Re: [sage-support] Error in operations of finite field
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Dima Pasechnik
Nov 22, 2019, 4:51:57 AM11/22/19
to sage-support, sage-devel
This is now https://trac.sagemath.org/ticket/28786
Note that it only happens if modulus is explicitly given.
On Fri, Nov 22, 2019 at 9:47 AM Dima Pasechnik <dim...@gmail.com> wrote:
>
> yes, I can confirm this is still giving an error in the latest Sage
> beta. (9.0.beta6).
> Note that actually it's two identical inputs, the 2nd executed after
> the 1st gives the error.
>
> I'll open a ticket.
>
> On Fri, Nov 22, 2019 at 7:53 AM Samanta <susantas...@gmail.com> wrote:
> >
> > I did not understand why the error has occurred. For the first time, it returned output but for the second time when I run the same code, I found an error "ValueError: the degree of the modulus does not equal the degree of the field" which is also not true as my irreducible polynomial has degree 6.
> > I am attaching my code and output for two consecutive times.
> >
> > sage: K.<a>=GF(2^6, modulus=x^6 + x^4 + x^3 + x + 1)
> > ....: x=a^9
> > ....: y=a^21
> > ....: z=1/x
> > ....: v=vector([1,y,y^2,y^3,y^4,y^5,y^6])
> > ....: S=matrix([[1,1,1,1,1,1,1],[1,z,z^2,z^3,z^4,z^5,z^6],[1,(z^2),(z^2)^2,(z^2)^3,(z^2)^4,(z^2)^5,(z^2)^6],[1,(z^3),(z^3)^2,(z^3)^3,(z^3)^4,(z^
> > ....: 3)^5,(z^3)^6],[1,(z^4),(z^4)^2,(z^4)^3,(z^4)^4,(z^4)^5,(z^4)^6],[1,(z^5),(z^5)^2,(z^5)^3,(z^5)^4,(z^5)^5,(z^5)^6],[1,(z^6),(z^6)^2,(z^6)^3
> > ....: ,(z^6)^4,(z^6)^5,(z^6)^6]])
> > ....: w=S*v
> > ....: w
> > ....:
> > (1, a^3 + a + 1, a^5 + a^4 + a^3 + a^2 + 1, a^4 + a^3 + a^2, a^5 + a^4 + a^3, a^3 + a^2 + 1, a^4 + a^3 + a^2 + a + 1)
> >
> > sage: K.<a>=GF(2^6, modulus=x^6 + x^4 + x^3 + x + 1)
> > ....: x=a^9
> > ....: y=a^21
> > ....: z=1/x
> > ....: v=vector([1,y,y^2,y^3,y^4,y^5,y^6])
> > ....: S=matrix([[1,1,1,1,1,1,1],[1,z,z^2,z^3,z^4,z^5,z^6],[1,(z^2),(z^2)^2,(z^2)^3,(z^2)^4,(z^2)^5,(z^2)^6],[1,(z^3),(z^3)^2,(z^3)^3,(z^3)^4,(z^
> > ....: 3)^5,(z^3)^6],[1,(z^4),(z^4)^2,(z^4)^3,(z^4)^4,(z^4)^5,(z^4)^6],[1,(z^5),(z^5)^2,(z^5)^3,(z^5)^4,(z^5)^5,(z^5)^6],[1,(z^6),(z^6)^2,(z^6)^3
> > ....: ,(z^6)^4,(z^6)^5,(z^6)^6]])
> > ....: w=S*v
> > ....: w
> > ....:
> > ---------------------------------------------------------------------------
> > ValueError Traceback (most recent call last)
> > <ipython-input-3-37bf7e6f8848> in <module>()
> > ----> 1 K = GF(Integer(2)**Integer(6), modulus=x**Integer(6) + x**Integer(4) + x**Integer(3) + x + Integer(1), names=('a',)); (a,) = K._first_ngens(1)
> > 2 x=a**Integer(9)
> > 3 y=a**Integer(21)
> > 4 z=Integer(1)/x
> > 5 v=vector([Integer(1),y,y**Integer(2),y**Integer(3),y**Integer(4),y**Integer(5),y**Integer(6)])
> >
> > /home/susanta/Desktop/SageMath/local/lib/python2.7/site-packages/sage/structure/factory.pyx in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:2162)()
> > 366 False
> > 367 """
> > --> 368 key, kwds = self.create_key_and_extra_args(*args, **kwds)
> > 369 version = self.get_version(sage_version)
> > 370 return self.get_object(version, key, kwds)
> >
> > /home/susanta/Desktop/SageMath/local/lib/python2.7/site-packages/sage/rings/finite_rings/finite_field_constructor.pyc in create_key_and_extra_args(self, order, name, modulus, names, impl, proof, check_irreducible, prefix, repr, elem_cache, **kwds)
> > 583
> > 584 if modulus.degree() != n:
> > --> 585 raise ValueError("the degree of the modulus does not equal the degree of the field")
> > 586 if check_irreducible and not modulus.is_irreducible():
> > 587 raise ValueError("finite field modulus must be irreducible but it is not")
> >
> > ValueError: the degree of the modulus does not equal the degree of the field
> >
> > --
> > You received this message because you are subscribed to the Google Groups "sage-support" group.
> > To unsubscribe from this group and stop receiving emails from it, send an email to sage-support...@googlegroups.com.
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Note that it only happens if modulus is explicitly given.
On Fri, Nov 22, 2019 at 9:47 AM Dima Pasechnik <dim...@gmail.com> wrote:
>
> yes, I can confirm this is still giving an error in the latest Sage
> beta. (9.0.beta6).
> Note that actually it's two identical inputs, the 2nd executed after
> the 1st gives the error.
>
> I'll open a ticket.
>
> On Fri, Nov 22, 2019 at 7:53 AM Samanta <susantas...@gmail.com> wrote:
> >
> > I did not understand why the error has occurred. For the first time, it returned output but for the second time when I run the same code, I found an error "ValueError: the degree of the modulus does not equal the degree of the field" which is also not true as my irreducible polynomial has degree 6.
> > I am attaching my code and output for two consecutive times.
> >
> > sage: K.<a>=GF(2^6, modulus=x^6 + x^4 + x^3 + x + 1)
> > ....: x=a^9
> > ....: y=a^21
> > ....: z=1/x
> > ....: v=vector([1,y,y^2,y^3,y^4,y^5,y^6])
> > ....: S=matrix([[1,1,1,1,1,1,1],[1,z,z^2,z^3,z^4,z^5,z^6],[1,(z^2),(z^2)^2,(z^2)^3,(z^2)^4,(z^2)^5,(z^2)^6],[1,(z^3),(z^3)^2,(z^3)^3,(z^3)^4,(z^
> > ....: 3)^5,(z^3)^6],[1,(z^4),(z^4)^2,(z^4)^3,(z^4)^4,(z^4)^5,(z^4)^6],[1,(z^5),(z^5)^2,(z^5)^3,(z^5)^4,(z^5)^5,(z^5)^6],[1,(z^6),(z^6)^2,(z^6)^3
> > ....: ,(z^6)^4,(z^6)^5,(z^6)^6]])
> > ....: w=S*v
> > ....: w
> > ....:
> > (1, a^3 + a + 1, a^5 + a^4 + a^3 + a^2 + 1, a^4 + a^3 + a^2, a^5 + a^4 + a^3, a^3 + a^2 + 1, a^4 + a^3 + a^2 + a + 1)
> >
> > sage: K.<a>=GF(2^6, modulus=x^6 + x^4 + x^3 + x + 1)
> > ....: x=a^9
> > ....: y=a^21
> > ....: z=1/x
> > ....: v=vector([1,y,y^2,y^3,y^4,y^5,y^6])
> > ....: S=matrix([[1,1,1,1,1,1,1],[1,z,z^2,z^3,z^4,z^5,z^6],[1,(z^2),(z^2)^2,(z^2)^3,(z^2)^4,(z^2)^5,(z^2)^6],[1,(z^3),(z^3)^2,(z^3)^3,(z^3)^4,(z^
> > ....: 3)^5,(z^3)^6],[1,(z^4),(z^4)^2,(z^4)^3,(z^4)^4,(z^4)^5,(z^4)^6],[1,(z^5),(z^5)^2,(z^5)^3,(z^5)^4,(z^5)^5,(z^5)^6],[1,(z^6),(z^6)^2,(z^6)^3
> > ....: ,(z^6)^4,(z^6)^5,(z^6)^6]])
> > ....: w=S*v
> > ....: w
> > ....:
> > ---------------------------------------------------------------------------
> > ValueError Traceback (most recent call last)
> > <ipython-input-3-37bf7e6f8848> in <module>()
> > ----> 1 K = GF(Integer(2)**Integer(6), modulus=x**Integer(6) + x**Integer(4) + x**Integer(3) + x + Integer(1), names=('a',)); (a,) = K._first_ngens(1)
> > 2 x=a**Integer(9)
> > 3 y=a**Integer(21)
> > 4 z=Integer(1)/x
> > 5 v=vector([Integer(1),y,y**Integer(2),y**Integer(3),y**Integer(4),y**Integer(5),y**Integer(6)])
> >
> > /home/susanta/Desktop/SageMath/local/lib/python2.7/site-packages/sage/structure/factory.pyx in sage.structure.factory.UniqueFactory.__call__ (build/cythonized/sage/structure/factory.c:2162)()
> > 366 False
> > 367 """
> > --> 368 key, kwds = self.create_key_and_extra_args(*args, **kwds)
> > 369 version = self.get_version(sage_version)
> > 370 return self.get_object(version, key, kwds)
> >
> > /home/susanta/Desktop/SageMath/local/lib/python2.7/site-packages/sage/rings/finite_rings/finite_field_constructor.pyc in create_key_and_extra_args(self, order, name, modulus, names, impl, proof, check_irreducible, prefix, repr, elem_cache, **kwds)
> > 583
> > 584 if modulus.degree() != n:
> > --> 585 raise ValueError("the degree of the modulus does not equal the degree of the field")
> > 586 if check_irreducible and not modulus.is_irreducible():
> > 587 raise ValueError("finite field modulus must be irreducible but it is not")
> >
> > ValueError: the degree of the modulus does not equal the degree of the field
> >
> > --
> > You received this message because you are subscribed to the Google Groups "sage-support" group.
> > To unsubscribe from this group and stop receiving emails from it, send an email to sage-support...@googlegroups.com.
> > To view this discussion on the web visit https://groups.google.com/d/msgid/sage-support/47e0cba1-d1be-40b7-b376-cfa537b68e29%40googlegroups.com.
Dima Pasechnik
Nov 22, 2019, 4:57:08 AM11/22/19
to sage-support, sage-devel
This is a variable name clash. Somehow, using 'x' for modulus creates a problem.
If I instead do
T.<xx>=GF(2)[]
K.<a>=GF(2^6, modulus=xx^6 + xx^4 + xx^3 + xx + 1)
...
then everything works as expected.
If I instead do
T.<xx>=GF(2)[]
K.<a>=GF(2^6, modulus=xx^6 + xx^4 + xx^3 + xx + 1)
...
then everything works as expected.
David Roe
Nov 22, 2019, 11:22:37 AM11/22/19
to sage-devel, sage-support
The issue is that you redefined x after defining K. I wrote more on the ticket.
David
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