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#268 )abbrev? with too little detail ←	↑	→ #27 Axiom on Windows GCL problems

#269 some issues with the 'Factored' domain

Edit detail for #269 some issues with the 'Factored' domain revision 2 of 3

	1 2 3
Editor: test1 Time: 2015/10/27 14:16:59 GMT+0
Note:

added:
Comment: In fact, in the past polynomial domains failed to provide 'factor' -- factoring
was done by separate routine.  Now polynomials provide 'factor' and the result
above is fully factored.


added:
Comment: Yes, if base domain is GCD domain '+' first looks for known common
factors.

Consider the following:

fricas

q:FR POLY INT := (x-1)*(x^2+1)

$\label{eq1}{\left(x - 1 \right)}\ {\left({{x}^{2}}+ 1 \right)}$

(1)

Type: Factored(Polynomial(Integer))

fricas

p:FR POLY INT := (x-1)*(2*x)

$\label{eq2}2 \ {\left(x - 1 \right)}\ x$

(2)

Type: Factored(Polynomial(Integer))

fricas

p+q

$\label{eq3}{\left(x - 1 \right)}\ {{\left(x + 1 \right)}^{2}}$

(3)

Type: Factored(Polynomial(Integer))

fricas

)tr MULTFACT )ma

   Packages traced: 
      MultivariateFactorize(Symbol,IndexedExponents(Symbol),
            Integer,Polynomial(Integer))
   Parameterized constructors traced:
      MULTFACT
factor(p+q)

   Internal Error
   The function factor with signature hashcode is missing from domain 
      Factored(Polynomial (Integer))

The documentation says:

  Others, like addition require somewhat more work, and unless 
  the argument domain provides a factor function, the result 
  may not be completely factored.

which is not true, as shown by the result of above.

Comment: In fact, in the past polynomial domains failed to provide factor: factoring was done by separate routine. Now polynomials provide factor and the result above is fully factored.

Furthermore, applying factor to should probably not first expand the expression and then factor it again. It should rather map over the already known factors.

Comment: Yes, if base domain is GCD domain + first looks for known common factors.

I'm not sure whether FR should always try to factor the result of an addition, at least, I don't think that this was the intention of the original author.

Another issue is raised by the documentation to expand: % -> R :

  expand(f) multiplies the unit and factors together, yielding an
  "unfactored" object. Note: this is purposely not called 'coerce' which would
  cause the interpreter to do this automatically.

I tested this and found it not to be true. Note that the domain was written already in 1985, so it might well be that the interpreters behaviour has changed in this respect.

Martin