PARI/GP中matsolve方法疑似存在BUG的技术问询

尺寸不匹配触发段错误 #

向matsolve(M, B)方法传入尺寸不符合要求的矩阵时，未收到任何参数合法性预警，反而直接触发段错误，报错信息如下：

*** matsolve: bug in PARI/GP (Segmentation Fault), please report.

尺寸匹配时返回结果错误 #

当传入尺寸正确的矩阵时，得到的返回结果不符合预期，测试代码如下：

{
w = ffgen(w^7 + w^2 + Mod(2,3)*w + Mod(1,3));

info = [
  2*w^6 + 2*w^5 + 2*w^4 + 2*w^3 + 2*w^2 + w, w^6 + w^5 + w^4 + 2*w^2 + 2;
  w^4 + w^3 + 2*w^2 + w + 1, w^6 + 2*w^5 + 2*w^4 + w^3 + 2*w^2;
  2*w^6 + w^5 + w^4 + w^3 + 2, 2*w^5 + 2*w^4 + 2*w^3 + 2*w + 2;
  w^5 + w^3 + 2*w^2 + w, w^6 + 2*w^5 + 2*w^4 + 2*w^3 + w^2 + 1;
  w^3 + w^2 + 2*w + 1, 2*w^6 + w^5 + 2*w^3 + w;
  2*w^6 + 2*w^5 + w^4 + 2*w^3 + 2*w + 2, w^6 + 2*w^4 + 2*w^2 + 1;
  w^6 + 2*w^5 + 2*w^4 + 2*w^3 + 2*w^2 + 2*w + 1, w^6 + 2*w^4 + 2*w^3 + w^2 + w + 1
];

result = [
  w^6 + 2*w^5 + w^3 + 2*w;
  2*w^6 + w^2 + w;
  w^4 + 2*w^2 + 2*w + 2;
  2*w^6 + 2*w^5 + w^4 + w^3 + 2*w^2;
  2*w^5 + w^4 + w;
  w^5 + 2*w^2 + w + 2;
  2*w^6 + w^5 + 2*w^4 + 2*w^3 + 2*w^2 + w
];

\\ lamda * info = result
lamda = matsolve(info, result);

calculated_result = mattranspose(mattranspose(lamda) *
                                 mattranspose(info));
}

代码执行输出如下：

? result
[                w^6 + 2*w^5 + w^3 + 2*w]
[                        2*w^6 + w^2 + w]
[                  w^4 + 2*w^2 + 2*w + 2]
[      2*w^6 + 2*w^5 + w^4 + w^3 + 2*w^2]
[                        2*w^5 + w^4 + w]
[                    w^5 + 2*w^2 + w + 2]
[2*w^6 + w^5 + 2*w^4 + 2*w^3 + 2*w^2 + w]

? calculated_result
[              w^6 + 2*w^5 + w^3 + 2*w]
[                      2*w^6 + w^2 + w]
[    2*w^5 + w^4 + w^3 + w^2 + 2*w + 2]
[w^6 + w^5 + 2*w^4 + 2*w^3 + 2*w^2 + w]
[      w^6 + w^4 + w^3 + w^2 + 2*w + 1]
[        2*w^4 + 2*w^3 + w^2 + 2*w + 1]
[                  2*w^4 + w^3 + w + 1]

对比两个输出可见，result和calculated_result仅前两行一致，剩余行全部不匹配。猜测当传入n×k的info矩阵和k×1的result矩阵时，GP会忽略info矩阵最后(n-k)行的数据，导致计算结果出错。

内容的提问来源于stack exchange，提问作者karakale