Hi Nils, I have now done a small amount of investigation, and my results and replies are below. All the best, Paul
On Thursday, 14 July 2016 8:15:35 AM AEST you wrote: > On Thursday, July 14, 2016 at 6:18:16 AM UTC-7, Paul Leopardi wrote: > > (1) You can create a BooleanFunction of 0 variables (a constant), but you > > cannot save it to a file. Same with a BooleanFunction of 1 variable. > > > > This seems to be connected with the truth-table problems: The "pickling" > > essentially stores > > <BooleanFunction>.truth_table(format="hex") > > which uniquely determines the function for n>=2 variables (since then the > number of bits in the truth table is a multiple of 4 and hence lines up > with the length of hex numbers), but fails to uniquely determine the number > of variables uniquely if n<2. The pickle format would need adjustment to > reliably handle the n=0,1 cases. > > We could get the right result by changing > > sage.crypto.boolean_function.BooleanFunction > > to > > def __reduce__(self): > if self.nvariables() <2: > return unpickle_BooleanFunction, (self.truth_table(format='int'),) > else > unpickle_BooleanFunction, (self.truth_table(format='hex'),) If that could be done cleanly without breaking existing code, I can't see why not. > > (2) You cannot evaluate the algebraic normal form of a BooleanFunction of > > 0 variables. In addition, the error message incorrectly says that the > > number of variables must be greater than 1, but you *can* evaluate the > > algebraic normal form of a function of 1 variable. > > > > As your traceback shows, this error originates in the > > BooleanPolynomialRing parent (which is also returned). It is documented as > needing n>1, but as you point out it does seem to handle n=1 more or less > correctly as well (perhaps other functionality breaks). The case n=1 seems OK using Sage 7.2 Ubuntu PPA: sage: b0 = BooleanFunction([0,0]) sage: b0.algebraic_normal_form() 0 sage: b1 = BooleanFunction([1,0]) sage: b1.algebraic_normal_form() x + 1 sage: b2 = BooleanFunction([0,1]) sage: b2.algebraic_normal_form() x sage: b3 = BooleanFunction([1,1]) sage: b3.algebraic_normal_form() 1 > This functionality is provided by PolyBoRi, which started as an > independently maintained library but currently does not have an independent > maintainer. I don't know what the process is to change/fix things there. > Certainly it would seem a lot of work for not much benefit to add support > for GF(2) in PolyBoRi itself. > > Would it be OK to represent 0-variable normal forms just as elements of > GF(2)? In that case we could just add at the start of algebraic_normal_form > the lines: > > if self._nvariables==0: > return GF(2)(self._truth_table[0]) > > and leave PolyBoRi alone. This would deserve special mention in the > documentation because it would be an anomalous return type. With n=1 and n=2, it is possible to create constant polynomials, but the constant 1 for n-1 does not equal the constant 1 for n=2: sage: b3 = BooleanFunction([1,1]) sage: an3 = b3.algebraic_normal_form() sage: an3 1 sage: an3.constant() True sage: an3.deg() 0 sage: bf = BooleanFunction([1,1,1,1]) sage: anf = bf.algebraic_normal_form() sage: anf 1 sage: anf.constant() True sage: anf.deg() 0 sage: anf == an3 False As for what you decide to do for n=0, it is up to you. I will work around it for now. -- Paul Leopardi - https://sites.google.com/site/paulleopardi/ -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
