Working with polynomials with non-commuting variables and symbolic rational coefficients

asked 2025-05-18 16:35:08 +0200

Ascot
1

I'm new to sage and need to work with polynomials in non-commuting variables but with symbolic rational coefficients. Looking through Lie algebras here and FreeAlgebra I can see hints that this is possible but it is not clear how I can do this where I can expand expressions and collect symbolic coefficients of the non-commuting monomials of the polynomials.

Any help or suggestions would be welcome.

answered 2025-05-18 20:28:28 +0200

FrédéricC

5466 ●4 ●45 ●122

updated 2025-06-12 21:40:38 +0200

something like this ?

sage: F = algebras.Free(SR,list('AB'))
sage: A, B = F.gens()
sage: (sin(x)*A+B)**2
sin(x)^2*A^2 + sin(x)*A*B + sin(x)*B*A + B^2

sage: Rx = PolynomialRing(QQ,'x')
sage: x = Rx.gen()
sage: F = algebras.Free(Rx,list('AB'))
sage: A, B = F.gens()
sage: x*A+(1/x)*B*A
x*A + 1/x*B*A

maybe ?

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I see. How would I create a polynomial ring now in the variables A and B with rational and symbolic coefficients, like the 'x' above? This is where I get stuck.

Ascot ( 2025-05-18 21:50:05 +0200 )edit

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Working with polynomials with non-commuting variables and symbolic rational coefficients

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Working with polynomials with non-commuting variables and symbolic rational coefficients