[sage-support] Re: var() definition in finite fields
Hi Peter, hi Martin, somehow both approaches I think don't work for me. For example, the square (m1^2) is carried in both approaches, even though it can be simplified to m1 in GF(2). I would like sage to account for the GF(2) in order to simplify terms. For example I would expect that x * (x + 1) is simplified to 0 if x is a variable in GF(2). Is there a way to do this or does sage lack that funcitonality? Thank you, Kim -- 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+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: var() definition in finite fields
On Wednesday, October 1, 2014 3:30:16 PM UTC-7, Kim Schoener wrote: Hi Peter, hi Martin, somehow both approaches I think don't work for me. For example, the square (m1^2) is carried in both approaches, even though it can be simplified to m1 in GF(2). I would like sage to account for the GF(2) in order to simplify terms. For example I would expect that x * (x + 1) is simplified to 0 if x is a variable in GF(2). It means that you want to work modulo the ideal (m1^2-m1,m2^2-m2,m3^2-m3,m4^2-m4). You can use sage: P.m1,m2,m3,m4=BooleanPolynomialRing() sage: m1^2+m1 0 sage: q=matrix(2,2,[m1,m2,m3,m4]) sage: q^2 [ m1 + m2*m3 m1*m2 + m2*m4] [m1*m3 + m3*m4m2*m3 + m4] Is there a way to do this or does sage lack that funcitonality? Thank you, Kim -- 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+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: var() definition in finite fields
Anything symbolic is in the symbolic ring SR, finite field elements are in GF(2). You can wrap finite field elements in the symbolic ring if you want to do symbolic computations with finite field coefficients: sage: SR(GF(5)(3)) * x 3*x sage: _ * 2 x though the symbolic elemnts still don't know anything about finite fields, they just carry the coefficients along. On Tuesday, September 30, 2014 3:14:03 PM UTC+1, Kim Schoener wrote: Heya! I want to do something relatively easy in Sage but can't figure out how. Hopefully you can help me. I want to do some symbolic operations (matrix/vector) in the GF(2). Let's start out with real numbers first: (m1, m2, m3, m4) = (var(m1), var(m2), var(m3), var(m4)) q = Matrix([ [m1, m2], [m3, m4], ]) print(q) print(q * q) Works pefectly: [m1 m2] [m3 m4] [ m1^2 + m2*m3 m1*m2 + m2*m4] [m1*m3 + m3*m4 m2*m3 + m4^2] But when I try the same thing in GF(2) by definiing q = Matrix(GF(2), [ [m1, m2], [m3, m4], ]) I get: [...] File parent.pyx, line 1069, in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8546) File coerce_maps.pyx, line 156, in sage.structure.coerce_maps.NamedConvertMap._call_ (sage/structure/coerce_maps.c:4930) File expression.pyx, line 857, in sage.symbolic.expression.Expression._integer_ (sage/symbolic/expression.cpp:5877) TypeError: unable to convert x (=m1) to an integer However, the matrix definition seems to be okay, when I do q = Matrix(GF(2), [ [1, 1 ], [1, 0], ]) print(q * q) I get [0 1] [1 1] which is what I'd expect. Why does it not work with variables when working in GF(2) and how can I get this to work the way I want it to? Thank you so much, Regards, Kim -- 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+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
[sage-support] Re: var() definition in finite fields
I'm not sure I understand fully what you're saying. I did m1 = SR(GF(2)(1)) * var(m1) m2 = SR(GF(2)(1)) * var(m2) m3 = SR(GF(2)(1)) * var(m3) m4 = SR(GF(2)(1)) * var(m4) but the Matrix definition q = Matrix(GF(2), [ [m1, m2], [m3, m4], ]) still results in the same error: unable to convert x (=x1) to an integer. How do I define a variable in the SR that I can work with? I can't seem to figure it out from the example you gave me. Thank you, Kim Am Dienstag, 30. September 2014 17:04:10 UTC+2 schrieb Volker Braun: Anything symbolic is in the symbolic ring SR, finite field elements are in GF(2). You can wrap finite field elements in the symbolic ring if you want to do symbolic computations with finite field coefficients: sage: SR(GF(5)(3)) * x 3*x sage: _ * 2 x though the symbolic elemnts still don't know anything about finite fields, they just carry the coefficients along. On Tuesday, September 30, 2014 3:14:03 PM UTC+1, Kim Schoener wrote: Heya! I want to do something relatively easy in Sage but can't figure out how. Hopefully you can help me. I want to do some symbolic operations (matrix/vector) in the GF(2). Let's start out with real numbers first: (m1, m2, m3, m4) = (var(m1), var(m2), var(m3), var(m4)) q = Matrix([ [m1, m2], [m3, m4], ]) print(q) print(q * q) Works pefectly: [m1 m2] [m3 m4] [ m1^2 + m2*m3 m1*m2 + m2*m4] [m1*m3 + m3*m4 m2*m3 + m4^2] But when I try the same thing in GF(2) by definiing q = Matrix(GF(2), [ [m1, m2], [m3, m4], ]) I get: [...] File parent.pyx, line 1069, in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8546) File coerce_maps.pyx, line 156, in sage.structure.coerce_maps.NamedConvertMap._call_ (sage/structure/coerce_maps.c:4930) File expression.pyx, line 857, in sage.symbolic.expression.Expression._integer_ (sage/symbolic/expression.cpp:5877) TypeError: unable to convert x (=m1) to an integer However, the matrix definition seems to be okay, when I do q = Matrix(GF(2), [ [1, 1 ], [1, 0], ]) print(q * q) I get [0 1] [1 1] which is what I'd expect. Why does it not work with variables when working in GF(2) and how can I get this to work the way I want it to? Thank you so much, Regards, Kim -- 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+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
Re: [sage-support] Re: var() definition in finite fields
Your matrix is over GF(2) not over the symbolic ring SR: sage: m1 = SR(GF(2)(1)) * var(m1) sage: m2 = SR(GF(2)(1)) * var(m2) sage: m3 = SR(GF(2)(1)) * var(m3) sage: m4 = SR(GF(2)(1)) * var(m4) sage: q = Matrix(SR, [ [m1, m2], [m3, m4], ]) sage: q^2 [ m1^2 + m2*m3 m1*m2 + m2*m4] [m1*m3 + m3*m4 m2*m3 + m4^2] On Tuesday 30 Sep 2014 08:46:42 Kim Schoener wrote: I'm not sure I understand fully what you're saying. I did m1 = SR(GF(2)(1)) * var(m1) m2 = SR(GF(2)(1)) * var(m2) m3 = SR(GF(2)(1)) * var(m3) m4 = SR(GF(2)(1)) * var(m4) but the Matrix definition q = Matrix(GF(2), [ [m1, m2], [m3, m4], ]) still results in the same error: unable to convert x (=x1) to an integer. How do I define a variable in the SR that I can work with? I can't seem to figure it out from the example you gave me. Thank you, Kim Am Dienstag, 30. September 2014 17:04:10 UTC+2 schrieb Volker Braun: Anything symbolic is in the symbolic ring SR, finite field elements are in GF(2). You can wrap finite field elements in the symbolic ring if you want to do symbolic computations with finite field coefficients: sage: SR(GF(5)(3)) * x 3*x sage: _ * 2 x though the symbolic elemnts still don't know anything about finite fields, they just carry the coefficients along. On Tuesday, September 30, 2014 3:14:03 PM UTC+1, Kim Schoener wrote: Heya! I want to do something relatively easy in Sage but can't figure out how. Hopefully you can help me. I want to do some symbolic operations (matrix/vector) in the GF(2). Let's start out with real numbers first: (m1, m2, m3, m4) = (var(m1), var(m2), var(m3), var(m4)) q = Matrix([ [m1, m2], [m3, m4], ]) print(q) print(q * q) Works pefectly: [m1 m2] [m3 m4] [ m1^2 + m2*m3 m1*m2 + m2*m4] [m1*m3 + m3*m4 m2*m3 + m4^2] But when I try the same thing in GF(2) by definiing q = Matrix(GF(2), [ [m1, m2], [m3, m4], ]) I get: [...] File parent.pyx, line 1069, in sage.structure.parent.Parent.__call__ (sage/structure/parent.c:8546) File coerce_maps.pyx, line 156, in sage.structure.coerce_maps.NamedConvertMap._call_ (sage/structure/coerce_maps.c:4930) File expression.pyx, line 857, in sage.symbolic.expression.Expression._integer_ (sage/symbolic/expression.cpp:5877) TypeError: unable to convert x (=m1) to an integer However, the matrix definition seems to be okay, when I do q = Matrix(GF(2), [ [1, 1 ], [1, 0], ]) print(q * q) I get [0 1] [1 1] which is what I'd expect. Why does it not work with variables when working in GF(2) and how can I get this to work the way I want it to? Thank you so much, Regards, Kim signature.asc Description: This is a digitally signed message part.
[sage-support] Re: var() definition in finite fields
Hello, I want to do some symbolic operations (matrix/vector) in the GF(2). Here is an alternative approach (assuming all your expressions are polynomials in m1, m2, m3 and m4): sage: R.m1,m2,m3,m4 = PolynomialRing(GF(2)) sage: q = Matrix(R, [[m1, m2], [m3, m4]]) sage: q [m1 m2] [m3 m4] sage: q*q [ m1^2 + m2*m3 m1*m2 + m2*m4] [m1*m3 + m3*m4 m2*m3 + m4^2] Note that the coefficients are elements of R = GF(2)[m1, m2, m3, m4], not of GF(2); cf. the other answers where they are in SR. Peter -- 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+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
