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Georgi Guninski on Wed, 15 Mar 2023 11:04:36 +0100
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Unexpected Mod(0,1) == Mod(x,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)
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- To: pari-dev@pari.math.u-bordeaux.fr
- Subject: Unexpected Mod(0,1) == Mod(x,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)
- From: Georgi Guninski <gguninski@gmail.com>
- Date: Wed, 15 Mar 2023 12:02:43 +0200
- Delivery-date: Wed, 15 Mar 2023 11:04:36 +0100
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I am experimenting with quotients of polynomial rings
and get unexpected Mod(0,1):
? mo=Mod(1,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)
%1 = Mod(Mod(0, y^2 - y), 1)
? mo=Mod(x,x*(x-1))*Mod(1,y*(y-1))*Mod(1,x+y-1)
%2 = Mod(0, 1)
In sagemath:
sage: K.<x,y>=QQ[]
sage: Kquo=K.quotient([x*(x-1),y*(y-1),x+y-1])
sage: Kquo(x)
-ybar + 1