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Date: Wed, 1 Dec 1999 19:13:53 -0800 (PST)
From: Adam Logan <adam@msri.org>
To: was@math.berkeley.edu
Subject: formulas from Wang's paper
Reply-to: adam@msri.org
Content-Type: text
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X-UIDL: ASSd9P[9e9)&b!!gN[!!

Well, I typed them in, so I'm mailing them to you.

It seems to me that the two basic problems that you haven't yet addressed are
(1) computing the Thetanullwerte and (2) going from values of i1, i2, and i3
(see below) to rational solutions for a_i.  See you tomorrow...

Adam

I2 = -240*a0*a6+40*a1*a5-16*a2*a4+6*a3^2
I4 = 48*a0*a4^3+48*a2^3*a6+4*a2^2*a4^2+1620*a0^2*a6^2+36*a1*a3^2*a5-12*a1*a3*a4^2-12*a2^2*a3*a5+300*a1^2*a4*a6+300*a0*a5^2*a2+324*a0*a6*a3^2-504*a0*a2*a4*a6-180*a0*a4*a3*a5-180*a1*a3*a2*a6+4*a1*a4*a2*a5-540*a0*a5*a1*a6-80*a1^2*a5^2
I6 = 176*a1^2*a5^2*a3^2+64*a1^2*a5^2*a4*a2+1600*a1^3*a5*a4*a6+1600*a1*a5^3*a0*a2-2240*a1^2*a5^2*a0*a6-160*a0*a4^4*a2-96*a0^2*a4^3*a6+60*a0*a4^3*a3^2+72*a1*a3^4*a5-24*a1*a3^3*a4^2+2250*a1^3*a3*a6^2-160*a2^4*a4*a6-96*a2^3*a0*a6^2+60*a2^3*a3^2*a6-24*a2^2*a3^3*a5+8*a2^2*a3^2*a4^2-900*a2^2*a1^2*a6^2-24*a2^3*a4^3-36*a2^4*a5^2-36*a1^2*a4^4+424*a0*a4^2*a2^2*a6+492*a0*a4^2*a2*a3*a5+20664*a0^2*a4*a6^2*a2+3060*a0^2*a4*a6*a3*a5-468*a0*a4*a3^2*a2*a6-198*a0*a4*a3^3*a5-640*a0*a4*a2^2*a5^2+3472*a0*a4*a2*a5*a1*a6-18600*a0*a4*a1^2*a6^2-876*a0*a4^2*a1*a6*a3+492*a1*a3*a2^2*a4*a6-238*a1*a3^2*a2*a4*a5+76*a1*a3*a2*a4^3+3060*a1*a3*a0*a6^2*a2+1818*a1*a3^2*a0*a6*a5-198*a1*a3^3*a2*a6+26*a1*a3*a2^2*a5^2-1860*a1^2*a3*a2*a5*a6+330*a1^2*a3^2*a6*a4+76*a2^3*a4*a3*a5-876*a2^2*a0*a6*a3*a5+616*a3^2*a5*a1*a6+2250*a0^2*a5^3*a3-900*a0^2*a5^2*a4^2-10044*a0^2*a6^2*a3^2+162*a0*a6*a3^4+28*a1*a4^2*a2^2*a5-640*a1^2*a4^2*a2*a6+26*a1^2*a4^2*a3*a5-1860*a1*a4*a0*a5^2*a3+616*a1*a4^3*a0*a5-18600*a0^2*a5^2*a6*a2+59940*a0^2*a5*a6^2*a1+330*a0*a5^2*a3^2*a2-119880*a0^3*a6^3-320*a1^3*a5^3
I10 = disc. of a6*x^6+a5*x^5+a4*x^4+a3*x^3+a2*x^2+a1*x+a0
i1 = I2^5/I10
i2 = I2^3*I4/I10
i3 = I2^2*I6/I10

h4 = v0^8+v1^8+v21^8+v23^8+v25^8+v3^8+v41^8+v43^8+v45^8+v5^8
h10 = (v0*v1*v21*v23*v25*v3*v41*v43*v45*v5)^2
h12 = (v0*v1*v21*v23*v25*v41)^4 + (v0*v21*v23*v25*v3*v43)^4 + (v1*v23*v25*v3*v41*v45)^4 + (v1*v21*v25*v3*v43*v45)^4 + (v0*v1*v21*v41*v43*v45)^4 + (v0*v23*v3*v41*v43*v45)^4 + (v0*v1*v21*v3*v41*v5)^4 + (v0*v1*v23*v3*v43*v5)^4 + (v1*v23*v25*v41*v43*v5)^4 + (v21*v25*v3*v41*v43*v5)^4 + (v0*v21*v23*v25*v45*v5)^4 + (v0*v1*v25*v3*v45*v5)^4 + (v21*v23*v3*v41*v45*v5)^4 + (v1*v21*v23*v43*v45*v5)^4 + (v0*v25*v41*v43*v45*v5)^4
h16 = v0^4*v1^4*v21^4*v23^4*v25^4*v3^8*v41^4 + v0^4*v1^8*v21^4*v23^4*v25^4*v3^4*v43^4 + v0^4*v21^4*v23^4*v25^4*v3^4*v41^8*v43^4 + v0^4*v1^4*v21^4*v23^4*v25^4*v41^4*v43^8 + v0^8*v1^4*v23^4*v25^4*v3^4*v41^4*v45^4 + v1^4*v21^8*v23^4*v25^4*v3^4*v41^4*v45^4 + v0^8*v1^4*v21^4*v25^4*v3^4*v43^4*v45^4 + v1^4*v21^4*v23^8*v25^4*v3^4*v43^4*v45^4 + v0^4*v1^4*v21^4*v23^8*v41^4*v43^4*v45^4 + v0^4*v1^4*v21^4*v25^8*v41^4*v43^4*v45^4 + v0^4*v1^8*v23^4*v3^4*v41^4*v43^4*v45^4 + v0^4*v21^8*v23^4*v3^4*v41^4*v43^4*v45^4 + v0^4*v23^4*v25^8*v3^4*v41^4*v43^4*v45^4 + v0^4*v1^4*v21^4*v3^8*v41^4*v43^4*v45^4 + v1^4*v21^4*v25^4*v3^4*v41^8*v43^4*v45^4 + v1^4*v23^4*v25^4*v3^4*v41^4*v43^8*v45^4 + v0^4*v1^4*v21^4*v23^4*v25^4*v41^4*v45^8 + v0^4*v21^4*v23^4*v25^4*v3^4*v43^4*v45^8 + v0^4*v1^4*v21^4*v23^8*v3^4*v41^4*v5^4 + v0^4*v1^4*v21^4*v25^8*v3^4*v41^4*v5^4 + v0^4*v1^4*v21^8*v23^4*v3^4*v43^4*v5^4 + v0^4*v1^4*v23^4*v25^8*v3^4*v43^4*v5^4 + v0^8*v1^4*v23^4*v25^4*v41^4*v43^4*v5^4 + v1^4*v21^8*v23^4*v25^4*v41^4*v43^4*v5^4 +v0^8*v21^4*v25^4*v3^4*v41^4*v43^4*v5^4 + v1^8*v21^4*v25^4*v3^4*v41^4*v43^4*v5^4 + v21^4*v23^8*v25^4*v3^4*v41^4*v43^4*v5^4 + v1^4*v23^4*v25^4*v3^8*v41^4*v45^4*v5^4 +v0^4*v1^4*v23^4*v3^4*v41^8*v43^4*v5^4 + v0^4*v1^4*v21^4*v3^4*v41^4*v43^8*v5^4 + v0^4*v1^8*v21^4*v23^4*v25^4*v45^4*v5^4 + v0^4*v1^4*v21^8*v25^4*v3^4*v45^4*v5^4 +v0^4*v1^4*v23^8*v25^4*v3^4*v45^4*v5^4 + v0^4*v21^4*v23^4*v25^4*v3^8*v45^4*v5^4 + v0^8*v21^4*v23^4*v3^4*v41^4*v45^4*v5^4 + v1^8*v21^4*v23^4*v3^4*v41^4*v45^4*v5^4 +v21^4*v23^4*v25^8*v3^4*v41^4*v45^4*v5^4 + v0^4*v21^4*v23^4*v25^4*v41^8*v45^4*v5^4 + v0^4*v1^4*v25^4*v3^4*v41^8*v45^4*v5^4 + v0^8*v1^4*v21^4*v23^4*v43^4*v45^4*v5^4 +v1^4*v21^4*v23^4*v25^8*v43^4*v45^4*v5^4 + v1^4*v21^4*v23^4*v3^8*v43^4*v45^4*v5^4 + v0^4*v1^8*v25^4*v41^4*v43^4*v45^4*v5^4 + v0^4*v21^4*v23^4*v25^4*v43^8*v45^4*v5^4 +v0^4*v23^8*v25^4*v41^4*v43^4*v45^4*v5^4 + v0^4*v25^4*v3^8*v41^4*v43^4*v45^4*v5^4 + v1^4*v21^4*v23^4*v41^8*v43^4*v45^4*v5^4 + v0^4*v21^4*v23^4*v25^4*v43^8*v45^4*v5^4 +v0^4*v1^4*v25^4*v3^4*v43^8*v45^4*v5^4 + v21^4*v23^4*v3^4*v41^4*v43^8*v45^4*v5^4 + v0^4*v1^4*v21^4*v3^4*v41^4*v45^8*v5^4 + v0^4*v1^4*v23^4*v3^4*v43^4*v45^8*v5^4 + v1^4*v23^4*v25^4*v41^4*v43^4*v45^8*v5^4 + v21^4*v25^4*v3^4*v41^4*v43^4*v45^8*v5^4 + v0^4*v1^4*v21^4*v23^4*v25^4*v41^4*v5^8 + v0^4*v21^4*v23^4*v25^4*v3^4*v43^4*v5^8 + v1^4*v23^4*v25^4*v3^4*v41^4*v45^4*v5^8 + v1^4*v21^4*v25^4*v3^4*v43^4*v45^4*v5^8 + v0^4*v1^4*v21^4*v41^4*v43^4*v45^4*v5^8 + v0^4*v23^4*v3^4*v41^4*v43^4*v45^4*v5^8
i1 = h12^5/h10^6
i2 = h12^3*h4/h10^4
i3 = h12^2*h16/h10^4