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FunctionField with more than 1 variable

asked 2017-01-04 08:41:55 -0500

castor gravatar image

I have tried the following to construct an appropriate function field:

F.<a,b>=FunctionField(QQ,2)

as a result I got

TypeError: create_key() got multiple values for keyword argument 'names'

after that I looked for the documentation but only find one variable examples. I also tried a few more versions like

F.<a,b>=FunctionField(QQ,names=('a','b'))

but did not work. Thank for any advice in this direction in advance.

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answered 2017-01-04 08:59:29 -0500

tmonteil gravatar image

This is indeed unfortunate, and the whole source code seems not to allow more than one undeterminate anyway. As a workaround, you can construct F as the fraction field of a polynomial ring:

sage: R.<a,b> = PolynomialRing(QQ) ; R
Multivariate Polynomial Ring in a, b over Rational Field
sage: F = R.fraction_field() ; F
Fraction Field of Multivariate Polynomial Ring in a, b over Rational Field
sage: a+b^2+1/b
(b^3 + a*b + 1)/b
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Thank you for the workaround, it helps to compute what I need. There is a small gap at the end, I need to define a polynomial ring over the function field and factor certain polynomials over it. The error message is that it is not implemeted, but I know some factors and I could reduce the problem to a quadratic polynomial.

castor gravatar imagecastor ( 2017-01-04 12:30:45 -0500 )edit

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Asked: 2017-01-04 08:41:55 -0500

Seen: 43 times

Last updated: Jan 04