In Sage 10.4, we tried to inject a RR number into a RR polynomial ring
quotient. It
works fine when the ideal had one (monomial) generator but precision is
lost when
it had two generators.
One generator example (works):
eps = var("eps")
edBaseRing=PolynomialRing(RR,[eps])
edIdeal=ideal(edBaseRing, [eps])
edRing=edBaseRing.quotient_ring(edIdeal)
print(RR(pi))
print(edBaseRing(pi))
print(edRing(pi))
yields:
3.14159265358979
3.14159265358979
3.14159265358979
But with 2 generators, injecting RR(pi) into the quotient loses precision.
The analogous output is:
3.14159265358979
3.14159265358979
3.14200000000000
Here's the full code:
eps, dlt = var("eps,dlt")
edBaseRing=PolynomialRing(RR,[eps, dlt])
edIdeal=ideal(edBaseRing, [eps, dlt])
edRing=edBaseRing.quotient_ring(edIdeal)
print(RR(pi))
print(edBaseRing(pi))
print(edRing(pi))
Looks like a bug! I isolated it from more complex code where the ideal was
simply all multiples of the two variables, and a RealField with non-default
bit precision was used.
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