maybe it helps if i give my full pice of code:
def calc_wights_by_sum_to_zero(s):
#create the equations
variables = [var("w" + str(i),domain=ZZ)for i in range(s.nvertices())]
equation = reduce(lambda f1,f2: f1 + f2, [variables[i] * s.vertex(i)
for i in range(s.nvertices())])
#calculate the result, containing a parameter r
result = solve(equation,variables)[0]
#get the name of the parameter
parameter = result[0].variables()[0]
#add the constrain r == 1
result.append(parameter == 1)
variables.append(parameter)
#get the result for r = 1
result = solve(result,variables)
return tuple( [ww.right_hand_side() for ww in result[0]][0:-1])
i know that the equations are always solveable in ZZ.
greatz
Am 30.07.2010 02:03, schrieb kcrisman:
>
> On Jul 29, 6:01 pm, Johannes <[email protected]> wrote:
>
>> Hi list,
>> i try to solve a linear equation in ZZ in the variables w_i:
>>
>> sage: variables = [var("w" + str(i),domain=ZZ)for i in range(s.nvertices())]
>> sage: eq
>> (w0 + w1 + w2 - 14*w3, w1 + 2*w2 - 8*w3, 2*w2 - 3*w3)
>> sage: result
>> [w0 == 15/2*r548, w1 == 5*r548, w2 == 3/2*r548, w3 == r548]
>>
>> up to here it's ok, but now im lookin for the smalest integer r548 > 0
>> solving this equatoins. in other words, the smalest r548 such that every
>> wi is in ZZ.
>> How can i do this?
>>
> This sounds sort of like integer programming, which is very tough in
> general. Although in this case r548=2 looks like it would give all
> integer wi, just by inspection. Presumably this wouldn't always be
> possible with whatever you are looking at, though. I suppose one
> could just do
>
> r548=1
> while all wi not integers:
> r548+=1
>
> or something, though obviously that's a hack.
>
> Another issue is that solve() does not actually take the domain into
> account necessarily. (In fact, I'm not sure what var(domain=blah)
> does, but someone else may want to clarify that.) At any rate, Maxima
> (which does our solving) is explicitly designed not to take
> assumptions of this kind into account - though, again, I don't know
> that domain=ZZ would pass that on to Maxima anyway; presumably this is
> a Pynac thing.
>
> Does anyone else have ideas for this?
> - kcrisman
>
>
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