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?
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?
Cheers,
Simon
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