我有一个问题，那里有一个规范的解决方案，任何旋转和镜像（在轴上）是另一种解决方案。
为了避免由于旋转引起的多解决问题，我设置了约束，即在可能的情况下矢量应该与轴对齐。
“镜子”解决方案现在是我的问题。
基本上一些值可以具有正解或负解。
这为2^d大小d问题提供了assume解决方案。
我尝试使用solve并将一些值固定为正值，这应该可以解决问题，但/* A parameter w0 in (0,1] */
assume(w0>=0);
assume(w0<1);
d:2$
/* d+1 extra points, the is one at x=0, for a total fo d+2 points */
s:d+1$
/* The unknown are w (weights of the first component) and x_S vectors of dimension d */
v:append([w1],makelist(x[i-s*floor(i/s)+1,floor(i/s)+1],i,0,d*s-1));
/* The different constraints */
e:append(
/* The sum of weights is 1 */
[w0+s*w1-1=0],
/* Some of the components are 0 to be aligned with the axis */
flatten(makelist(makelist(x[i,j]=0,j,i+1,d),i,1,s-1)),
/* The mean is 0 */
makelist(sum(x[i,j],i,1,s)=0,j,1,d),
/* All vectors have length squared of x[1,1]^2, x[1,:] is skipped as only its first component is non-zero*/
makelist(sum(x[i,j]^2,j,1,d)-x[1,1]^2=0,i,2,s),
/* The diagonal of the covariance matrix is 1, w0*0 +w1*sum(x_i^2)=1*/
makelist(w1*sum(x[i,j]^2,i,1,s)-1=0,j,1,d),
/* The off-diagonal elements are 0. The dependancy on w1 can be eliminated since the equation is =0. */
flatten(makelist(makelist(sum(x[i,jj]*x[i,jj+j],i,1,s)=0,j,1,d-jj),jj,1,d-1))
);
/* THIS IS NOT WORKING AS I EXPECTED, I WANT SOLUTION ONLY WITH x[i,i]>0 */
assume(x[1,1]>0,x[2,2]>0);
solution:solve(e,v)$
number_solutions=length(solution);
仍然会找到负面解决方案。
到目前为止，这是我的代码：
solve有没有办法强迫check_canonical(sol):=block([],
/* Extract the expression x[i,i]=... */
diag_expr0:makelist(sublist(sol,lambda([e],(if lhs(e)=x[i,i] then true else false))),i,1,d),
diag_expr1:flatten(diag_expr0),
/* Get the right hand side */
diag_expr2:makelist(rhs(diag_expr1[i]),i,1,d),
/* Check for the rhs to be positive */
pos_diag:sublist(diag_expr2,lambda([e],if e>0 then true else false)),
/* If all the elelment are positive, then this is a canonical solution */
if length(pos_diag)=d then true else false
)$
canonical_solution:flatten(sublist(solutions,check_canonical));
仅探索问题的某些解决方案？
解： 根据罗伯特的评论，我能够获得如下的“规范”解决方案：
{{1}}
我不是Maxima的专家，但它确实有效，但我认为避免探索不符合某些标准的解决方案会更有趣。
答案 0 :(得分：1)
solve不会尝试过滤解决方案集。您必须过滤solve返回的结果。看看sublist。