Just to confirm, after I installed sagemath_coxeter3 the computation which was reported on sage-support as failing, and which produced the traceback saying that coxeter3 needed to be installed, now works fine:
┌─────────────────────────────────────────────┐
│ SageMath version 10.6.beta4, Release Date: 2025-01-18 │
│ Using Python 3.12.5. Type "help()" for help. │
└─────────────────────────────────────────────┘
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┃ Warning: this is a prerelease version, and it may be unstable. ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: R.<v> = LaurentPolynomialRing(ZZ, 'v')
sage: W = CoxeterGroup('A3', implementation='coxeter3')
sage: H = IwahoriHeckeAlgebra(W, v**2); Cp=H.Cp()
sage: Cp.product_on_basis(W([1,2,1]), W([3,1]))
(v^-1+v)*Cp[1,2,1,3]
sage: Cp.product_on_basis(W([1,2,1]), W([3,1,2]))
(v^-1+v)*Cp[1,2,1,3,2] + (v^-1+v)*Cp[1,2,1]
- Marc