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## RE: [Axiom-developer] Re: "Factoring" Expression Integer/ simplifyingpow

**From**: |
Page, Bill |

**Subject**: |
RE: [Axiom-developer] Re: "Factoring" Expression Integer/ simplifyingpowers (an example) |

**Date**: |
Mon, 6 Mar 2006 19:43:54 -0500 |

On Monday, March 06, 2006 6:42 AM Martin Rubey wrote:
>* ...*
>* Francois Maltey wrote:*
>* > // Is it an axiom bug in axiom ?*
>* > I don't understand why (x+y+1)^2 ::DMP([x],Integer) gives me an *
>* > Expression Integer, not an error. //*
>* *
>* Well, even (x+y+1)^2 ::DMP([x,y],Integer) gives an EXPR INT. *
>* The reason is, that :: has a very high precedence. So you are*
>* converting 2 to a DMP([x],INT) -- or a DMP([x,y], INT) -- and*
>* then you compute (1+x+y) to the power of that polynomial...*
Hmmm... that is interesting.
(1) -> x^1
(1) x
Type: Polynomial Integer
Ok, here the interpreter finds ^:(%,NNI)->% in 'Polynomial Integer'.
(2) -> x^(1::POLY INT)
(2) x
Type: Expression Integer
So, here the interpreter finds ^:(%,%)->% in 'Expression Integer',
and the coercion POLY INT -> EXPR INT, just like this:
(3) -> x^(y::POLY(INT))
y
(3) x
Type: Expression Integer
But how can we explain these results?
(4) -> x^(1::DMP([x],Integer))
(4) x
Type: Fraction Polynomial Integer
(5) -> x^(1::SUP(INT))
(5) x
Type: Expression SparseUnivariatePolynomial Integer
And why not this?
(6) -> x^(y::DMP([y],INT))
There are 4 exposed and 0 unexposed library operations named ^
having 2 argument(s) but none was determined to be applicable.
Use HyperDoc Browse, or issue
)display op ^
to learn more about the available operations. Perhaps
package-calling the operation or using coercions on the arguments
will allow you to apply the operation.
Cannot find a definition or applicable library operation named ^
with argument type(s)
Variable x
DistributedMultivariatePolynomial([y],Integer)
Perhaps you should use "@" to indicate the required return type,
or "$" to specify which version of the function you need.
Regards,
Bill Page.

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