define a polynomial ring

polynomial

asked 2013-11-24 07:24:27 +0200

gundamlh
157 ●15 ●21 ●28

updated 2013-11-24 07:26:09 +0200

Dear all,

sage: R.<x> = PolynomialRing(QQ); R
Univariate Polynomial Ring in x over Rational Field
sage: R([1,2,3])
3*x^2 + 2*x + 1
sage: R1.<x> = PolynomialRing(QQ,1); R1
Multivariate Polynomial Ring in x over Rational Field
sage: R1([1,2,3])
---------------------------------------------------------------------------    
TypeError: Could not find a mapping of the passed element to this ring.

  Note that a multivariate polynomial ring is returned when an
  explicit number is given.

     sage: PolynomialRing(QQ,"x",1)
     Multivariate Polynomial Ring in x over Rational Field
     sage: PolynomialRing(QQ,"x",0)
     Multivariate Polynomial Ring in no variables over Rational Field

I want to know the reason .. Why

a multivariate polynomial ring is returned when an explicit number is given.

Does it offer users of SAGE any simplicity/convenience?

Thanks in advance!

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sage: PolynomialRing(QQ,"x",2) Multivariate Polynomial Ring in x0, x1 over Rational Field sage: R = PolynomialRing(QQ,"x",5); R Multivariate Polynomial Ring in x0, x1, x2, x3, x4 over Rational Field sage: R.inject_variables() Defining x0, x1, x2, x3, x4 sage: x0 in R True

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Thanks! Quick and in detail!

gundamlh ( 2013-11-24 08:06:41 +0200 )edit

For PolynomialRing(QQ,"x",n) the integer n must be < 2**15 (otherwise "OverflowError: value too large to convert to short"). Do you know a way for having arbitrary large integer n ?

Sébastien Palcoux ( 2014-01-03 07:13:13 +0200 )edit

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