Sorry to bug you again. Is there a kind soul who would get me started on this? Thanks.
On 10/10/2011 20:13, Christian Burisch wrote:
Hi All, William Stein referred me into here. I am working on a project analysing a function that uses multidimensional generalisations of complex numbers. A bit like cyclotomic fields, but where the unity roots are not complex numbers but actually different dimensions. There is one of these unity roots r_n per order n such that r_n^n=1. r_4 = i of course, traditionally defined as the sqrt(-1) rather than 4th root of 1. As an example let's call r_3 = j, so a 3-dimensional number (analogous to complex numbers) has the form: a + jb + j^2c The equations I am working on grow really huge very quickly and then simplify right down again. They are extremely tedious and error prone to work out by hand. I have been eyeing Mathematica, but its expensive and I don't know if it would help. Looking for alternatives I hit upon Sage. Can Sage do that sort of thing? Here is an example of an expansion: I'd like to say: V_2(p,e)=-V(p-e)-e V_3(p,e)=j/3(V_2(p,e)+V_2(p,ej)+V_2(p,ej^2)) Can I say something like expand V_3(p,1) whereupon Sage tells me that V_3(p,1)=-j/3(V(p-1)+V(p-j)+V(p-j^2) - (1+j+j^2)) p is the coordinate of a point. The value of function V at that point is V(p). e is just a constant that is passed in to determine the dimension we are looking at. For example: V_2(p,1)=-(V(p-1)+1) V_2(p,j)=-(V(p-j)+j) V_2(p,1+i)=-(V(p-i-i)+1+i) Thanks and best regards, Christian Burisch
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