MathAction changed pages

[AxiomSources]

Wed, 01 Jul 2026 21:03:43 +0000

??changed: -For up-to-date information about Axiom see http://axiom-developer.org Axiom is no longer actively developed. Last version is available as a Debian package. Copy of old Axiom website is preserved at https://www.nongnu.org/axiom

[FriCAS Library Examples]

Wed, 01 Jul 2026 20:37:14 +0000

??changed: - ExampleTrigonometricConstants ExampleTrigonometricConstants

[RecurrenceRelationOperator]

Wed, 01 Jul 2026 20:13:07 +0000

++added: RecurrenceOperator is included in FriCAS, content below is kept for historical reasons.

[OtherComputerAlgebraSystems]

Wed, 01 Jul 2026 19:44:08 +0000

++added: Sympy -- See: https://sympy.org Due to size and complexity access to Sage (see: https://sagemath.org) is not feasible.

[BugTracker]

Mon, 22 Jun 2026 23:01:49 +0000

??changed: -FriCAS bugs should be reported in FriCAS bug tracker at SourceForge: -http://sourceforge.net/p/fricas/bugs/ FriCAS bugs should be reported in FriCAS bug tracker at Github: https://github.com/fricas/fricas/issues/

[FriCASIntegration] another silly algebraic case, totally different form from WA

Thu, 04 Jun 2026 18:27:18 +0000

??changed: -Subject: another silly algebraic case, totally different form from WA Subject: another silly algebraic case, totally different form from WA (it's not obvious that (t-x)(t+x)=1)

[#218 New version Reduce 3.8 includes MathML]

Sun, 31 May 2026 22:43:59 +0000

++added: From test1 Sun May 31 22:43:59 +0000 2026 From: test1 Date: Sun, 31 May 2026 22:43:59 +0000 Subject: Message-ID: <20260531224359+0000@wiki.fricas.org> Category: Reduce => MathAction

[ExampleTrigonometricConstants]

Mon, 02 Mar 2026 18:17:05 +0000

??changed: - Example of computations with trigonometric constants Consider the problem: Let $t := (5/9)\pi$. Simplify $tan(t) + 4sin(t)$. We can solve it by noting that involved numbers can be expressed in terms of roots of $1$, Namely, first we express trigonometric functions in terms of complex exponentials. Since $(5/9)\pi$ is a rational multiple of $\pi$ we get root of $1$, in this case root of degree $18$. But we also need $i$, which leads to root of degree $36$. Corresponding field is extention by cyclotomic polynomial, so we build it: \begin{axiom} cyclotomic(36)$CyclotomicUtilities )set output algebra on )set output tex off cF := SAE(FRAC(INT), SUP(FRAC(INT)), %) )set output tex on )set output algebra off \end{axiom} Now, we can express all ingredients in terms of generator: \begin{axiom} et := (generator()$cF)^10 ct := (et + 1/et)/2 st := (et - 1/et)/(2*(generator()$cF)^9) \end{axiom} and our expression is: \begin{axiom} ex := (4*ct + 1)*st/ct \end{axiom} Now we can find minimal polynomial and find its roots: \begin{axiom} minimalPolynomial(%) \end{axiom} and we see that the result is $\sqrt(3)$. We could also observe that the expression above is a member of smaller cyclotomic field and from that infer expression $2\cos(\pi/6)$. Consder now expression $$ i(5\sin((5\pi)/7)-5\sin((4\pi)/7)+5\sin((3\pi)/7) -5\sin((2\pi)/7)) -5\cos((5\pi)/7)+5\cos((4\pi)/7) $$ $$ -5\cos((3\pi)/7)+5\cos((2\pi)/7) -10\cos(\pi/7)+6. $$ Now we need root of $1$ of degree $28$, so we build the field: \begin{axiom} cyclotomic(28)$CyclotomicUtilities )set output algebra on )set output tex off cF2 := SAE(FRAC(INT), SUP(FRAC(INT)), %) )set output tex on )set output algebra off \end{axiom} Root of degree $4$ that is generator to power $7$ gives us imaginary unit $i$, Suare of generator gives us primitive root of degree $7$, that is $\exp(\pi/7)$: \begin{axiom} im2 := generator()$cF2^7 e1 := generator()$cF2^2 \end{axiom} We express trigonometric functions in terms of this \begin{axiom} c1 := (e1 + 1/e1)/2 e2 := e1^2 c2 := (e2 + 1/e2)/2 s2 := (e2 - 1/e2)/(2*im2) e3 := e1^3 c3 := (e3 + 1/e3)/2 s3 := (e3 - 1/e3)/(2*im2) e4 := e1^4 c4 := (e4 + 1/e4)/2 s4 := (e4 - 1/e4)/(2*im2) e5 := e1^5 c5 := (e5 + 1/e5)/2 s5 := (e5 - 1/e5)/(2*im2) \end{axiom} Using this we can compute the expression: \begin{axiom} im2*(5*s5 - 5*s4 + 5*s3 - 5*s2) - 5*c5 + 5*c4 - 5*c3 + 5*c2 - 10*c1 + 6 \end{axiom}

[ExampleFreeModule]

Fri, 27 Feb 2026 08:25:13 +0000

??changed: - How to use FreeFreeModule Commit https://github.com/fricas/fricas/commit/e5785c16bf7552522aac47ab5bb698244bffe090 removed the domain FreeAbelianGroup from FriCAS. See also https://groups.google.com/g/fricas-devel/c/yYgfAC-KWhg/m/p23BP5ZSBQAJ . It can be replaced by FreeModule as follows. \begin{axiom} )version Z ==> Integer FreeAbelianGroup X ==> FreeModule(Integer,X) A ==> FreeAbelianGroup(M) M ==> Matrix Z m1 := matrix [[1,2],[3,4]] m2 := matrix [[8,3]] m3 := matrix [[6],[7]] a1 := m1::A; a2:=m2::A;a3:=m3::A; x1 := 2*a1+a2 x2 := 3*a1-5*a3 x1+x2 \end{axiom}

[Symbolic Integration]

Wed, 23 Jul 2025 14:26:04 +0000

??changed: -Unfortunately, due to a bug during final processing this result got mangled and elliptic -integral part is dropped, giving wrong result. - -We gets correct result when we keep only algebraic part Below is result when we keep only algebraic part