On Mar 12, 2009, at 12:32 AM, Simon King wrote:
> Dear Supporters,
>
> the following works:
> sage: R=PolynomialRing(QQ,['a','x1','y1'])
> sage: S=PolynomialRing(QQ,['x1','y1','z'])
> sage: R('x1+a')+S('x1+z')
> a + 2*x1 + z
>
> The following does not work:
> sage: R=PolynomialRing(QQ,['a','x','y1'])
> sage: S=PolynomialRing(QQ,['x1','y1','z'])
> sage: R('x+a')+S('x1+z')
> Traceback (most recent call last):
> TypeError: unsupported operand parent(s) for '+': 'Multivariate
> Polynomial Ring in a, x, y1 over Rational Field' and 'Multivariate
> Polynomial Ring in x1, y1, z over Rational Field'
>
> Why?
>
> In both cases, the polynomial rings have some variable names in
> common, some not. In the first case, we have a successful coercion to
> a common parent:
> sage: R=PolynomialRing(QQ,['a','x1','y1'])
> sage: S=PolynomialRing(QQ,['x1','y1','z'])
> sage: (R('x1+a')*S('x1+z')).parent()
> Multivariate Polynomial Ring in a, x1, y1, z over Rational Field
>
> So, why is the corresponding operation not done in the second example?
Because the ordering of variables is ambiguous. Should it be QQ
[a,x,x1,y1,z] or QQ[a,x1,x,y1,z]?
sage: QQ['x,y'] == QQ['y,x']
False
> Second (related) question: If R and S are polynomial rings over the
> same base ring, how can I form the polynomial ring (over the same base
> ring) whose variables are the union of the variables of R and of S? Is
> this an easy (speed wise) operation?
Relatively easy.
sage: R = QQ['a,b,c,d']
sage: S = QQ['x,y,z']
sage: all_vars = list(set(R.variable_names() + S.variable_names()))
sage: PolynomialRing(R.base_ring(), all_vars)
Multivariate Polynomial Ring in a, c, b, d, y, x, z over Rational Field
- Robert
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