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[Axiom-math] How to make symbolic computations?
From: |
Fabio S. |
Subject: |
[Axiom-math] How to make symbolic computations? |
Date: |
Tue, 28 Feb 2006 12:54:01 +0100 (CET) |
Hi,
I am facing a problem that I can't solve and I can't find any help on the
book.
The problem is the following: assume you have a field k (let's say k=Q,
but I would like to more general if possible) and take two variable x and
y which do not commute.
I would like to build the non-commutative algebra h=k[x,y] and then I
would like to make computations in h using some predefined rules for x and
y. As an example, take the three equations
x*y*x=y*x*y
x*x=a*x+b
y*y=a*y+b
where a and b are (generic, if possible) elements of k.
Then, I would like to be able to reduce polynomials in x and y according
to the previous rules. For example,
(x+y)^2 (=x^2+x*y+y*x+y^2)
should reduce to
a*(x+y)+2*b+x*y+y*x
and
(x+y)^3
(
=(x+y)(x+y)^2
=(x+y)(a(x+y)+2b+xy+yx)
=axx+axy+ayx+ayy+2bx+2by+xxy+xyx+yxy+yyx
=a^2x+ab+axy+ayx+a^2y+ab+2bx+2by+(ax+b)y+xyx+yxy+(ay+b)x
=a^2x+ab+axy+ayx+a^2y+ab+2bx+2by+axy+by+xyx+yxy+ayx+bx
=xyx+yxy+axy+axy+ayx+ayx+a^2x+2bx+bx+a^2y+2by+by+ab+ab
)
should reduce to
2*x*y*x+2*a*x*y+2*a*y*x+(a^2+3*b)*x+(a^2+3*b)*y+2*a*b
Is this possible? I think it should, but I couldn't find how... :-((
Thanks for your help
Fabio
- [Axiom-math] How to make symbolic computations?,
Fabio S. <=