#16360: Conversion of function field elements to pari
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Reporter: saraedum | Owner:
Type: defect | Status:
Priority: major | needs_review
Component: commutative algebra | Milestone: sage-6.3
Keywords: pari, resultant, function | Resolution:
field | Merged in:
Authors: Julian Rueth | Reviewers:
Report Upstream: N/A | Work issues:
Branch: u/saraedum/ticket/16360 | Commit:
Dependencies: | Stopgaps:
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Changes (by {'newvalue': u'Julian Rueth', 'oldvalue': ''}):
* status: new => needs_review
* author: => Julian Rueth
Old description:
> The resultant does not work for function fields if the variable names are
> not chosen wisely:
> {{{
> sage: K.<x> = FunctionField(QQ)
> sage: R.<y> = K[]
> sage: y.resultant(y+x)
> PariError: variable must have higher priority in gtopoly
> }}}
>
> The resultant is wrong over extensions of function fields:
> {{{
> sage: K.<a> = FunctionField(QQ)
> sage: R.<b> = K[]
> sage: L.<b> = K.extension(b^2-a)
> sage: R.<x> = L[]
> sage: f=x^2-a
> sage: g=x-b
> sage: f.resultant(g)
> -b + a^2 # should be 0 since f and g have the common root b
> }}}
New description:
The resultant does not work for function fields if the variable names are
not chosen wisely
{{{
sage: K.<x> = FunctionField(QQ)
sage: R.<y> = K[]
sage: y.resultant(y+x)
PariError: variable must have higher priority in gtopoly
}}}
The resultant is wrong over extensions of function fields
{{{
sage: K.<a> = FunctionField(QQ)
sage: R.<b> = K[]
sage: L.<b> = K.extension(b^2-a)
sage: R.<x> = L[]
sage: f=x^2-a
sage: g=x-b
sage: f.resultant(g)
-b + a^2 # should be 0 since f and g have the common root b
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/16360#comment:2>
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