# Math software for symbolic computation with customizable rules.

I am looking for software where we can define operations and rules of manipulation. For example, defining multiplication of $$x,y \in A$$ to be $$x\cdot y:= xy-yx$$ and $$x^{2k}=1$$ and $$y^{3k}=1$$, $$\forall k \gt 0$$. Also, we should be able to impose commutativity or non-commutativity, etc... I have heard of mathematica, maple, sagemath,.. , but I don't know which of those can accomplish what I want. Please give me some recommendations.

• Mathematica can do almost anything that you might want to do symbolically using your own custom rules and many built-in functions. – Somos May 19 at 8:13
• awesome. thanks! – TheLast Cipher May 19 at 8:15

$$f := (x,y)\mapsto xy-yx$$
simplify(f,{x^2=xy,y^2=yx}$These belong to the standard capabilities of computer algebra systems. • what about imposing non-commutativity and non-associativity and other rules? – TheLast Cipher May 19 at 8:11 • Non-commutativity holds in the first place. You have to specify$xy=yx\$ to establish commutativity. Same for associativity. – Wuestenfux May 19 at 8:14