Rather than "lying" or expecting the system prove that "x^2+1 is
irreducible in R" I think the usual approach in Axiom would be to
introduce a declaration in the algebra library to this effect, i.e.
introduce a new category such as "Irreducible(x^2+1,R)".
On Fri, Mar 19, 2010 at 3:31 AM, Ralf He
c(a + %i b) + d(a + %i b)%j
but if we try to multiply these out
ca + c %i b + da%j + d %i b%j
which implies a new algebra which is not completely defined, for instance, we
have some freedom to choose the properties of %i%j without violating the
correctness of both inner and outer complex nu
On Friday 19 Mar 2010 00:40:20 Bill Page wrote:
> On Thu, Mar 18, 2010 at 8:27 PM, Waldek Hebisch wrote:
> I think that to understand Waldek's point it is import to look at
> ComplexCategory.
>
> http://axiom-wiki.newsynthesis.org/Complex
>
> E.g.
>
> if R has IntegralDomain then
>I
I think that to understand Waldek's point it is import to look at
ComplexCategory.
if R has Field then-- this is a lie; we must know that
Field-- x^2+1 is irreducible in R
Exactly.
If we want to do mathematics, why do you distribute lies? Unfortunate
On Thu, Mar 18, 2010 at 8:27 PM, Waldek Hebisch wrote:
> Ralf Hemmecke wrote:
>> On 03/18/2010 11:17 PM, Waldek Hebisch wrote:
>> >
>> > It is a math problem: if base R is a field that does not contain
>> > square root of -1, then Complex(R) is again a field. But we have
>> > no way to check this
Ralf Hemmecke wrote:
> On 03/18/2010 11:17 PM, Waldek Hebisch wrote:
> >
> > It is a math problem: if base R is a field that does not contain
> > square root of -1, then Complex(R) is again a field. But we have
> > no way to check this condition, so need hardcode the choice. To
> > allow building
On 03/18/2010 11:17 PM, Waldek Hebisch wrote:
Bill Page wrote:
On Thu, Mar 18, 2010 at 1:53 PM, Martin Baker wrote:
...
The problem is that complex numbers are defined over CommutativeRing
and even types like this are not valid.
(1) -> myType:Complex Complex Integer
? Complex(Complex(Integer)
Bill Page wrote:
> On Thu, Mar 18, 2010 at 1:53 PM, Martin Baker wrote:
> > ...
> > The problem is that complex numbers are defined over CommutativeRing
> > and even types like this are not valid.
> > (1) -> myType:Complex Complex Integer
> >
> > ? Complex(Complex(Integer)) is not a valid type.
> >
Martin Baker wrote:
> How would one go about building a set of domains to represent
> hypercomplex numbers without defining each one individually as a
> separate domain? For example: complex numbers, double numbers, dual
> numbers, dual complex, dual quaternion, dual vectors, split complex,
> split
On Thu, Mar 18, 2010 at 1:53 PM, Martin Baker wrote:
> ...
> The problem is that complex numbers are defined over CommutativeRing
> and even types like this are not valid.
> (1) -> myType:Complex Complex Integer
>
> Complex(Complex(Integer)) is not a valid type.
> (1) ->
>
> Even if this was acce
How would one go about building a set of domains to represent
hypercomplex numbers without defining each one individually as a
separate domain? For example: complex numbers, double numbers, dual
numbers, dual complex, dual quaternion, dual vectors, split complex,
split quaternion and so on.
What I
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