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Factoring a polynomial over a finite ring

Hello Im following a 101 algebra course, and I would like to factor a polynomial on a finite field like F_9 for example.

R = PolynomialRing(GF(9),'x') x = R.gen() f = x^4+x^2-1 f in R f.factor()

i get an error message Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_68.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDkpLCd4JykKeCA9IFIuZ2VuKCkKZiA9IHheNCt4XjItMQpmIGluIFI="),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

File "/tmp/tmpYgKq_W/___code___.py", line 3, in <module> R = PolynomialRing(GF(_sage_const_9 ),'x') File "factory.pyx", line 364, in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:1244) File "/home/sage/sage-6.3/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.py", line 414, in create_key_and_extra_args raise ValueError("parameter 'conway' is required if no name given") ValueError: parameter 'conway' is required if no name given

%% im running sage 6.3 notebook on windows through Oracle VM winbox Im a totally new user, and ive looked at the tutorial and the forum but couldnt find any example or reason why this would not work thank you for your help %%

Factoring a polynomial over a finite ringField

Hello Im following a 101 algebra course, and for example, I would like to factor a polynomial on a finite field like ~~F_9 for example.~~F_9 (F_9 == ZZ/9ZZ is a field because 9 is a power of a prime number, 3)

R = PolynomialRing(GF(9),'x') x = R.gen() f = x^4+x^2-1 f in R f.factor()

i get an error message Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_68.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDkpLCd4JykKeCA9IFIuZ2VuKCkKZiA9IHheNCt4XjItMQpmIGluIFI="),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

File "/tmp/tmpYgKq_W/___code___.py", line 3, in <module> R = PolynomialRing(GF(_sage_const_9 ),'x') File "factory.pyx", line 364, in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:1244) File "/home/sage/sage-6.3/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.py", line 414, in create_key_and_extra_args raise ValueError("parameter 'conway' is required if no name given") ValueError: parameter 'conway' is required if no name given

%% im running sage 6.3 notebook on windows through Oracle VM winbox Im a totally new user, and ive looked at the tutorial and the forum but couldnt find any example or reason why this would not work thank you for your help %%

Factoring a polynomial over a finite Field

Hello Im following a 101 algebra course, and for example, I would like to factor a polynomial on a finite field like F_9 (F_9 == ZZ/9ZZ is a field because 9 is a power of a prime number, 3)

R = ~~PolynomialRing(GF(9),'x')~~ PolynomialRing(GF(9),'x')

x = ~~R.gen()~~ R.gen()

f = ~~x^4+x^2-1~~ x^4+x^2-1

f in R R

f.factor()

i get an error ~~message~~ message

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_68.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDkpLCd4JykKeCA9IFIuZ2VuKCkKZiA9IHheNCt4XjItMQpmIGluIFI="),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

File "/tmp/tmpYgKq_W/___code___.py", line 3, in <module> R = PolynomialRing(GF(_sage_const_9 ),'x') File "factory.pyx", line 364, in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:1244) File "/home/sage/sage-6.3/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.py", line 414, in create_key_and_extra_args raise ValueError("parameter 'conway' is required if no name given") ValueError: parameter 'conway' is required if no name given

%% im running sage 6.3 notebook on windows through Oracle VM winbox Im a totally new user, and ive looked at the tutorial and the forum but couldnt find any example or reason why this would not work thank you for your help %%

Factoring a polynomial over a finite Field

Hello Im following a 101 algebra course, and for example, I would like to factor a polynomial on a finite field like F_9 (F_9 == ZZ/9ZZ is a field because 9 is a power of a prime number, 3)

R = PolynomialRing(GF(9),'x')

x = R.gen()

f = x^4+x^2-1

f in R

f.factor()

i get an error message

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_68.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- coding: utf-8 --\n" + _support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDkpLCd4JykKeCA9IFIuZ2VuKCkKZiA9IHheNCt4XjItMQpmIGluIFI="),globals())+"\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module>

File "/tmp/tmpYgKq_W/___code___.py", line 3, in <module> R = PolynomialRing(GF(_sage_const_9 ),'x') File "factory.pyx", line 364, in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:1244) File "/home/sage/sage-6.3/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.py", line 414, in create_key_and_extra_args raise ValueError("parameter 'conway' is required if no name given") ValueError: parameter 'conway' is required if no name given

%% im running sage 6.3 notebook on windows through Oracle VM winbox Im a totally new user, and ive looked at the tutorial and the forum but couldnt find any example or reason why this would not work thank you for your help %%

Factoring a polynomial over a finite Field

Hello Im

I'm following a 101 algebra course, and for example, I would like to factor a polynomial on a finite field like F_9 (F_9 == ZZ/9ZZ is a field because 9 is a power of a prime number, 3)

R = PolynomialRing(GF(9),'x') PolynomialRing(GF(9),'x') x = R.gen() R.gen() f = x^4+x^2-1 x^4+x^2-1 f in R f.factor()R f.factor()

i get an error message

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_68.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -- -*- coding: utf-8 --\n" -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDkpLCd4JykKeCA9IFIuZ2VuKCkKZiA9IHheNCt4XjItMQpmIGluIFI="),globals())+"\n"); _support_.preparse_worksheet_cell(base64.b64decode("UiA9IFBvbHlub21pYWxSaW5nKEdGKDkpLCd4JykKeCA9IFIuZ2VuKCkKZiA9IHheNCt4XjItMQpmIGluIFI="),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) File "", line 1, in <module> <module> File "/tmp/tmpYgKq_W/___code___.py", line 3, in <module> R = PolynomialRing(GF(_sage_const_9 ),'x') File "factory.pyx", line 364, in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:1244) File "/home/sage/sage-6.3/local/lib/python2.7/site-packages/sage/rings/finite_rings/constructor.py", line 414, in create_key_and_extra_args raise ValueError("parameter 'conway' is required if no name given") ValueError: parameter 'conway' is required if no name given
%% im given

i'm running sage 6.3 notebook on windows through Oracle VM ~~winbox Im~~ winbox. I'm a totally new user, and ~~ive~~ i've looked at the tutorial and the forum ~~but couldnt~~ but couldn't find any example or reason why this would not ~~work~~ work. thank you for your ~~help %%~~help.

Revision history [back]

Factoring a polynomial over a finite ring

Factoring a polynomial over a finite ringField

Factoring a polynomial over a finite Field

Factoring a polynomial over a finite Field

Factoring a polynomial over a finite Field