a very easy example would be this:
sage: p1 = vector([-3,1,1])
sage: p2 = vector([1,-3,1])
sage: p = vector([0,-2,1])
#now i'm looking for some x,y such that
#x * p1 + y * p1 == p
x,y = var('x,y')
sage: assume(x > 0)
sage: assume(y > 0)
sage: solve([x * p1 + y * p2 == p],x,y)
[]
#but: x = 1/4 and y = 3/4 is a solution of this equation.
in the end i need this kind of calculation for every latticepoint on the
border of a lattice-simplex. like the example above shows how it should
work for a line, it also should be extendable to n+1 points on each n
dimensional facet of the simplex, where the points p0,....,pn are given
as the vertices of the facet.
greatz Johannes
Am 15.07.2011 03:27, schrieb William Stein:
> On Thu, Jul 14, 2011 at 7:39 PM, Johannes <dajo.m...@web.de> wrote:
>> Hi list,
>> i have given a finite set of points (lets call it V \subset ZZ^n) and
>> have to express some other points p_0,\dots,p_k \in ZZ^n as affine (or
>> convex) combination of elements from V.
>> How can i do this?
>> I tried it with span(ZZ,V) but that leads to ZZ^n and the p_i are
>> written with respect to the default basis.
>> otherwise i tried it with the sage.geometry.triangulation module, but
>> i'm not sure if i used it the right way.
>
> Can you provide an explicit example, for example some Sage code one
> can paste in that defines your points in a simple situation?
> This always makes answering questions easier...
>
>>
>> greatz Johannes
>>
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>
>
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