-16T18:55:44Z")
Diagram of the iterated regularisation algorithm Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (307.8 KB) --- ## [Hügelschäffer Egg: construction of an egg-shaped curve and its surface of revolution](https://community.wolfram.com/t/hugelschaffer-egg-construction-of-an-egg-shaped-curve-and-its-surface-of-revolution/28340)
**Author:** [@alatorre](https://community.wolfram.com/u/alatorre)\ **Replies:** 1\ **Last updated:** [October 15, 2026, 4:50pm UTC](https://community.wolfram.com/t/hugelschaffer-egg-construction-of-an-egg-shaped-curve-and-its-surface-of-revolution/28340 "2026-10-15T16:50:40Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (243.5 KB) --- ## [An introduction to multivariate zeta functions](https://community.wolfram.com/t/an-introduction-to-multivariate-zeta-functions/28317)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 1\ **Last updated:** [October 12, 2026, 3:26pm UTC](https://community.wolfram.com/t/an-introduction-to-multivariate-zeta-functions/28317 "2026-10-12T15:26:24Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.7 MB) --- ## [When are flat lists treated as rows or columns in vector and matrix operations?](https://community.wolfram.com/t/when-are-flat-lists-treated-as-rows-or-columns-in-vector-and-matrix-operations/28309)
**Author:** [@jgourle21](https://community.wolfram.com/u/jgourle21)\ **Replies:** 4\ **Last updated:** [October 12, 2026, 10:48am UTC](https://community.wolfram.com/t/when-are-flat-lists-treated-as-rows-or-columns-in-vector-and-matrix-operations/28309 "2026-10-12T10:48:46Z")
Is there documentation that explains how Mathematica functions handle vectors and matrices. I assume there is some simple reasoning for when {a,b} is a column and when it’s a row that would allow me to avoid detouring t… --- ## [Algebraic Hirota construction of one- and two-soliton solutions of the DNLS equation and their Bohmian trajectories](https://community.wolfram.com/t/algebraic-hirota-construction-of-one-and-two-soliton-solutions-of-the-dnls-equation-and-their-bohmian-trajectories/28298)
**Author:** [@kvbloh](https://community.wolfram.com/u/kvbloh)\ **Replies:** 1\ **Last updated:** [October 9, 2026, 8:01pm UTC](https://community.wolfram.com/t/algebraic-hirota-construction-of-one-and-two-soliton-solutions-of-the-dnls-equation-and-their-bohmian-trajectories/28298 "2026-10-09T20:01:21Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (10.8 MB) --- ## [Colored four-arc curve plot with equation labels](https://community.wolfram.com/t/colored-four-arc-curve-plot-with-equation-labels/28295)
**Author:** [@camelon](https://community.wolfram.com/u/camelon)\ **Replies:** 1\ **Last updated:** [October 9, 2026, 2:50pm UTC](https://community.wolfram.com/t/colored-four-arc-curve-plot-with-equation-labels/28295 "2026-10-09T14:50:03Z")
The curve defined by x²+y²=4|x|+4|y| can be expanded, quadrant by quadrant, into the equations of four circles, splitting the whole curve into four regions, each corresponding to a semicircular arc. When drawing the plot… --- ## [Basel, Hankel, and a recent proof of ζ(5) irrationality](https://community.wolfram.com/t/basel-hankel-and-a-recent-proof-of-5-irrationality/28282)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [October 7, 2026, 2:52pm UTC](https://community.wolfram.com/t/basel-hankel-and-a-recent-proof-of-5-irrationality/28282 "2026-10-07T14:52:21Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (56.1 KB) --- ## [Monoidal alphabets for generalized harmonic sums](https://community.wolfram.com/t/monoidal-alphabets-for-generalized-harmonic-sums/28280)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 1\ **Last updated:** [October 7, 2026, 7:52am UTC](https://community.wolfram.com/t/monoidal-alphabets-for-generalized-harmonic-sums/28280 "2026-10-07T07:52:53Z")
Open in Wolfram Cloud ↗ AffinePolyBaseSupport.wl (13.9 KB) DOWNLOAD-DESKTOP-NOTEBOOK.nb (598.3 KB) --- ## [Gravitational waveform from radial infall at the third-and-half post-Newtonian order](https://community.wolfram.com/t/gravitational-waveform-from-radial-infall-at-the-third-and-half-post-newtonian-order/28271)
**Author:** [@GDiRusso](https://community.wolfram.com/u/GDiRusso)\ **Replies:** 1\ **Last updated:** [October 5, 2026, 7:50pm UTC](https://community.wolfram.com/t/gravitational-waveform-from-radial-infall-at-the-third-and-half-post-newtonian-order/28271 "2026-10-05T19:50:26Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (5.8 MB) --- ## [Hügelschäffer egg](https://community.wolfram.com/t/hugelschaffer-egg/28264)
**Author:** [@alatorre](https://community.wolfram.com/u/alatorre)\ **Replies:** 0\ **Last updated:** [October 5, 2026, 2:59pm UTC](https://community.wolfram.com/t/hugelschaffer-egg/28264 "2026-10-05T14:59:16Z")
Open in Wolfram Cloud ↗ --- ## [A human-AI theorem connecting spontaneous and field-induced mechanisms of collective behavior in one dimension](https://community.wolfram.com/t/a-human-ai-theorem-connecting-spontaneous-and-field-induced-mechanisms-of-collective-behavior-in-one-dimension/28223)
**Author:** [@wyinbnl](https://community.wolfram.com/u/wyinbnl)\ **Replies:** 1\ **Last updated:** [September 30, 2026, 9:13pm UTC](https://community.wolfram.com/t/a-human-ai-theorem-connecting-spontaneous-and-field-induced-mechanisms-of-collective-behavior-in-one-dimension/28223 "2026-09-30T21:13:12Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (917.1 KB) --- ## [Fixing Reduce\[ForAll\[…\]\]: a quantifier-syntax pitfall](https://community.wolfram.com/t/fixing-reduce-forall-a-quantifier-syntax-pitfall/28184)
**Author:** [@camelon](https://community.wolfram.com/u/camelon)\ **Replies:** 1\ **Last updated:** [September 27, 2026, 6:54pm UTC](https://community.wolfram.com/t/fixing-reduce-forall-a-quantifier-syntax-pitfall/28184 "2026-09-27T18:54:35Z")
Why can’t we solve this identity for the values of a, b, t? Reduce\[ForAll\[{x, y}, {x \> 0, y \> 0, t \> 0, t^2 + 2 t x + x^2 + 2 t y + 12 + y^2 == a^2 + b^2 - 2 a x + x^2 - 2 b y + y^2}\], {a, b, t}, Reals\] Reduce\[ForAll\[{… --- ## [Classifying quantum cloning machines: a moduli space approach in Wolfram Language](https://community.wolfram.com/t/classifying-quantum-cloning-machines-a-moduli-space-approach-in-wolfram-language/28175)
**Author:** [@mauricee](https://community.wolfram.com/u/mauricee)\ **Replies:** 1\ **Last updated:** [September 25, 2026, 8:56pm UTC](https://community.wolfram.com/t/classifying-quantum-cloning-machines-a-moduli-space-approach-in-wolfram-language/28175 "2026-09-25T20:56:14Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.0 MB) --- ## [An intuitive exploration of OpenAI's Navier–Stokes singularity construction (for the $1M Millennium Prize Problem)](https://community.wolfram.com/t/an-intuitive-exploration-of-openais-navier-stokes-singularity-construction-for-the-1m-millennium-prize-problem/28013)
**Author:** [@jayantap](https://community.wolfram.com/u/jayantap)\ **Replies:** 4\ **Last updated:** [September 25, 2026, 2:34am UTC](https://community.wolfram.com/t/an-intuitive-exploration-of-openais-navier-stokes-singularity-construction-for-the-1m-millennium-prize-problem/28013 "2026-09-25T02:34:39Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (2.5 MB) --- ## [Area of a revolution surface when rotating a sinusoid function](https://community.wolfram.com/t/area-of-a-revolution-surface-when-rotating-a-sinusoid-function/28165)
**Author:** [@alatorre](https://community.wolfram.com/u/alatorre)\ **Replies:** 0\ **Last updated:** [September 24, 2026, 1:50pm UTC](https://community.wolfram.com/t/area-of-a-revolution-surface-when-rotating-a-sinusoid-function/28165 "2026-09-24T13:50:49Z")
Open in Wolfram Cloud ↗ --- ## [Hadamard matrix of order 668](https://community.wolfram.com/t/hadamard-matrix-of-order-668/28083)
**Author:** [@edp](https://community.wolfram.com/u/edp)\ **Replies:** 1\ **Last updated:** [September 22, 2026, 7:55pm UTC](https://community.wolfram.com/t/hadamard-matrix-of-order-668/28083 "2026-09-22T19:55:03Z")
Open in Wolfram Cloud ↗ DOWNLOAD-DESKTOP-NOTEBOOK.nb (212.1 KB) --- ## [Is my new mean for elementary asymmetric functions with singularities existent and non-equivalent to their Cauchy Principal Value?](https://community.wolfram.com/t/is-my-new-mean-for-elementary-asymmetric-functions-with-singularities-existent-and-non-equivalent-to-their-cauchy-principal-value/28077)
**Author:** [@bharathk98](https://community.wolfram.com/u/bharathk98)\ **Replies:** 3\ **Last updated:** [September 22, 2026, 7:24pm UTC](https://community.wolfram.com/t/is-my-new-mean-for-elementary-asymmetric-functions-with-singularities-existent-and-non-equivalent-to-their-cauchy-principal-value/28077 "2026-09-22T19:24:42Z")
Motivations First Motivation: I got a “new mean” by indirectly attempting to establish the relationship between the uniform probability measure and normalized Hausdorff measure. This is the third open problem in Section … [Next page](https://community.wolfram.com/tag/algebra/38.md?match_all_tags=true&page=1&tags%5B%5D=algebra)