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initial version

lcm seems to work correctly on RR and QQ:

sage: R.<s> = PolynomialRing(RR); R
Univariate Polynomial Ring in s over Real Field with 53 bits of precision
sage: lcm([(s+5)**2, s])
s^3 + 10.0000000000000*s^2 + 25.0000000000000*s

sage: R.<s> = PolynomialRing(QQ); R
Univariate Polynomial Ring in s over Rational Field
sage: lcm([(s+5)**2, s])
s^3 + 10*s^2 + 25*s

But gcd works on RDF but not on RR:

sage: R.<s> = PolynomialRing(RDF); R
Univariate Polynomial Ring in s over Real Double Field
sage: gcd([(s+5)**2, s])
1.0

sage: R.<s> = PolynomialRing(RR); R
Univariate Polynomial Ring in s over Real Field with 53 bits of precision
sage: gcd([(s+5)**2, s])
TypeError: 'MinusInfinity' object cannot be interpreted as an index

This looks weird. If your polynomials have rational (or integers) coefficients, you can use QQ instead of RDF.

click to hide/show revision 2
No.2 Revision

lcm seems to work correctly on RR and QQ:

sage: R.<s> = PolynomialRing(RR); R
Univariate Polynomial Ring in s over Real Field with 53 bits of precision
sage: lcm([(s+5)**2, s])
s^3 + 10.0000000000000*s^2 + 25.0000000000000*s

sage: R.<s> = PolynomialRing(QQ); R
Univariate Polynomial Ring in s over Rational Field
sage: lcm([(s+5)**2, s])
s^3 + 10*s^2 + 25*s

But gcd works on RDF but not on RR:

sage: R.<s> = PolynomialRing(RDF); R
Univariate Polynomial Ring in s over Real Double Field
sage: gcd([(s+5)**2, s])
1.0

sage: R.<s> = PolynomialRing(RR); R
Univariate Polynomial Ring in s over Real Field with 53 bits of precision
sage: gcd([(s+5)**2, s])
TypeError: 'MinusInfinity' object cannot be interpreted as an index

But:

sage: ((s+5)**2).gcd(s)
1.00000000000000

This looks weird. If your polynomials have rational (or integers) coefficients, you can use QQ instead of RDF.