Revised tests are consistent with Nils' reply. I replaced pi by 10/3. I
compared the quotient by one variable of the
two variable ring with a quotient by the one variable in the one variable ring
and got the results below, the first
is consistent with the naive approx. Integers()(a*1000)/1000:
3.33300000000000
versus
3.33333333333333
eps = var("eps")
edBaseRing=PolynomialRing(RR,[eps])
edIdeal=ideal(edBaseRing, [eps])
edRing=edBaseRing.quotient_ring(edIdeal)
rat = 10/3
print(RR(rat))
print(edBaseRing(rat))
print(edRing(rat))
3.33333333333333
3.33333333333333
3.33333333333333
eps, dlt = var("eps,dlt")
edBaseRing=PolynomialRing(RR,[eps, dlt])
#edIdeal=ideal(edBaseRing, [eps, dlt])
edIdeal=ideal(edBaseRing, [eps])
edRing=edBaseRing.quotient_ring(edIdeal)
print(RR(rat))
print(edBaseRing(rat))
print(edRing(rat))
3.33333333333333
3.33333333333333
3.33300000000000
________________________________________
From: sage-support@googlegroups.com <sage-support@googlegroups.com> on behalf
of Nils Bruin <nbr...@sfu.ca>
Sent: Wednesday, March 5, 2025 11:49 PM
To: sage-support
Subject: [sage-support] Re: Bug Polynomial Quotient with 2 ideal generator
rings over RR lose precision of base ring.
I definitely wouldn't expect nontrivial polynomial arithmetic to work reliably
over RR without special measures. There are definitely methods for algebraic
geometry with floats, but it needs very special attention to numerical
stability. That is already true for linear algebra over RR and for polynomial
algebra it is even worse.
I am pretty sure sage does NOT have facilities for this at the moment. Even for
linear algebra, I wouldn't trust that sage would select a numerically stable
approach over RR. There is a good chance it will hit just generic
implementations that are written for exact linear algebra.
However, the computations you are doing would trigger no polynomial arithmetic
at all, so the "loss of precision" is very suspect. It's also very suspect
that it ends up with a number that has a very precise number of decimal digits.
Indeed, replacing "pi" with something else, such as RR(1/3) or sqrt(2) gives
the exact same rounding.
I suspect you're hitting code that somehow tries to call the Singular library
and, since that doesn't support floats, it looks like it takes a very naive
approximation
Integers()(a*1000)/1000. That DOES look like a bug. An error would be more
informative here.
It makes sense this would only happen in a multivariate polynomial ring
(regardless of what ideal you're actually using): univariate polynomial rings
would just use euclidean division and not rely on the singular library. That
would still be numerically unstable in many cases, but in a trivial case such
as this one, that would not be an issue.
On Wednesday, 5 March 2025 at 10:51:29 UTC-8 Seth Chaiken wrote:
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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