For anyone experienced with other symbolic mathematics systems, it is very difficult to understand why Axiom returns a complicated error message in this case! axiom solve(x+1.1,
As with any software, one must learn the correct syntax of commands. For some unknown reason, Axiom does not have a solve function with signature:
and axiom solve(x+1.1)
Type: List(Equation(Fraction(Polynomial(Float))))axiom solve(x+11/10,
Type: List(Equation(Polynomial(Float)))axiom solve(x+ 11/10,
Type: List(Equation(Polynomial(Float)))axiom solve(x+11/10,
Type: List(Equation(Polynomial(Float)))One should be careful interpreting these results. The second one solves it to 5 binary digit accuracy (closest binary to
I'm confused. Perhaps that's because I expect Axiom to behave like other similar software, but what is the meaning of
when we're trying to solve an equation with real coefficients? Doesn't an accuracy need to be specified? (and there doesn't seem to be a default).
Of course, yes. However, there is a dilemma: when you give Axiom an equation with floating point coefficients, should Axiom "solve" this symbolically, as if axiom solve(x^2 - 1.234)
Type: List(Equation(Fraction(Polynomial(Float))))The package is numsolve.spad and you see that these restrictions are well documented. So the above signature is really not meant to be used at the moment. A similar situation occurs, for example So a lot of Axiom failures are not bugs, but by design. One way to improve the user interface would seem to be to automatically lifting a polynomial over f(x) = (x+1)(x+2) ... (x+20) = x^{20} + 210 x^{19} + ... + 20! = 0
where a change of the coefficient 210 by 2 So if we want numerically accurate solutions, we should use a robust numerical library. I believe this is not yet available in Axiom (the NAG version allowed interface with its Fortran libraries, at extra costs). If we are really (no pun intended) only using truely floating point coefficients, then it can easily be converted to Fraction Integer, but one has to beware that the algorithm would take a very long time because exact arithmetic with large integer coefficients are expensive.
Also, while Very bewildering to a beginning user! My impression, from looking at the algebra library, is that Axiom does not appear to handle (i.e. solve) polynomials with real coefficients. It produces them as results, but doesn't accept them as inputs. Is this basically correct?
I think the idea is to convert your
Yes, as explained above. Symbolic methods do not work well with |

property change--Bill Page, Wed, 18 May 2005 06:54:00 -0500 reply