https://community.wolfram.com RSS Feed for Wolfram Community showing any discussions tagged with Algebra sorted by active. https://community.wolfram.com/groups/-/m/t/3663531 ![enter image description here][1] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Screenshot2026-03-16220458.png&userId=3662999 In the Wolfram Problem Generator Arithmetic summary Advanced, I keep seeing WPGDivide in the step-by-step solutions. Can't find anything about this anywhere. Is it a glitch? Edit:Oops I'm dumb, just realized "WPG" probably means "Wolfram Problem Generator". Regardless, why is this showing up and what does it mean? My apologies if this is something obvious. R L 2026-03-17T05:07:17Z https://community.wolfram.com/groups/-/m/t/3661214 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/f809057d-e31a-4da3-bf17-e4e9252d8e8e Daniel Carvalho 2026-03-14T20:45:10Z https://community.wolfram.com/groups/-/m/t/3661203 The plane y = x intersects to the sphere (x - 5)^2 + (y - 5)^2 + z^2 = 4 and the resulting circumference rotates around the line x = y = z. A very special inclined toroid is generated. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/5202df1f-bdc5-4b8a-b635-4fde5f52e22a Alejandro Latorre Chirot 2026-03-14T17:34:44Z https://community.wolfram.com/groups/-/m/t/3657317 Hello everybody: Just a suggestion. There is a strong relation between **continued fractions** and function **FindTransientRepeat[]** and this last is not referenced neither in the help of **ContinuedFraction[]** nor in the help of **FromContinuedFraction[]**. These lacks of links in the help **See also** sections made me to spend some time in writing my own **FindTransientRepeat[]** which, by pure chance, I found later into the 6800+ functions in Mathematica. My main point is that **FindTransientRepeat[]** should appear in the **See also** sections of helps of **ContinuedFraction[]** and **FromContinuedFraction[]**. This is what I was doing: We can expand **5 + 2 Sqrt[7]** and find **10.291502622129181181003231507**. How can I find the first quadratic irrational expression from the given decimal expansion?. The following steps do that work for low numbers in the quadratic irrational: xx = 10.2915026221291811810032315073; cf = ContinuedFraction[xx]; tr = FindTransientRepeat[cf, 2]; yy = FromContinuedFraction[{Flatten[tr]}] (*output*) 5 + 2 Sqrt[7] QuadraticIrrationalQ[yy] True César Lozada Cesar Lozada 2026-03-11T01:43:43Z https://community.wolfram.com/groups/-/m/t/3657254 In this notebook, among other things, a tube-shaped surface is built around a curve and when making different cuts with planes on it, it is necessary to determine whether the resulting curves are asymptotic or geodesic lines or both. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/8b0841d6-e740-4c0a-9f05-260c3eb213a9 Alejandro Latorre Chirot 2026-03-11T21:26:07Z https://community.wolfram.com/groups/-/m/t/3653839 ![enter image description here][1] ![enter image description here][2] ![enter image description here][3] This is my own try at making this work with the substitution method. It’s manageable if you know the equation well, but the steps get really tedious with a complex quadratic equation. L = m x + n y; ellipseOriginal = (x + x0)^2/a^2 + (y + y0)^2/b^2 == 1; ellipseHomogenized1 = ellipseOriginal /. {x0 -> x0*L, y0 -> y0*L, 1 -> L^2} How to use code to automatically generate such a homogeneous quadratic equation by combining the linear equation and the quadratic curve? [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-03-09_080042.png&userId=3593842 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-03-09_080112.png&userId=3593842 [3]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-03-09_080217.png&userId=3593842 Bill Blair 2026-03-09T00:04:31Z https://community.wolfram.com/groups/-/m/t/3655786 (a) A curve Gamma is defined by the parameterization {Cos[t], Sin[t], f[t]}. Calculate the function f[t] so that the main normals of Gamma are parallel to the XY plane. Calculate the torsion and curvature in that case. (b) Determine the function Phi[t] so that Phi[0] = 1. And the normal planes to the curve {Sin[t]^2, Sin[t] Cos[t], Phi[t]} pass through the origin. Calculate the curvature and torsion in such a case. &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/85458994-5e0a-46f9-b55f-b9c123973de3 Alejandro Latorre Chirot 2026-03-09T16:25:24Z https://community.wolfram.com/groups/-/m/t/3651601 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/9c1d2066-2395-413c-bb7d-c4f9226eeeef Leslie Ann Goldberg 2026-03-06T17:55:51Z https://community.wolfram.com/groups/-/m/t/3647733 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/b04b6551-fecf-465d-b02d-63d95abd751c Tigran Nersissian 2026-03-02T11:53:13Z https://community.wolfram.com/groups/-/m/t/3651129 The envelope of a family of spheres that looks like a tangerine. In fact, with different resources of Geometry we can recreate several forms existing in nature, the relationship is undeniable! &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/fa09a4bd-fed1-4ade-bae0-650b6a9184d5 Alejandro Latorre Chirot 2026-03-06T14:29:57Z https://community.wolfram.com/groups/-/m/t/3650601 <p> Define a sequence of finite sets $S_m \subset \mathbb{N}$ by the initial conditions $$S_1 = \{0\}, \qquad S_2 = \{1\},$$ and the recurrence for $m \ge 3$: $$S_m = \operatorname{Inc}\!\Big(\,\zeta\!\big(\,\zeta(S_{m-1}) \cup \zeta(S_{m-2})\,\big)\Big),$$ where the operations are defined as follows. </p> <hr> <h3>Definitions</h3> <p><strong>Characteristic function.</strong> Each finite set $A \subset \mathbb{N}$ is identified with its characteristic function $\mathbf{1}_A : \mathbb{N} \to \mathbb{F}_2$, where $\mathbf{1}_A(n) = 1$ if $n \in A$ and $0$ otherwise. </p> <p><strong>Subset-sum (zeta) transform $\zeta$.</strong> Given a finite set $A \subset \mathbb{N}$, define $\zeta(A)$ as the set whose characteristic function is $$\mathbf{1}_{\zeta(A)}(t) \;=\; \sum_{s \,\subseteq\, t} \mathbf{1}_A(s) \pmod{2},$$ where $s \subseteq t$ means that every bit set in the binary representation of $s$ is also set in $t$ (i.e. $s \mathbin{\&} t = s$, the bitwise AND condition). This is the <em>Möbius/zeta transform on the Boolean lattice</em> $2^{\mathbb{N}}$, reduced modulo $2$. </p> <p><strong>Union $\cup$ (pointwise OR over $\mathbb{F}_2$).</strong> Given two finite sets $A, B \subset \mathbb{N}$, the operation $A \cup B$ is simply the set union. Equivalently, in terms of characteristic functions: $$\mathbf{1}_{A \cup B}(n) = \mathbf{1}_A(n) \lor \mathbf{1}_B(n).$$ </p> <p><strong>Increment $\operatorname{Inc}$.</strong> $\operatorname{Inc}(A) = \{a + 1 \mid a \in A\}$, i.e. shift every element up by one. </p> <hr> <h3>Computed values</h3> <p>Carrying out the recurrence by hand (or by computer), the first several sets are:</p> $$\begin{aligned} S_1 &= \{0\}, \\ S_2 &= \{1\}, \\ S_3 &= \{1\}, \\ S_4 &= \{2\}, \\ S_5 &= \{2,\, 3,\, 4\}, \\ S_6 &= \{3,\, 5,\, 7\}, \\ S_7 &= \{3,\, 5,\, 8\}, \\ S_8 &= \{4,\, 6,\, 8,\, 9,\, 12,\, 14,\, 16\}. \end{aligned}$$ <hr> <h3>Question</h3> <p> Is there a <strong>closed-form expression</strong> for the set $S_m$, or equivalently a closed-form formula for the membership predicate $$P(m,\, r) \;=\; [r \in S_m]$$ as a function of $(m, r)$? </p> <p> Any structural insight is welcome: a characterisation in terms of binary representations of $m$ and $r$, asymptotic growth of $|S_m|$ or $\max S_m$, etc. </p> Tigran Nersissian 2026-03-06T07:43:05Z https://community.wolfram.com/groups/-/m/t/3649946 If $f:\mathbb{N}\to\mathbb{R}$ and $g:\mathbb{N}\to\mathbb{R}$ are arbitrary functions, I want to calculate this equation with Mathematica: $$\small{\begin{equation} c=\inf\left\{|1-\mathbf{c_1}|:\forall(\epsilon>0)\exists(\mathbf{c_1}>0)\forall(r\in\mathbb{N})\exists(v\in\mathbb{N})\left(\left|\frac{f(r)}{g(v)}-\mathbf{c_1}\right|<\varepsilon\right)\right\}, \end{equation}}$$ Here is what it does: To obtain $c$, we want $\mathbf{c_1}$ must satisfy the following: 1. $\mathbf{c_1}$ is positive 2. $\mathbf{c_1}$ satisfies 1. and the quantified statement in Equation 3. $\mathbf{c_1}$ satisfies 1. and 2., and has the smallest absolute difference from $1$. Here is what I tried: Clear["Global`*"] F[r_] := F[r] = r! + 1 G[v_] := G[v] = 2 v! + 1 (* G can be any arbitrary function *) c[r_] := FindMinimum[{N[1 - RealAbs[1 - F[r]/G[v]]], Between[v, {1, 10000}] && v \[Element] Integers}, {v}] Limit[c[r], r -> Infinity] However, I get the following error message: During evaluation of In[552]:= FindMinimum::eqineq: Constraints in {v\[Element]\[DoubleStruckCapitalZ],1<=v,v<=10000} are not all equality or inequality constraints. With the exception of integer domain constraints for linear programming, domain constraints or constraints with Unequal (!=) are not supported. Out[556]= \!\(\*UnderscriptBox[\(\[Limit]\), \(r \[Rule] \[Infinity]\)]\) FindMinimum[{N[1 - RealAbs[1 - F[r]/G[v]]], Between[v, {1, 10000}] && v \[Element] Integers}, {v}] Bharath Krishnan 2026-03-05T17:57:17Z https://community.wolfram.com/groups/-/m/t/3649769 ![Special Functions: A Computational Approach now available in Wolfram Notebook format][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=SpecialFunctionsAComputationalApproachnowavailableinWolframNotebookformat.png&userId=20103 [2]: https://www.wolframcloud.com/obj/4a2dc2d7-e361-4e5e-9336-8922f7cde0a3 Tigran Ishkhanyan 2026-03-05T13:10:41Z https://community.wolfram.com/groups/-/m/t/3647051 [![The entropy bagel: complex roots of Littlewood polynomials][1]][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=_test.jpg&userId=11733 [2]: https://www.wolframcloud.com/obj/97dc0591-1fe8-45a9-9cf7-8074051c6b12 Ed Pegg 2026-02-27T17:34:59Z https://community.wolfram.com/groups/-/m/t/3648128 ![Bohmian trajectories and the role of nodal surface manifolds in hydrogen eigenstates: Part 2][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=Bohmiantrajectoriesandtheroleofnodalsurfacemanifoldsinhydrogeneigenstates-crop-video-.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/57d77365-9bdd-4072-b8da-4686c29f6f82 Klaus von Bloh 2026-03-03T10:25:54Z https://community.wolfram.com/groups/-/m/t/3647724 ![SO(3) Gauge Theory for Classical Mechanics in UD][1] &[Wolfram Notebook][2] [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=5904SO%283%29gaugetheoryforclassicalmechanicsinUD.gif&userId=20103 [2]: https://www.wolframcloud.com/obj/d2ea36cc-f66d-4bd4-ac0d-f75831617d79 Brian Beckman 2026-03-02T03:13:38Z https://community.wolfram.com/groups/-/m/t/3647422 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/6e9d9326-7297-433f-8f78-fcc4c875f934 Aisha Benzine 2026-03-01T04:17:27Z https://community.wolfram.com/groups/-/m/t/3646527 The following code is the method I have tried to use myself: however, the results are incorrect when judging the parity of some functions. What methods can be used to accurately determine the parity of each type of function? f[x_] := x^3 dn = FunctionDomain[f[x], x] Reduce[ForAll[x, dn, #], x, Reals] & /@ {f[-x] == -f[x], f[-x] == f[x]} There were no errors in judging the parity of the following functions. f[x_] := x^3 dn = FunctionDomain[f[x], x] Reduce[ForAll[x, dn, #], x, Reals] & /@ {f[-x] == -f[x], f[-x] == f[x]} f[x_] := x - Sin@x dn = FunctionDomain[f[x], x] Reduce[ForAll[x, dn, #], x, Reals] & /@ {f[-x] == -f[x], f[-x] == f[x]} However, errors occur in the following cases: The judgment is incorrect when the domain of the function is not symmetric about the origin. f[x_] := x^2 - Abs@x + 1 dn = -1 <= x <= 4 Reduce[ForAll[x, dn, #], x, Reals] & /@ {f[-x] == -f[x], f[-x] == f[x]} ![enter image description here][1] Errors occur when judging the parity of functions containing parameters. f[x_] := 1/(a^x - 1) + 1/2 dn = FunctionDomain[f[x], x] Reduce[ForAll[x, dn, #], x, Reals] & /@ {f[-x] == -f[x], f[-x] == f[x]} ![enter image description here][2] What methods can correctly determine the parity of each type of function? [1]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-02-27_135824.png&userId=3593842 [2]: https://community.wolfram.com//c/portal/getImageAttachment?filename=2026-02-27_135950.png&userId=3593842 Bill Blair 2026-02-27T06:00:52Z https://community.wolfram.com/groups/-/m/t/3643430 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/3a661d87-7c7f-4644-92f2-fed752a570f9 Housam Binous 2026-02-22T17:22:34Z https://community.wolfram.com/groups/-/m/t/3643405 &[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/a96a4215-964f-42cb-81ec-bb4b06e2a64f Housam Binous 2026-02-22T08:42:43Z