Dear Vincent,
thank You for Your advice.
Probably I am extremely slow-witted, but I know PolynomialRing, polygen etc
Using Your suggestion I get _polynomials_ like x0, x1, x2, x3, x4 or x0 +
2*x1
which have a degree, a constant term, which can be partially differentiated
etc.
What I do _not_ get is a variable which assumes values in a certain finite
field.
Unfortunately SAGE let me specify var('x',domain = GF(3)) but ignores the
specification of the domain:
x is essentially a variable which assumes complex values.
I consider to write variable elements of F.<a> = GF(2^2)
as c_1*a+c_o with complex variables c_o and c_1.
But then I have to implement all arithmetic in F and its extension fields
by hand.
This is not what I expect is the right way to do it in SAGE.
What do You recommend? Best Eggart
Am Montag, 14. September 2015 00:15:31 UTC+2 schrieb vdelecroix:
>
> Hello,
>
> You would better use polynomial variables
>
> sage: R = PolynomialRing(GF(3), 'x', 5)
> sage: R.gens()
> (x0, x1, x2, x3, x4)
> sage: x0,x1,x2,x3,x4 = R.gens()
> sage: x0 + 2*x1
> x0 - x1
>
> But you can only do polynomial computations with them
>
> sage: x0 ** x1
> Traceback (most recent call last):
> ...
> TypeError: non-integral exponents not supported
>
> Is that enough for your purpose?
>
> Vincent
>
> On 13/09/15 19:04, eggartmumie wrote:
> > Hi,
> >
> > in the context of HFE pf post quantum cryprography
> > I had to realize that symbolic variables are real or complex only.
> > SAGE ignores a 'domain=F' in var('x',domain=F) for some finite field F!
> > Is it possible to define symbolic variables as elements of a finite
> field?
> > I need such variables in order to determine the public set of
> polynomials
> > given the private conversion T\circ iso^{-1} \circ P\circ iso\circ S
> > where S and T are matrix transformations of vectors over some field F,
> > iso is the vector space isomorphism of F^n to the extension field E,
> > and P is some polynomial on E.
> > It is easy to determine the conversion of a given vector over F.
> > But how can I compute the n multivariate polynomials if the argument
> > is a symbolic vector over F?
> > I am using SAGE 6.2.
> > Any indication is very much appreciated, best Eggart
> >
>
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