       Problem with Expand and Modulus in Mathematica 9?

• To: mathgroup at smc.vnet.net
• Subject: [mg129277] Problem with Expand and Modulus in Mathematica 9?
• From: Ralf Hemmecke <hemmecke at gmail.com>
• Date: Fri, 28 Dec 2012 05:37:03 -0500 (EST)
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Can someone confirm that the following code gives different results for r1 for different versions of Mathematica and different operating systems. Or is this just an issue of my installation?

---BEGIN CODE---
m = 2147483629
q = -285170499
q1 = 1/q
q2 = PowerMod[q,-1,m]
Mod[q*q2, m]
p1 = 527660967 + 978421595*n
p2 = 1999783961 + 1587123368*n + 1965760814*n^2
r1 = Expand[q1*p1*p2,Modulus->m]
r2 = Expand[q2*p1*p2,Modulus->m]
s1 = Expand[Expand[q1*p1*p2],Modulus->m]
s2 = Expand[Expand[q2*p1*p2],Modulus->m]
---END CODE

Value of r1
Mathematica 8
1808010833 + 1914426603*n + 640234431*n^2 + 1087084730*n^3

Mathematica 9 (64bit Debian 6.0)
1651432217 + 309632549*n + 188919829*n^2 + 1597920481*n^3

Mathematica 9 (32bit Debian 6.0, 64bit CPU)
1823075307 + 33175446*n + 2081129601*n^2 + 580053941*n^3

The values of r2, s1, s2 agree with that of r1 as computed in Mathematica 8.

Ralf

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