picking coefficients
- To: mathgroup at smc.vnet.net
- Subject: [mg118151] picking coefficients
- From: Kent Holing <KHO at statoil.com>
- Date: Thu, 14 Apr 2011 04:50:50 -0400 (EDT)
I have a general polynomial in 4 variables a,b,c,d. >From all terms N a^i b^j c^k d^l for i,j,k,l positive integers (all or some of i,j,k,l may be 0) with N a numerical (integer) coefficient ( N/= 0, N may be negative or positive) of the polynomial, I want to pick among these terms only those where N /== 0 mod 8. Is it an easy way to achieve this, using Mathematica? Example/testcase: For Q(x) = x^4 + (2a+1) x^3 + 2b x^2 + 2c x + 2d + 1 = 0 where a, b, c and d are integers, let the polynomial be the discriminant of the quartic Q(x) = 0. The result of the above request should then be 5 + 4a(a+1) +4b(b+1) + 4c(c+1) + 4d(d+1), showing that the discriminant == 5 mod 8 and therefore not a square. In fact, this shows that the Galois group of the quartic must be either Z4, D4 or S4. Kent Holing