Executing the following code on Sagecell:
R.<x> = PolynomialRing(ZZ)
f=-7x^4 + 3x^3 - 4*x^2 - x - 6
f%5
I get the following output:
3*x^4 + 3*x^3 - 4*x^2 - x + 4
Why are there negative coefficients on the output? The output should be:
3*x^4 + 3*x^3 +x^2 +4*x + 4
Ok, I found out that f%5 does not work exactly how I thought it did, it does not apply mod 5 to all coefficients. Instead we should use a ring to do the modular:
R.<x> = PolynomialRing(ZZ)
f=-7*x^4 + 3*x^3 - 4*x^2 - x - 5
Rmod.<x> = PolynomialRing(Integers(5))
Rmod(f)
The above will output:
3*x^4 + 3*x^3 + x^2 + 4*x + 4
Asked: 2025-05-05 22:00:59 +0200
Seen: 101 times
Last updated: May 06
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