Hi supporters,
I am using SageMath (version 8.9) in my Ubuntu 18.04 LTS and during the
calculation of inverse of a matrix in the quotient ring
GF(2)[x]/<x^8+x^2+1>, I am getting an error "NotImplementedError".
However, the determinant of the matrix is a unit in the ring so it is
invertible. Also, I have run the same code in the SageCell
(https://sagecell.sagemath.org/) and get no error.
I am attaching the details of the error and a picture of the solution from
SageCell. I can't get any idea how to overcome this problem without
installing the latest version of SageMath. Please guide me.
Thanks
Code:
---------------------------------------------
R = PolynomialRing(GF(2),'x')
S = R.quotient(x^8 + x^2 + 1,'a')
a = S.gen()
M= matrix([[a,a],[a^2,1]])
~M
Error in SageMath 8.9:
-------------------------------------------
Traceback (most recent call last): File "<stdin>", line 1, in <module> File
"_sage_input_5.py", line 10, in <module> exec
compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" +
_support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDIpLCd4JykKUyA9IFIucXVvdGllbnQoeF44ICsgeF4yICsgMSkKYSA9IFMuZ2VuKCkKTT0gbWF0cml4KFtbYSxhXSxbYV4yLDFdXSkKfk0="),globals())+"\\n");
execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>
File "/tmp/tmpT8yobj/___code___.py", line 7, in <module> exec compile(u'~M
File "", line 1, in <module> File "sage/matrix/matrix0.pyx", line 5389, in
sage.matrix.matrix0.Matrix.__invert__
(build/cythonized/sage/matrix/matrix0.c:35644) File
"sage/matrix/matrix1.pyx", line 628, in
sage.matrix.matrix1.Matrix.matrix_over_field
(build/cythonized/sage/matrix/matrix1.c:8265) File "sage/rings/ring.pyx",
line 1317, in sage.rings.ring.CommutativeRing.fraction_field
(build/cythonized/sage/rings/ring.c:11715) File "sage/rings/ring.pyx", line
996, in sage.rings.ring.Ring.is_integral_domain
(build/cythonized/sage/rings/ring.c:8473) NotImplementedError
Result in SageCell:
----------------------------------
[ a^5 + a^3 + a a^6 + a^4 + a^2]
[a^7 + a^5 + a^3 a^6 + a^4 + a^2]
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