Hi Kevin, On 2014-07-27, Kevin Buzzard <[email protected]> wrote: > [I've just build a degree 6 poly. Now let's build a degree 12 one] > > sage: h=expand((g.subs(x+2/x))*x^6)
Let's work without the x^6 factor: sage: g x^6 + 2*x^3 + x + 1 sage: g.subs(x+2/x).expand() 2/x + 1/x^3 + 1/x^6 No idea what is going wrong here. Let's try different ways to substitute: sage: g(x=x+2/x).expand() 2/x + 1/x^3 + 1/x^6 Same problem. Whithout expanding, it seems to be fine: sage: g.subs(x+2/x) (((x + 2/x)^3 + 2)*(x + 2/x)^2 + 1)*(x + 2/x) + 1 I guess the above form comes from Horner's scheme. Now, really strange: If one copy-and-pastes the above expression and expands it, then all is fine! sage: ((((x + 2/x)^3 + 2)*(x + 2/x)^2 + 1)*(x + 2/x) + 1).expand() x^6 + 12*x^4 + 2*x^3 + 60*x^2 + 13*x + 26/x + 240/x^2 + 16/x^3 + 192/x^4 + 64/x^6 + 161 That is all very puzzling to me---and is yet another reason for my creed that one should use *proper* polynomials and not symbolic expressions (see below for the underlying types). > Am I some sort of a victim of some secret property of the letter 'x'? Not of the letter 'x', but of the fact that the variable x is pre-defined in Sage as a symbolic expression, which often enough causes trouble to those who expect to work with polynomials. Note that x is *not* the generator of a polynomial ring: sage: type(x) <type 'sage.symbolic.expression.Expression'> whereas your polynomial g is a proper polynomial (there are various underlying implementations of polynomials in Sage, for different purposes, and this one relies on FLINT): sage: type(g) <type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'> > I > wanted to use x rather than another letter because that would save me from > having to define the ring GF(3)[x,1/x] which would have involved some > thinking on my part ;-) Well, the polynomial ring already is there: sage: g.parent() Univariate Polynomial Ring in x over Finite Field of size 3 and the fraction field will automatically be created when needed. So, you could do: sage: g.parent().inject_variables() Defining x The preceding line works if you are in an interactive session. Alternatively (or if you write a program), you could explicitly define it: sage: x = g.parent().gen() sage: type(x) <type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint'> Now, the substitution works out of the box, and "expansion" of symbolic expressions is not needed, since we work with proper polynomials and their quotients. sage: g.subs(x+2/x) (x^12 + 2*x^9 + x^7 + 2*x^6 + 2*x^5 + x^3 + 1)/x^6 My general recommendation is: Unless you want to do calculus, get used to define x as the generator of an appropriate polynomial ring, taking care of the underlying range of coefficients. This is totally easy in an interactive session: sage: P.<x> = QQ[] # or GF(3)['x'] in your case The above line both defines P and x, as polynomial ring over the rationals, and its generator. In a program, you should write P = QQ['x'] # or GF(3)['x'] in your case x = P.gen() instead. Best regards, Simon -- 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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
