1
$\begingroup$

While trying to calculate the SmithDecomposition of an integer 293x329 matrix with less than 3000 non-zero elements in the range -4 to 3 several errors occur, none of them which seem to make any sense at all:

In[254]:= SmithDecomposition[tmat]

During evaluation of In[254]:= Part::partw: Part 296 of {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,<<245>>} does not exist.

During evaluation of In[254]:= Drop::drop: Cannot drop positions 1 through 296 in {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,<<245>>}.

During evaluation of In[254]:= Part::partw: Part 297 of {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,<<245>>} does not exist.

During evaluation of In[254]:= Part::partw: Part 298 of {1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,<<245>>} does not exist.

During evaluation of In[254]:= General::stop: Further output of Part::partw will be suppressed during this calculation.

During evaluation of In[254]:= HermiteDecomposition::latm: Matrix contains an entry that is not rational.

During evaluation of In[254]:= Set::shape: Lists {System`SmithDecompositionDump`tmpu$84833,System`SmithDecompositionDump`hnf$84833} and HermiteDecomposition[{{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<279>>},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<279>>},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<279>>},<<46>>,{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,<<279>>},<<2546>>}] are not the same shape.

During evaluation of In[254]:= HermiteDecomposition::latm: Matrix contains an entry that is not rational.

During evaluation of In[254]:= Set::shape: Lists {System`SmithDecompositionDump`tmpv$84833,System`SmithDecompositionDump`hnf$84833} and HermiteDecomposition[{{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<2546>>},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<2546>>},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<2546>>},<<46>>,{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,<<2546>>},<<279>>}] are not the same shape.

During evaluation of In[254]:= HermiteDecomposition::latm: Matrix contains an entry that is not rational.

During evaluation of In[254]:= General::stop: Further output of HermiteDecomposition::latm will be suppressed during this calculation.

During evaluation of In[254]:= Set::shape: Lists {System`SmithDecompositionDump`tmpu$84833,System`SmithDecompositionDump`hnf$84833} and HermiteDecomposition[{{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<2546>>},{0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<2546>>},{0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,<<2546>>},<<46>>,{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,<<2546>>},<<279>>}] are not the same shape.

During evaluation of In[254]:= General::stop: Further output of Set::shape will be suppressed during this calculation.

Out[254]= $Aborted 

I checked that all elements of the matrix are integers and interestingly the HermiteDecomposition does work. Trying to calculate the SmithDecomposition of the Hermite upper diagonal form results in the same error though.

Does anybody know what is going on?

The matrix in compressed form (use Uncompress to get the actual matrix) is the following

"1:eJztXcnO5LYRHi+XwE+RS24BWtRGHX00kFPyBE6QAeYQOJhxDnkXP2y6xarB/3d/\
bPFjiWxKzqXF1kLWzmJxqT/+/Ze/fvz+w4cPX364/vzt3z9//vLPHz9//vm/X/5w/f/\
jf3795V8///rpHx+/vb1ye+8vn778+tN314Jb+vXau+XT9fLh43dvX/n0ze3Wu68+/\
umbt3XcXrisv93663+6vd3168VdwkX+Deul78JlCpd5vQzhzWFcL6MLF/\
kX3pzCd1P4N4d/c3hzDrX48M/LvwCLX9bLMqx4dpdOrvp/DNfOyXUO1yvs4SrvOx+\
ufaBXN8jzQf6PUt8k9c1TuHr5L+07ac914blzoT3Xh/rd0MlVno9LuM7ynpf3lvC/\
7wIcfR++64fwfj8GfPpJrnNov/fC7yXUP1xCPYPAM0g9g+A1SD3DOMpV3p/lPR/+\
j0LP0YX3x17uy/fjFOofBY5RvxM4pktobxI4Jqln6kO70xjwnIS+\
k9B3WgIcs9B17kL9s3w/Cz6z8G0e5L7QaR4DPedZ7nt534f6Z61/Ce/7S3jPd/\
Jf8PTCLz92cpX/Aq8XvP0s3wkf/RLqW0QuF+HnIvUvbpCr/\
Bc5WYZRrvJf5GSZ5XvBY1nk/xX+\
71d5v3gpdHqnv0jhKntScFoYpDDqy1f5WQs3RQoFp3f0q27UO6O01c36std3rnz/\
PuiZFtxFC3qnl0bdKGC4WWp2yxgKfSc194pFP+\
ijUQuTFuZJC7MUvBSGi7Q1OC0o7oO2PszSxOClMF4EntENWpC2RiXmOAnKo9c7i7w8dfJo\
0kZvYh4Kk5Bu0kYnL8BPSrq5E+Bvwh0Ko1Q4T/pICX4T5LXgFWZ/EVB9J215ZYF3+\
nIv9Xglglca3iR3LSydPFoUi2XotaB3Jr0zS6OL10dLaN1duosWRin0emeYpTDpI6+\
PRBJcd5F3uk4LTgu9FoS8V+\
vrpCAS5TqvBeHOVR47LQiEzumdXguDFsavhUUKwgLnZi14LSxS6C8CT6+\
4904LvYDRD18LAkY/\
akHU6loQIvReXh6Ey1cABR4VbDf08vIw6J1J6hmUGsOsjxTmQdk0KllU+J0K/\
1VNtaAVjor7KNLiJtF3N3Xy+aRsmnq9IyrsplEfKTEnBUzVwU3Kr1lrvtn+UFC+zyo/\
s1Y4qyDNs36upJu1Qq8V+k4LvdTsBy2IkXFeFPbKZGnCK+m8snsRI+\
MWZcqiErUoERYVraX/\
ekdfVmFblD6LSt0iJvda0EfKgmX6ekcrVFCX2X387Ye3zt3NhXvv3HXgnru7FxyR+\
zfD3R7eHeDdEd11+O4E4MJtEXBF2ppBWxiDujTwAC7m+wV8j+h6j38r/L7Hn2/rvtY4v+\
9ptQ5zLkSl98CuFWAa7o/B2lhdtcWAQTJiXSTIeA/\
XehOCVYq28FWqMahkGF2zPibaubUxCME9G3kIMLpIPBzUskKMdHaNTGeku9fIEC1BNzEAh\
cDCmlPKUEArjiUB8zHdUGCW427ktV35ChjWsjJM7619WX9PsPVm3T4nXZR6u6+\
YbsH6us5ies/\
bW7zFEMUFr17HOfAuwvc6ljHTBjMCyzOsF1vXBzKEeHUhhAkGF0P4npkrwkinTo0wsrp7I\
FwKCdSnDRjcgyGBATuH6KEudEC95akRRgb9LN0H6i8H9OpZEEb95YCEzE3Y5YZGAHoYHuO\
LMUv3YQfYu3uslviu2a98GHCHu3AsEGEadLofxpU0caAnMEMV9lCiPaPuDHlxhKCQfx0Jv\
9Ri28oK6KNQrGAMER7E2cMyaWRY14BAwDDCFBJ2cLGFhEhAgz5jfxMbf2Y4bUZ4B5EmiAP\
1fcbWH4s0JBllc9KJzhl6zAq7JWIYlMaKZ11FejBphEQvxkzMtmYZVJcV0NDPGLB7VoRVe\
MkVcKbXbp8sliisLCQMcimLUQvhJ6YXe71WhCvzEgpkxHXHqNldd7tpsPAy7i+\
OUKSxjaUEHdtjexDCQpx1lXApp7emSE91HZqqkxQFTFlc/\
CeIsIcdm5mQbZABrYiYsOS0YPbSI2gT1GEioDSlRaTCXgPoH9R1bgsNyakYRLq7OUFfohj\
JsGLjOEjViEcp8hIxuLrkJexmzPWvayEJohPRtmaJzsk007HZQ5zprJiJOGDD5gVrhSVIS\
hMSxyJb6NrsQ+qqhMRxS2LAFRmjMkGtUuEr+\
0whcscjUoYH8GUUM0IyGACbcQTNzmEmCtEsL4noYBNGFgXAsIGrK5BY9LA3bRc9Jm5Tapm\
iWfSwL1yLaysI2DNsgT+\
FugSCP9hBiDgTdrehVBjDHqe1TuFg4jQx0mhhZocgJDPHXMrxsJtIAmHGn28hwmIfYZYJA\
WDUmlBBc4Sl0MAIh9fN5r+yAmFwmZkD+7qj9Jlcj2dyMbiFpjQocUJOlYceHAzQ+\
1Jr9Zl9QJaFs+vJROkxrbqL7jDFiq0yJHZeMkjgPv/\
1q1aLDbfMq0sxuFSYyrztj1oNhUwDpG5syQPBH9wY7uuYXdJ4mAElmohWVJ63RqsYFhzDw\
BO2EF88zm9hvtU+\
9LYPf8osG1xwZOP1MwG14x37r0hhWHG7212wg8CsG2emDfZ3TQMWdh8f0wy3hgdWxJCcUL\
fugntMRn5LBfjTesyABe4y627hx1RnsIB9MbRRe0i1fQP865eSdpf0cWOsc8LUKbV5vNb4\
LGBRZkF4uX4IYgGHjpUldQcsMGS4Bntr6RO3e7TW7vpMrFkYCzzmLzXkSIsrBchwHCzd1+\
jgMV948enRrBw+9aWDdCiHcU1bgvc+\
d1ADzo0x7N9KYVzgsJAVC1jv8bCAMBwOC9hvnkSH4KgD9pDnxjh9I8bx+kJkETvcQ+\
ITNLD/ALWFWnUbWVtkjcBxR2iU2qJOxMTg3Yj0tbA8fIdVzQyHfk8HDgR5MO/\
RiCwcrLtdwL5zo0z0luIFPEr03LrZgBbW1beH017Pr2+1Jk330kJi4UNlX4OhDoNx+\
iyMXXY6eKhvbGFJ3fW39j195nkReLJwG0sjzdTBcyj4KGRqoVG7K3DLzI13+\
DTlw0kJHBfig5MPJw+1FhwGmpl3zpi2XK0w4KOTm7DrDWgsPpO5Aa+C89fNS7TsHjQ+\
7PnUHvTr/RKOQ5gXDYxYqRX9mJINRJN2GLGmz0nEeEx48SfRQjuHGPrildHn0KFCy3+\
pbaR2DTAfctVEj16qb2EoSczuRE7XrDtSI9bO2A9/\
b3fUgU9TP8lMJhybwuPUO3w++Sno0EWOF2/BypU6BYmxiPbtZXZfLi1J4xP7Gzl1/\
Mw8tp9/1QLfWvDBS0Xda50OGShJ7LmnDsoptRmZwc3up7YrJczsQynZwd5rKdmp6pnjw+\
FP3TO0EN9pYO8kPvn+1JyvuzOvKjfhsf4dPic/\
st7oaEf2lOIQQ3Xi2KzIoXx2Hap5SmTlY1arHSYXuNlu7NVuEZlIQykrZ47IEikOOH2zzy\
gwo9D9T5UM1LHbHYIO5rOz2jhrtcxMW4ezPRyu5z1af0zQ99T9cQuerr0/\
LnXSTrv9cbM9L0wvgS1BZ8+\
g8P941FNemEcd7cajIlJy5qgEE49qYVaD4SZxODB1NjyzW6mBfUmleshIjokza8vRNABTv\
QUNOJqs23eIt+BVlFqbxFDSPEoqdio5gwXWllKpS1sYCUNvO3J+\
H34X860UzVqICmNtgadYRM5zhOdVQFnvmGQIlXteu1TbT1g0Wy4mc0ITq8+\
ZWJt9v3ShqBpO9XC4OIw92mxev74D3wqtdcf5MU6iWYQ9K6ZDDUT+\
D6dDdSPTdh0i4tVN9P7NjlCIxC9t5HUrtceG2KuBNbbuDvEdUsr87nb2R3LKtDD7W3N02+\
G0NIeTnapjf5xdp13ZiViNBs6HKdVvUpYAn/lSRqo7JnlQZW+l1FoqzAtzZBpnBDrcWp/\
X2zOG6i6S++fMI9Z2eXHmdeY14wQOZ2c6iVTXpWS7s+D2OWyGDma/utmxk8MZrU5xroTD+\
bNOceaAw1m1KI+/\
1JxlKflN73kdzg3WBHXq0qHuDH8DGONMZOfgJs5Pdmpu2qOh6XtsIpYLZ83B+dSKQZa+\
TszhHGm416u8Nv/1K/ZdJE/bsXp/fPKSwxnkDpcRCGKBc8WdBLdjZeByOKdbu/\
Di7G2Hkx0oJbgPOAluuG85mq2G2kLkdMPrJx3u3+\
pSJ5IX3Dy6xf0b9q7qxlao9WdQfnEfQHmOVjqU2/\
NqX8sKcWNy20VoVmpe2i4P6fsDYvTF1hOP/\
bE8lJISJq8ytr8QN5wFDMegK++jev2pRy6SPwv3LemrDFwk6xPjvTYQU8CZnHaYU2vhJK6\
6O9LK7PhzkexXpTj0e9vz6nD+rIj1PFjEEGfKKtX7R+\
wkXoVUyj4UOu2n2N5fyAuc0SrirTBzwnaf1j47yXg2xA7mYvsOGhj740xZkRloxkYRkXSc\
j6qynBE6hLM+nWLuK4axOYqCc/Tg2ZLK+\
WZa8CfN8ktFBKp6mfbcNA2suKu8m2aH3ZfmlZJMJpzKuwPPu4PZMTl6Gqa6OSpcaL+\
ew3mCWqDv0db/wvxDbfTSzUofzs5EnVxTZj+ki+RWMufyPdw+bGIcEMlVVJObLpJ3pwW+\
VR2TRbLm2OnQwr6v9Piki2TYqSqThXZfukh2GzuPmfjD62PQLpIJp2ovgleMRjK14N4/\
vZ8vdTKbg7lIOHjretCFdt7g7CuH83+b3XXIZF852r7xquetOCrzSSnbV8oaMfOxB9vbN+\
HzH6yZOUrNrjucoYSK8TewMw/\
n9jjcyk5IdZxzgfLwakpULMcq9uWIPuBgIzWODtgvKbUekditZJ7Ld5HcCK9fnxqTHUyHU\
usfzCsdIif6M6tvmh0BRk7TbyHKah+3mH3EBuaE28085SKn0+PVpXVXpRH+\
GT7pd4d8VHVP8sQ+TANeW6kdJ/h02XbziO2wrgL36GXW0LewysDBs/4iXjw8Ua+\
cn4qtBpR1aoyDNRavjyqFG9YszGN4F55TFrEE8BytHaQPnipVWbvheUwRDYBnFkV0CJ4BV\
HlMBs/q4eqFHILn5ERGgPDUmB6eocLuJPzth7d3b+904Pfb6++f7y8bL2fXFf1+q/\
kdH0QfU2BTmKA/m63Fa9irHor1GyTM5/\
kuYsDziaL1PpxPJFuOFh2onld82RoNMrRlJ7OzJYl7GmVe+\
N0mtVxarS7bUrlkeIy4si88v+Xe4u02YYtxq09j6vtm4mCktCxvDe/\
pvtUmJa6JHV2acrp3l7cv0NKSoUA51XCmJwe2XQn8/\
EIZ3UdVjnNvU082cdinyiRaP1GD5zrLSSrTjEPNxO1zDDRjY+\
4Zgx5gKknGLdEwSkBqA4kd03M671QxZbSp55nokVzYtKp7Qp7YMm96ckx/\
jsilmYNNCxGVTKCHqR3HVj2UiOxDh3yl5pDm5cUqm7tqHacPOdqT+ulmp1mMLmYUM+\
F7NsbY0K4NCm+\
PJAhVg2OYeJsGo7fbCxkmxvxltmDurI8GxS//qfV5hjU2vrtlnfKEqel6jvVla9Sj6slA/\
rnp2Ha5NpQr2ts+qxlA0EffS3Vbn8N276M+fIPhKEGQLUMFe+\
MqNHiGQo6gZxjuTVuepCEIm8Q6057ndAYUNvlGLx+\
0R22ws3DXl81fGvFIVaYcs5JoUHJUJkcNzJTYbNuKNodIYaFNnBeziGOOqjKSw9SSQcAgK\
VHKvR1o4uh0RCpgKBrI/3sI4jA/\
QMPaymilFAQkizI6sk3xNUO4P5wFJSsN9y27t7N8cYZmA45Hke3jFHysuAeP0EQ0ovNDa/\
HK4tDeTVHH6ZmG6KZmpdH7SdMZVjJuYzL0JyYW3OwrJTBpYhOT0dpiExWIfLEx6+\
cx7K3JtsWFPIN2qOkUoDcd8xe5Cs8b3cTwseczsHJbsPKFjRKzjfoZNHepNg3tRMYnMoFo\
hlsk8XT8lt5QHtUMhi4f+zhjKmHN2eACkkVgy6jak7FaTh/\
GG6Esp8v6SSKYVtSJmpl1Q6QAZYhhfseRpnvR+\
hPW2e1oSko0ajdcOUgZG3gmBDninabflOJtNsYZakYk3qHQ6yVqPVMrfVsd8EmxL7iX6TV\
QywyJQcqYt/HIETDkSSiAs4pU5/\
H6Cup88no8cyp4ajW3BXSnJ4kWNlU54qK9STzGYqeJT455eK7pyVNcacDyYrPbnqLnoO28\
jShGrrz1fmaxSm3OqDVZmGQBmm+\
xkpQmg173W3s2bEQ2TIw5ePs8ddlLmoRn7HmBtOM33YAPdw/\
uGJpjrHkKWVFdWXPdOVqyJVj5diutMep5Ri2J+mPFPLt+K/\
5pnxjf3VT7iA1M2beWaNlSlOap7uzTTqJWpVGFI8SGmU01ErwxZmQvn2Q7GYps1ieLf77d\
41Aw1J0hq49dFNc5gcUnibXJZXvVRbbs7SSanEnkmZS8ZTwKz86bzp+/u/fXLcIRrfV/\
RR/rPg=="
$\endgroup$
  • 1
    $\begingroup$ Hm. With the matrix that you posted in compressed form, I cannot reproduce the problem (running version 12). $\endgroup$ – Henrik Schumacher Jun 5 at 21:06
  • 1
    $\begingroup$ Works here too... maybe try restarting kernel to rule out lingering definitions. $\endgroup$ – bill s Jun 5 at 23:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.