Hi all,
Continuing the
question<https://groups.google.com/forum/?fromgroups#!topic/sage-support/cvtz4Zh-WYQ>
...
Input data:
sage: K=GF(2^8,'a',modulus=ZZ['x']("x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 1"))
sage: K.multiplicative_generator()
a^4 + a^3 + a
sage: P=PolynomialRing(K,'x')
sage: pol=P.random_element(5)
sage: pol
(a^7 + a^5 + a^3 + 1)*x^5 + (a^5 + a^4 + a^3 + a^2 + a + 1)*x^4 + (a^7 +
a^3 + a^2 + a)*x^3 + (a^5 + a^2)*x^2 + (a^6 + a^5 + a^4 + 1)*x + a^3
1. How to represent *pol *using multiplicative generator? The output must
be b^(i1)*x^5 + b^(i2)*x^4 + b^(i3)*x^3 + b^(i4)*x^2 + b^(i5)*x + a^3,
where b = K.multiplicative_generator(), i1-i5 logarithmic representation of
(a^7
+ a^5 + a^3 + 1), (a^5 + a^4 + a^3 + a^2 + a + 1)...
I have a correct function:
sage: b=K.multiplicative_generator()
sage: P(["({0})^{1}".format(b,i.log(b)) for i in pol.coeffs()]) == pol
True
sage: ["({0})^{1}".format(b,i.log(b)) for i in pol.coeffs()]
['(a^4 + a^3 + a)^27', '(a^4 + a^3 + a)^234', '(a^4 + a^3 + a)^195', '(a^4
+ a^3 + a)^134', '(a^4 + a^3 + a)^79', '(a^4 + a^3 + a)^101']
If I have one program then the above method suits me. But if two, i.e. one
program represents polynomial in the form b^(i1)*x^5 ... and returns b and
another program tries to restore it, then I worry about the phrase
The docs for multiplicative_generator() say: "return a generator of
the multiplicative group", then add "Warning: This generator might
change from one version of Sage to another."
2. So the question is how to uniquely reconstruct the original *pol*, if I
have *modulus*, *multiplicative generator *and* representation of pol as *
b^(i1)*x^5...?
Regards,
Oleksandr
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