Re: Groebner bases over the integers

Hi,

you are completely right, computing over the rationals would make it
possible to reduce the polynomial y-x to 0. For the situation where I
want to simplify a formula

phi(y-x)

this would mean, however, that I have to carry out the reduction really
using rationals. From a practical point of view I would prefer not to
do that. Not that I would not see that the computation of bases and
reduction gets much simpler when using Q, I just expect loads of other
problems to pop up when I start using Q that I don't want to deal with
at this point.

In a similar situation, for instance,

phi(y)

I would end up with the expression

phi(-a/2)

although "-a/2" is known to range over the integers (given that "a" is
part of an integer solution of the equations "2*x+a=0, 2*y+a=0" and
hence even). I don't want to work with such "ill-shaped"/"badly-typed"
formulas.

Cheers, Philipp

.

Relevant Pages

  • Re: Why does Cantor a target for cranks?
    ... instead we talk about the abstract rationals which are ... after which we cite an infinite sequence of zero digits) and others ... is in the sub-sequence that generates computable reals or not. ... computing algorithm that enumerates the integers, ...
    (sci.math)
  • Re: Arithmetic on computable reals
    ... |It is fairly obvious that all rationals are D-computable. ... separately to show that it holds for irrationals. ... then, is keep computing terms of the sequence r1,r2,r3,... ... Then apply the equivalence of D-computability with computability. ...
    (sci.math)
  • Re: Range#member? Oddity
    ... and that's not possible for ranges of real numbers. ... Being enumerable means the possibility of a "succ" operation, and therefore of traversing the whole set with "each" (which may take infinite time). ... only rational numbers and rationals are countably infinite ... work with a set of rational numbers - in computing terms you can certainly ...
    (comp.lang.ruby)
  • Re: Arithmetic on computable reals
    ... The computable reals are ... a vector space over the rationals with a countable algebraic ... and its unique representation as a linear combination ... of the particular sum we are dealing with by computing the ...
    (sci.math)
  • Re: Parametrized for loop
    ... assignments in the loop were continuous assignments. ... you could use a shift to shift out the unused bits ... The zeroes shifted in will not affect the reduction ... you would be computing almost the same thing as last time, ...
    (comp.lang.verilog)