lcm and gcd of polynomials over the irrationals

gundamlh
167 ●15 ●21 ●29

Dear all,

I want to calculate the least common multiple of a list of polynomials with coefficients defined over RR or RDF in SAGE. Is it possible?

sage: R.<s> = PolynomialRing(RDF); R
Univariate Polynomial Ring in s over Real Double Field
sage: H = matrix(1,2, [(s+5)**2, s]); H
[s^2 + 10.0*s + 25.0                   s]
sage: lcm(H[0,0], H[0,1])
TypeError: Singular error:
   ? not implemented
   ? error occurred in or before poly.lib::lcm line 852: `           q=gcd(p,i[k]);`
   ? leaving poly.lib::lcm
   skipping text from `;` error at token `)`

Thanks in advance!

answered 11 years ago

tmonteil
27483 ●32 ●205 ●519 http://wiki.sagemath.o...

updated 11 years ago

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.

link

Comments

Thanks! But if some coef. is sqrt(2) or pi ...

gundamlh ( 11 years ago )

for the gcd, working in the symbolic ring `SR` works, not for the lcm (lack of conversion to the singular lib).

tmonteil ( 11 years ago )

OK, perhaps it is not implemented in those cases. Oh, can we call NumPy or Maxima to do it instead?

gundamlh ( 11 years ago )

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