Τετάρτη, 12 Ιανουαρίου 2011

A CONFIGURATION (Case 3)

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Let ABC be a triangle and P a point.

The circle (B, BP) intersects AB at Ac1 (between A,B) and Ac2 (on the extension of BA) AND BC at A1c (between B,C) and A2c (on the extension of BC). The circle (C, CP) intersects AC at Ab1 (between A,C) and Ab2 AND BC at A1b (between B,C) and A2b (on the extension of CB).

3. The lines Ab1A1b and Ac1A1c intersect at A3.

Which is the locus of P such that ABC, A3B3C3 are perspective?

Solution
by Francisco Javier García Capitán

The locus looks like Neuberg cubic + three circle arcs:

This is Neuberg Cubic:

Neuberg cubic in dotted line with the locus, showing that they are not exactly the same, but very very close:

The "circle arcs":

The algebraic curve of the eight degree of which the arcs are part, that is they are not really circle arcs:

Equations:

1. The Neuberg-like curve is part of a curve of degree 14 with 20178 terms

2. The equation of the octic (in barycentrics):

64 a^6 b^4 c^8 x^6 y^2 + 256 a^5 b^5 c^8 x^6 y^2 -
128 a^4 b^6 c^8 x^6 y^2 - 256 a^3 b^7 c^8 x^6 y^2 +
64 a^2 b^8 c^8 x^6 y^2 + 256 a^4 b^5 c^9 x^6 y^2 +
512 a^3 b^6 c^9 x^6 y^2 - 256 a^2 b^7 c^9 x^6 y^2 -
128 a^4 b^4 c^10 x^6 y^2 - 256 a^3 b^5 c^10 x^6 y^2 +
384 a^2 b^6 c^10 x^6 y^2 - 256 a^2 b^5 c^11 x^6 y^2 +
64 a^2 b^4 c^12 x^6 y^2 - 16 a^8 b^2 c^8 x^5 y^3 -
112 a^7 b^3 c^8 x^5 y^3 - 48 a^6 b^4 c^8 x^5 y^3 +
1136 a^5 b^5 c^8 x^5 y^3 - 496 a^4 b^6 c^8 x^5 y^3 -
528 a^3 b^7 c^8 x^5 y^3 + 48 a^2 b^8 c^8 x^5 y^3 +
16 a b^9 c^8 x^5 y^3 + 48 a^7 b^2 c^9 x^5 y^3 +
256 a^6 b^3 c^9 x^5 y^3 + 208 a^5 b^4 c^9 x^5 y^3 +
768 a^4 b^5 c^9 x^5 y^3 + 1104 a^3 b^6 c^9 x^5 y^3 -
256 a^2 b^7 c^9 x^5 y^3 - 80 a b^8 c^9 x^5 y^3 -
16 a^6 b^2 c^10 x^5 y^3 + 16 a^5 b^3 c^10 x^5 y^3 +
32 a^4 b^4 c^10 x^5 y^3 - 416 a^3 b^5 c^10 x^5 y^3 +
496 a^2 b^6 c^10 x^5 y^3 + 144 a b^7 c^10 x^5 y^3 -
80 a^5 b^2 c^11 x^5 y^3 - 384 a^4 b^3 c^11 x^5 y^3 -
352 a^3 b^4 c^11 x^5 y^3 - 384 a^2 b^5 c^11 x^5 y^3 -
80 a b^6 c^11 x^5 y^3 + 80 a^4 b^2 c^12 x^5 y^3 +
176 a^3 b^3 c^12 x^5 y^3 + 16 a^2 b^4 c^12 x^5 y^3 -
80 a b^5 c^12 x^5 y^3 + 16 a^3 b^2 c^13 x^5 y^3 +
128 a^2 b^3 c^13 x^5 y^3 + 144 a b^4 c^13 x^5 y^3 -
48 a^2 b^2 c^14 x^5 y^3 - 80 a b^3 c^14 x^5 y^3 +
16 a b^2 c^15 x^5 y^3 + a^10 c^8 x^4 y^4 + 10 a^9 b c^8 x^4 y^4 -
19 a^8 b^2 c^8 x^4 y^4 - 392 a^7 b^3 c^8 x^4 y^4 -
494 a^6 b^4 c^8 x^4 y^4 + 1788 a^5 b^5 c^8 x^4 y^4 -
494 a^4 b^6 c^8 x^4 y^4 - 392 a^3 b^7 c^8 x^4 y^4 -
19 a^2 b^8 c^8 x^4 y^4 + 10 a b^9 c^8 x^4 y^4 + b^10 c^8 x^4 y^4 -
6 a^9 c^9 x^4 y^4 - 54 a^8 b c^9 x^4 y^4 + 8 a^7 b^2 c^9 x^4 y^4 +
872 a^6 b^3 c^9 x^4 y^4 + 716 a^5 b^4 c^9 x^4 y^4 +
716 a^4 b^5 c^9 x^4 y^4 + 872 a^3 b^6 c^9 x^4 y^4 +
8 a^2 b^7 c^9 x^4 y^4 - 54 a b^8 c^9 x^4 y^4 - 6 b^9 c^9 x^4 y^4 +
13 a^8 c^10 x^4 y^4 + 104 a^7 b c^10 x^4 y^4 +
140 a^6 b^2 c^10 x^4 y^4 - 168 a^5 b^3 c^10 x^4 y^4 +
334 a^4 b^4 c^10 x^4 y^4 - 168 a^3 b^5 c^10 x^4 y^4 +
140 a^2 b^6 c^10 x^4 y^4 + 104 a b^7 c^10 x^4 y^4 +
13 b^8 c^10 x^4 y^4 - 8 a^7 c^11 x^4 y^4 - 56 a^6 b c^11 x^4 y^4 -
232 a^5 b^2 c^11 x^4 y^4 - 728 a^4 b^3 c^11 x^4 y^4 -
728 a^3 b^4 c^11 x^4 y^4 - 232 a^2 b^5 c^11 x^4 y^4 -
56 a b^6 c^11 x^4 y^4 - 8 b^7 c^11 x^4 y^4 - 14 a^6 c^12 x^4 y^4 -
84 a^5 b c^12 x^4 y^4 + 46 a^4 b^2 c^12 x^4 y^4 +
360 a^3 b^3 c^12 x^4 y^4 + 46 a^2 b^4 c^12 x^4 y^4 -
84 a b^5 c^12 x^4 y^4 - 14 b^6 c^12 x^4 y^4 + 28 a^5 c^13 x^4 y^4 +
140 a^4 b c^13 x^4 y^4 + 120 a^3 b^2 c^13 x^4 y^4 +
120 a^2 b^3 c^13 x^4 y^4 + 140 a b^4 c^13 x^4 y^4 +
28 b^5 c^13 x^4 y^4 - 14 a^4 c^14 x^4 y^4 - 56 a^3 b c^14 x^4 y^4 -
52 a^2 b^2 c^14 x^4 y^4 - 56 a b^3 c^14 x^4 y^4 -
14 b^4 c^14 x^4 y^4 - 8 a^3 c^15 x^4 y^4 - 24 a^2 b c^15 x^4 y^4 -
24 a b^2 c^15 x^4 y^4 - 8 b^3 c^15 x^4 y^4 + 13 a^2 c^16 x^4 y^4 +
26 a b c^16 x^4 y^4 + 13 b^2 c^16 x^4 y^4 - 6 a c^17 x^4 y^4 -
6 b c^17 x^4 y^4 + c^18 x^4 y^4 + 16 a^9 b c^8 x^3 y^5 +
48 a^8 b^2 c^8 x^3 y^5 - 528 a^7 b^3 c^8 x^3 y^5 -
496 a^6 b^4 c^8 x^3 y^5 + 1136 a^5 b^5 c^8 x^3 y^5 -
48 a^4 b^6 c^8 x^3 y^5 - 112 a^3 b^7 c^8 x^3 y^5 -
16 a^2 b^8 c^8 x^3 y^5 - 80 a^8 b c^9 x^3 y^5 -
256 a^7 b^2 c^9 x^3 y^5 + 1104 a^6 b^3 c^9 x^3 y^5 +
768 a^5 b^4 c^9 x^3 y^5 + 208 a^4 b^5 c^9 x^3 y^5 +
256 a^3 b^6 c^9 x^3 y^5 + 48 a^2 b^7 c^9 x^3 y^5 +
144 a^7 b c^10 x^3 y^5 + 496 a^6 b^2 c^10 x^3 y^5 -
416 a^5 b^3 c^10 x^3 y^5 + 32 a^4 b^4 c^10 x^3 y^5 +
16 a^3 b^5 c^10 x^3 y^5 - 16 a^2 b^6 c^10 x^3 y^5 -
80 a^6 b c^11 x^3 y^5 - 384 a^5 b^2 c^11 x^3 y^5 -
352 a^4 b^3 c^11 x^3 y^5 - 384 a^3 b^4 c^11 x^3 y^5 -
80 a^2 b^5 c^11 x^3 y^5 - 80 a^5 b c^12 x^3 y^5 +
16 a^4 b^2 c^12 x^3 y^5 + 176 a^3 b^3 c^12 x^3 y^5 +
80 a^2 b^4 c^12 x^3 y^5 + 144 a^4 b c^13 x^3 y^5 +
128 a^3 b^2 c^13 x^3 y^5 + 16 a^2 b^3 c^13 x^3 y^5 -
80 a^3 b c^14 x^3 y^5 - 48 a^2 b^2 c^14 x^3 y^5 +
16 a^2 b c^15 x^3 y^5 + 64 a^8 b^2 c^8 x^2 y^6 -
256 a^7 b^3 c^8 x^2 y^6 - 128 a^6 b^4 c^8 x^2 y^6 +
256 a^5 b^5 c^8 x^2 y^6 + 64 a^4 b^6 c^8 x^2 y^6 -
256 a^7 b^2 c^9 x^2 y^6 + 512 a^6 b^3 c^9 x^2 y^6 +
256 a^5 b^4 c^9 x^2 y^6 + 384 a^6 b^2 c^10 x^2 y^6 -
256 a^5 b^3 c^10 x^2 y^6 - 128 a^4 b^4 c^10 x^2 y^6 -
256 a^5 b^2 c^11 x^2 y^6 + 64 a^4 b^2 c^12 x^2 y^6 +
384 a^6 b^6 c^6 x^6 y z + 256 a^5 b^7 c^6 x^6 y z -
512 a^4 b^8 c^6 x^6 y z - 256 a^3 b^9 c^6 x^6 y z +
128 a^2 b^10 c^6 x^6 y z + 256 a^5 b^6 c^7 x^6 y z +
1024 a^4 b^7 c^7 x^6 y z + 256 a^3 b^8 c^7 x^6 y z -
512 a^2 b^9 c^7 x^6 y z - 512 a^4 b^6 c^8 x^6 y z +
256 a^3 b^7 c^8 x^6 y z + 768 a^2 b^8 c^8 x^6 y z -
256 a^3 b^6 c^9 x^6 y z - 512 a^2 b^7 c^9 x^6 y z +
128 a^2 b^6 c^10 x^6 y z + 80 a^8 b^4 c^6 x^5 y^2 z -
176 a^7 b^5 c^6 x^5 y^2 z + 1424 a^6 b^6 c^6 x^5 y^2 z +
400 a^5 b^7 c^6 x^5 y^2 z - 1552 a^4 b^8 c^6 x^5 y^2 z -
272 a^3 b^9 c^6 x^5 y^2 z + 48 a^2 b^10 c^6 x^5 y^2 z +
48 a b^11 c^6 x^5 y^2 z + 240 a^7 b^4 c^7 x^5 y^2 z +
768 a^6 b^5 c^7 x^5 y^2 z + 2480 a^5 b^6 c^7 x^5 y^2 z +
2176 a^4 b^7 c^7 x^5 y^2 z + 80 a^3 b^8 c^7 x^5 y^2 z -
384 a^2 b^9 c^7 x^5 y^2 z - 240 a b^10 c^7 x^5 y^2 z -
80 a^6 b^4 c^8 x^5 y^2 z + 1520 a^5 b^5 c^8 x^5 y^2 z +
352 a^4 b^6 c^8 x^5 y^2 z + 352 a^3 b^7 c^8 x^5 y^2 z +
1008 a^2 b^8 c^8 x^5 y^2 z + 432 a b^9 c^8 x^5 y^2 z -
560 a^5 b^4 c^9 x^5 y^2 z - 1024 a^4 b^5 c^9 x^5 y^2 z +
416 a^3 b^6 c^9 x^5 y^2 z - 1152 a^2 b^7 c^9 x^5 y^2 z -
240 a b^8 c^9 x^5 y^2 z + 48 a^4 b^4 c^10 x^5 y^2 z -
848 a^3 b^5 c^10 x^5 y^2 z + 528 a^2 b^6 c^10 x^5 y^2 z -
240 a b^7 c^10 x^5 y^2 z + 272 a^3 b^4 c^11 x^5 y^2 z +
432 a b^6 c^11 x^5 y^2 z - 48 a^2 b^4 c^12 x^5 y^2 z -
240 a b^5 c^12 x^5 y^2 z + 48 a b^4 c^13 x^5 y^2 z -
12 a^10 b^2 c^6 x^4 y^3 z - 24 a^9 b^3 c^6 x^4 y^3 z -
316 a^8 b^4 c^6 x^4 y^3 z - 208 a^7 b^5 c^6 x^4 y^3 z +
1912 a^6 b^6 c^6 x^4 y^3 z + 256 a^5 b^7 c^6 x^4 y^3 z -
1544 a^4 b^8 c^6 x^4 y^3 z - 48 a^3 b^9 c^6 x^4 y^3 z -
44 a^2 b^10 c^6 x^4 y^3 z + 24 a b^11 c^6 x^4 y^3 z +
4 b^12 c^6 x^4 y^3 z + 8 a^9 b^2 c^7 x^4 y^3 z -
120 a^8 b^3 c^7 x^4 y^3 z + 1072 a^7 b^4 c^7 x^4 y^3 z +
3136 a^6 b^5 c^7 x^4 y^3 z + 4480 a^5 b^6 c^7 x^4 y^3 z +
2128 a^4 b^7 c^7 x^4 y^3 z - 304 a^3 b^8 c^7 x^4 y^3 z -
136 a b^10 c^7 x^4 y^3 z - 24 b^11 c^7 x^4 y^3 z +
68 a^8 b^2 c^8 x^4 y^3 z + 368 a^7 b^3 c^8 x^4 y^3 z +
144 a^6 b^4 c^8 x^4 y^3 z + 5376 a^5 b^5 c^8 x^4 y^3 z +
904 a^4 b^6 c^8 x^4 y^3 z + 624 a^3 b^7 c^8 x^4 y^3 z +
368 a^2 b^8 c^8 x^4 y^3 z + 288 a b^9 c^8 x^4 y^3 z +
52 b^10 c^8 x^4 y^3 z - 80 a^7 b^2 c^9 x^4 y^3 z -
1536 a^5 b^4 c^9 x^4 y^3 z - 1824 a^4 b^5 c^9 x^4 y^3 z +
432 a^3 b^6 c^9 x^4 y^3 z - 576 a^2 b^7 c^9 x^4 y^3 z -
224 a b^8 c^9 x^4 y^3 z - 32 b^9 c^9 x^4 y^3 z -
72 a^6 b^2 c^10 x^4 y^3 z - 512 a^5 b^3 c^10 x^4 y^3 z +
136 a^4 b^4 c^10 x^4 y^3 z - 1232 a^3 b^5 c^10 x^4 y^3 z +
184 a^2 b^6 c^10 x^4 y^3 z - 112 a b^7 c^10 x^4 y^3 z -
56 b^8 c^10 x^4 y^3 z + 128 a^5 b^2 c^11 x^4 y^3 z +
208 a^4 b^3 c^11 x^4 y^3 z + 432 a^3 b^4 c^11 x^4 y^3 z +
128 a^2 b^5 c^11 x^4 y^3 z + 336 a b^6 c^11 x^4 y^3 z +
112 b^7 c^11 x^4 y^3 z - 8 a^4 b^2 c^12 x^4 y^3 z +
144 a^3 b^3 c^12 x^4 y^3 z - 16 a^2 b^4 c^12 x^4 y^3 z -
224 a b^5 c^12 x^4 y^3 z - 56 b^6 c^12 x^4 y^3 z -
48 a^3 b^2 c^13 x^4 y^3 z - 64 a^2 b^3 c^13 x^4 y^3 z +
32 a b^4 c^13 x^4 y^3 z - 32 b^5 c^13 x^4 y^3 z +
20 a^2 b^2 c^14 x^4 y^3 z + 24 a b^3 c^14 x^4 y^3 z +
52 b^4 c^14 x^4 y^3 z - 8 a b^2 c^15 x^4 y^3 z -
24 b^3 c^15 x^4 y^3 z + 4 b^2 c^16 x^4 y^3 z +
4 a^12 c^6 x^3 y^4 z + 24 a^11 b c^6 x^3 y^4 z -
44 a^10 b^2 c^6 x^3 y^4 z - 48 a^9 b^3 c^6 x^3 y^4 z -
1544 a^8 b^4 c^6 x^3 y^4 z + 256 a^7 b^5 c^6 x^3 y^4 z +
1912 a^6 b^6 c^6 x^3 y^4 z - 208 a^5 b^7 c^6 x^3 y^4 z -
316 a^4 b^8 c^6 x^3 y^4 z - 24 a^3 b^9 c^6 x^3 y^4 z -
12 a^2 b^10 c^6 x^3 y^4 z - 24 a^11 c^7 x^3 y^4 z -
136 a^10 b c^7 x^3 y^4 z - 304 a^8 b^3 c^7 x^3 y^4 z +
2128 a^7 b^4 c^7 x^3 y^4 z + 4480 a^6 b^5 c^7 x^3 y^4 z +
3136 a^5 b^6 c^7 x^3 y^4 z + 1072 a^4 b^7 c^7 x^3 y^4 z -
120 a^3 b^8 c^7 x^3 y^4 z + 8 a^2 b^9 c^7 x^3 y^4 z +
52 a^10 c^8 x^3 y^4 z + 288 a^9 b c^8 x^3 y^4 z +
368 a^8 b^2 c^8 x^3 y^4 z + 624 a^7 b^3 c^8 x^3 y^4 z +
904 a^6 b^4 c^8 x^3 y^4 z + 5376 a^5 b^5 c^8 x^3 y^4 z +
144 a^4 b^6 c^8 x^3 y^4 z + 368 a^3 b^7 c^8 x^3 y^4 z +
68 a^2 b^8 c^8 x^3 y^4 z - 32 a^9 c^9 x^3 y^4 z -
224 a^8 b c^9 x^3 y^4 z - 576 a^7 b^2 c^9 x^3 y^4 z +
432 a^6 b^3 c^9 x^3 y^4 z - 1824 a^5 b^4 c^9 x^3 y^4 z -
1536 a^4 b^5 c^9 x^3 y^4 z - 80 a^2 b^7 c^9 x^3 y^4 z -
56 a^8 c^10 x^3 y^4 z - 112 a^7 b c^10 x^3 y^4 z +
184 a^6 b^2 c^10 x^3 y^4 z - 1232 a^5 b^3 c^10 x^3 y^4 z +
136 a^4 b^4 c^10 x^3 y^4 z - 512 a^3 b^5 c^10 x^3 y^4 z -
72 a^2 b^6 c^10 x^3 y^4 z + 112 a^7 c^11 x^3 y^4 z +
336 a^6 b c^11 x^3 y^4 z + 128 a^5 b^2 c^11 x^3 y^4 z +
432 a^4 b^3 c^11 x^3 y^4 z + 208 a^3 b^4 c^11 x^3 y^4 z +
128 a^2 b^5 c^11 x^3 y^4 z - 56 a^6 c^12 x^3 y^4 z -
224 a^5 b c^12 x^3 y^4 z - 16 a^4 b^2 c^12 x^3 y^4 z +
144 a^3 b^3 c^12 x^3 y^4 z - 8 a^2 b^4 c^12 x^3 y^4 z -
32 a^5 c^13 x^3 y^4 z + 32 a^4 b c^13 x^3 y^4 z -
64 a^3 b^2 c^13 x^3 y^4 z - 48 a^2 b^3 c^13 x^3 y^4 z +
52 a^4 c^14 x^3 y^4 z + 24 a^3 b c^14 x^3 y^4 z +
20 a^2 b^2 c^14 x^3 y^4 z - 24 a^3 c^15 x^3 y^4 z -
8 a^2 b c^15 x^3 y^4 z + 4 a^2 c^16 x^3 y^4 z +
48 a^11 b c^6 x^2 y^5 z + 48 a^10 b^2 c^6 x^2 y^5 z -
272 a^9 b^3 c^6 x^2 y^5 z - 1552 a^8 b^4 c^6 x^2 y^5 z +
400 a^7 b^5 c^6 x^2 y^5 z + 1424 a^6 b^6 c^6 x^2 y^5 z -
176 a^5 b^7 c^6 x^2 y^5 z + 80 a^4 b^8 c^6 x^2 y^5 z -
240 a^10 b c^7 x^2 y^5 z - 384 a^9 b^2 c^7 x^2 y^5 z +
80 a^8 b^3 c^7 x^2 y^5 z + 2176 a^7 b^4 c^7 x^2 y^5 z +
2480 a^6 b^5 c^7 x^2 y^5 z + 768 a^5 b^6 c^7 x^2 y^5 z +
240 a^4 b^7 c^7 x^2 y^5 z + 432 a^9 b c^8 x^2 y^5 z +
1008 a^8 b^2 c^8 x^2 y^5 z + 352 a^7 b^3 c^8 x^2 y^5 z +
352 a^6 b^4 c^8 x^2 y^5 z + 1520 a^5 b^5 c^8 x^2 y^5 z -
80 a^4 b^6 c^8 x^2 y^5 z - 240 a^8 b c^9 x^2 y^5 z -
1152 a^7 b^2 c^9 x^2 y^5 z + 416 a^6 b^3 c^9 x^2 y^5 z -
1024 a^5 b^4 c^9 x^2 y^5 z - 560 a^4 b^5 c^9 x^2 y^5 z -
240 a^7 b c^10 x^2 y^5 z + 528 a^6 b^2 c^10 x^2 y^5 z -
848 a^5 b^3 c^10 x^2 y^5 z + 48 a^4 b^4 c^10 x^2 y^5 z +
432 a^6 b c^11 x^2 y^5 z + 272 a^4 b^3 c^11 x^2 y^5 z -
240 a^5 b c^12 x^2 y^5 z - 48 a^4 b^2 c^12 x^2 y^5 z +
48 a^4 b c^13 x^2 y^5 z + 128 a^10 b^2 c^6 x y^6 z -
256 a^9 b^3 c^6 x y^6 z - 512 a^8 b^4 c^6 x y^6 z +
256 a^7 b^5 c^6 x y^6 z + 384 a^6 b^6 c^6 x y^6 z -
512 a^9 b^2 c^7 x y^6 z + 256 a^8 b^3 c^7 x y^6 z +
1024 a^7 b^4 c^7 x y^6 z + 256 a^6 b^5 c^7 x y^6 z +
768 a^8 b^2 c^8 x y^6 z + 256 a^7 b^3 c^8 x y^6 z -
512 a^6 b^4 c^8 x y^6 z - 512 a^7 b^2 c^9 x y^6 z -
256 a^6 b^3 c^9 x y^6 z + 128 a^6 b^2 c^10 x y^6 z +
64 a^6 b^8 c^4 x^6 z^2 - 128 a^4 b^10 c^4 x^6 z^2 +
64 a^2 b^12 c^4 x^6 z^2 + 256 a^5 b^8 c^5 x^6 z^2 +
256 a^4 b^9 c^5 x^6 z^2 - 256 a^3 b^10 c^5 x^6 z^2 -
256 a^2 b^11 c^5 x^6 z^2 - 128 a^4 b^8 c^6 x^6 z^2 +
512 a^3 b^9 c^6 x^6 z^2 + 384 a^2 b^10 c^6 x^6 z^2 -
256 a^3 b^8 c^7 x^6 z^2 - 256 a^2 b^9 c^7 x^6 z^2 +
64 a^2 b^8 c^8 x^6 z^2 + 80 a^8 b^6 c^4 x^5 y z^2 +
240 a^7 b^7 c^4 x^5 y z^2 - 80 a^6 b^8 c^4 x^5 y z^2 -
560 a^5 b^9 c^4 x^5 y z^2 + 48 a^4 b^10 c^4 x^5 y z^2 +
272 a^3 b^11 c^4 x^5 y z^2 - 48 a^2 b^12 c^4 x^5 y z^2 +
48 a b^13 c^4 x^5 y z^2 - 176 a^7 b^6 c^5 x^5 y z^2 +
768 a^6 b^7 c^5 x^5 y z^2 + 1520 a^5 b^8 c^5 x^5 y z^2 -
1024 a^4 b^9 c^5 x^5 y z^2 - 848 a^3 b^10 c^5 x^5 y z^2 -
240 a b^12 c^5 x^5 y z^2 + 1424 a^6 b^6 c^6 x^5 y z^2 +
2480 a^5 b^7 c^6 x^5 y z^2 + 352 a^4 b^8 c^6 x^5 y z^2 +
416 a^3 b^9 c^6 x^5 y z^2 + 528 a^2 b^10 c^6 x^5 y z^2 +
432 a b^11 c^6 x^5 y z^2 + 400 a^5 b^6 c^7 x^5 y z^2 +
2176 a^4 b^7 c^7 x^5 y z^2 + 352 a^3 b^8 c^7 x^5 y z^2 -
1152 a^2 b^9 c^7 x^5 y z^2 - 240 a b^10 c^7 x^5 y z^2 -
1552 a^4 b^6 c^8 x^5 y z^2 + 80 a^3 b^7 c^8 x^5 y z^2 +
1008 a^2 b^8 c^8 x^5 y z^2 - 240 a b^9 c^8 x^5 y z^2 -
272 a^3 b^6 c^9 x^5 y z^2 - 384 a^2 b^7 c^9 x^5 y z^2 +
432 a b^8 c^9 x^5 y z^2 + 48 a^2 b^6 c^10 x^5 y z^2 -
240 a b^7 c^10 x^5 y z^2 + 48 a b^6 c^11 x^5 y z^2 +
294 a^10 b^4 c^4 x^4 y^2 z^2 - 276 a^9 b^5 c^4 x^4 y^2 z^2 +
142 a^8 b^6 c^4 x^4 y^2 z^2 + 624 a^7 b^7 c^4 x^4 y^2 z^2 -
916 a^6 b^8 c^4 x^4 y^2 z^2 - 664 a^5 b^9 c^4 x^4 y^2 z^2 +
492 a^4 b^10 c^4 x^4 y^2 z^2 + 304 a^3 b^11 c^4 x^4 y^2 z^2 -
18 a^2 b^12 c^4 x^4 y^2 z^2 + 12 a b^13 c^4 x^4 y^2 z^2 +
6 b^14 c^4 x^4 y^2 z^2 - 276 a^9 b^4 c^5 x^4 y^2 z^2 -
388 a^8 b^5 c^5 x^4 y^2 z^2 + 816 a^7 b^6 c^5 x^4 y^2 z^2 +
1552 a^6 b^7 c^5 x^4 y^2 z^2 + 1032 a^5 b^8 c^5 x^4 y^2 z^2 -
1592 a^4 b^9 c^5 x^4 y^2 z^2 - 976 a^3 b^10 c^5 x^4 y^2 z^2 -
48 a^2 b^11 c^5 x^4 y^2 z^2 - 84 a b^12 c^5 x^4 y^2 z^2 -
36 b^13 c^5 x^4 y^2 z^2 + 142 a^8 b^4 c^6 x^4 y^2 z^2 +
816 a^7 b^5 c^6 x^4 y^2 z^2 + 8072 a^6 b^6 c^6 x^4 y^2 z^2 +
5776 a^5 b^7 c^6 x^4 y^2 z^2 - 876 a^4 b^8 c^6 x^4 y^2 z^2 +
1104 a^3 b^9 c^6 x^4 y^2 z^2 + 264 a^2 b^10 c^6 x^4 y^2 z^2 +
240 a b^11 c^6 x^4 y^2 z^2 + 78 b^12 c^6 x^4 y^2 z^2 +
624 a^7 b^4 c^7 x^4 y^2 z^2 + 1552 a^6 b^5 c^7 x^4 y^2 z^2 +
5776 a^5 b^6 c^7 x^4 y^2 z^2 + 3952 a^4 b^7 c^7 x^4 y^2 z^2 -
432 a^3 b^8 c^7 x^4 y^2 z^2 - 336 a^2 b^9 c^7 x^4 y^2 z^2 -
336 a b^10 c^7 x^4 y^2 z^2 - 48 b^11 c^7 x^4 y^2 z^2 -
916 a^6 b^4 c^8 x^4 y^2 z^2 + 1032 a^5 b^5 c^8 x^4 y^2 z^2 -
876 a^4 b^6 c^8 x^4 y^2 z^2 - 432 a^3 b^7 c^8 x^4 y^2 z^2 +
276 a^2 b^8 c^8 x^4 y^2 z^2 + 168 a b^9 c^8 x^4 y^2 z^2 -
84 b^10 c^8 x^4 y^2 z^2 - 664 a^5 b^4 c^9 x^4 y^2 z^2 -
1592 a^4 b^5 c^9 x^4 y^2 z^2 + 1104 a^3 b^6 c^9 x^4 y^2 z^2 -
336 a^2 b^7 c^9 x^4 y^2 z^2 + 168 a b^8 c^9 x^4 y^2 z^2 +
168 b^9 c^9 x^4 y^2 z^2 + 492 a^4 b^4 c^10 x^4 y^2 z^2 -
976 a^3 b^5 c^10 x^4 y^2 z^2 + 264 a^2 b^6 c^10 x^4 y^2 z^2 -
336 a b^7 c^10 x^4 y^2 z^2 - 84 b^8 c^10 x^4 y^2 z^2 +
304 a^3 b^4 c^11 x^4 y^2 z^2 - 48 a^2 b^5 c^11 x^4 y^2 z^2 +
240 a b^6 c^11 x^4 y^2 z^2 - 48 b^7 c^11 x^4 y^2 z^2 -
18 a^2 b^4 c^12 x^4 y^2 z^2 - 84 a b^5 c^12 x^4 y^2 z^2 +
78 b^6 c^12 x^4 y^2 z^2 + 12 a b^4 c^13 x^4 y^2 z^2 -
36 b^5 c^13 x^4 y^2 z^2 + 6 b^4 c^14 x^4 y^2 z^2 +
28 a^12 b^2 c^4 x^3 y^3 z^2 + 8 a^11 b^3 c^4 x^3 y^3 z^2 +
844 a^10 b^4 c^4 x^3 y^3 z^2 - 608 a^9 b^5 c^4 x^3 y^3 z^2 -
872 a^8 b^6 c^4 x^3 y^3 z^2 + 1200 a^7 b^7 c^4 x^3 y^3 z^2 -
872 a^6 b^8 c^4 x^3 y^3 z^2 - 608 a^5 b^9 c^4 x^3 y^3 z^2 +
844 a^4 b^10 c^4 x^3 y^3 z^2 + 8 a^3 b^11 c^4 x^3 y^3 z^2 +
28 a^2 b^12 c^4 x^3 y^3 z^2 - 136 a^11 b^2 c^5 x^3 y^3 z^2 -
216 a^10 b^3 c^5 x^3 y^3 z^2 - 1008 a^9 b^4 c^5 x^3 y^3 z^2 -
464 a^8 b^5 c^5 x^3 y^3 z^2 + 1824 a^7 b^6 c^5 x^3 y^3 z^2 +
1824 a^6 b^7 c^5 x^3 y^3 z^2 - 464 a^5 b^8 c^5 x^3 y^3 z^2 -
1008 a^4 b^9 c^5 x^3 y^3 z^2 - 216 a^3 b^10 c^5 x^3 y^3 z^2 -
136 a^2 b^11 c^5 x^3 y^3 z^2 + 204 a^10 b^2 c^6 x^3 y^3 z^2 +
624 a^9 b^3 c^6 x^3 y^3 z^2 - 848 a^8 b^4 c^6 x^3 y^3 z^2 +
4496 a^7 b^5 c^6 x^3 y^3 z^2 + 12552 a^6 b^6 c^6 x^3 y^3 z^2 +
4496 a^5 b^7 c^6 x^3 y^3 z^2 - 848 a^4 b^8 c^6 x^3 y^3 z^2 +
624 a^3 b^9 c^6 x^3 y^3 z^2 + 204 a^2 b^10 c^6 x^3 y^3 z^2 -
592 a^8 b^3 c^7 x^3 y^3 z^2 + 2736 a^7 b^4 c^7 x^3 y^3 z^2 +
6560 a^6 b^5 c^7 x^3 y^3 z^2 + 6560 a^5 b^6 c^7 x^3 y^3 z^2 +
2736 a^4 b^7 c^7 x^3 y^3 z^2 - 592 a^3 b^8 c^7 x^3 y^3 z^2 -
296 a^8 b^2 c^8 x^3 y^3 z^2 - 64 a^7 b^3 c^8 x^3 y^3 z^2 -
1208 a^6 b^4 c^8 x^3 y^3 z^2 + 3008 a^5 b^5 c^8 x^3 y^3 z^2 -
1208 a^4 b^6 c^8 x^3 y^3 z^2 - 64 a^3 b^7 c^8 x^3 y^3 z^2 -
296 a^2 b^8 c^8 x^3 y^3 z^2 + 304 a^7 b^2 c^9 x^3 y^3 z^2 +
704 a^6 b^3 c^9 x^3 y^3 z^2 - 1936 a^5 b^4 c^9 x^3 y^3 z^2 -
1936 a^4 b^5 c^9 x^3 y^3 z^2 + 704 a^3 b^6 c^9 x^3 y^3 z^2 +
304 a^2 b^7 c^9 x^3 y^3 z^2 - 104 a^6 b^2 c^10 x^3 y^3 z^2 -
752 a^5 b^3 c^10 x^3 y^3 z^2 + 1072 a^4 b^4 c^10 x^3 y^3 z^2 -
752 a^3 b^5 c^10 x^3 y^3 z^2 - 104 a^2 b^6 c^10 x^3 y^3 z^2 -
64 a^5 b^2 c^11 x^3 y^3 z^2 + 208 a^4 b^3 c^11 x^3 y^3 z^2 +
208 a^3 b^4 c^11 x^3 y^3 z^2 - 64 a^2 b^5 c^11 x^3 y^3 z^2 +
140 a^4 b^2 c^12 x^3 y^3 z^2 + 184 a^3 b^3 c^12 x^3 y^3 z^2 +
140 a^2 b^4 c^12 x^3 y^3 z^2 - 104 a^3 b^2 c^13 x^3 y^3 z^2 -
104 a^2 b^3 c^13 x^3 y^3 z^2 + 28 a^2 b^2 c^14 x^3 y^3 z^2 +
6 a^14 c^4 x^2 y^4 z^2 + 12 a^13 b c^4 x^2 y^4 z^2 -
18 a^12 b^2 c^4 x^2 y^4 z^2 + 304 a^11 b^3 c^4 x^2 y^4 z^2 +
492 a^10 b^4 c^4 x^2 y^4 z^2 - 664 a^9 b^5 c^4 x^2 y^4 z^2 -
916 a^8 b^6 c^4 x^2 y^4 z^2 + 624 a^7 b^7 c^4 x^2 y^4 z^2 +
142 a^6 b^8 c^4 x^2 y^4 z^2 - 276 a^5 b^9 c^4 x^2 y^4 z^2 +
294 a^4 b^10 c^4 x^2 y^4 z^2 - 36 a^13 c^5 x^2 y^4 z^2 -
84 a^12 b c^5 x^2 y^4 z^2 - 48 a^11 b^2 c^5 x^2 y^4 z^2 -
976 a^10 b^3 c^5 x^2 y^4 z^2 - 1592 a^9 b^4 c^5 x^2 y^4 z^2 +
1032 a^8 b^5 c^5 x^2 y^4 z^2 + 1552 a^7 b^6 c^5 x^2 y^4 z^2 +
816 a^6 b^7 c^5 x^2 y^4 z^2 - 388 a^5 b^8 c^5 x^2 y^4 z^2 -
276 a^4 b^9 c^5 x^2 y^4 z^2 + 78 a^12 c^6 x^2 y^4 z^2 +
240 a^11 b c^6 x^2 y^4 z^2 + 264 a^10 b^2 c^6 x^2 y^4 z^2 +
1104 a^9 b^3 c^6 x^2 y^4 z^2 - 876 a^8 b^4 c^6 x^2 y^4 z^2 +
5776 a^7 b^5 c^6 x^2 y^4 z^2 + 8072 a^6 b^6 c^6 x^2 y^4 z^2 +
816 a^5 b^7 c^6 x^2 y^4 z^2 + 142 a^4 b^8 c^6 x^2 y^4 z^2 -
48 a^11 c^7 x^2 y^4 z^2 - 336 a^10 b c^7 x^2 y^4 z^2 -
336 a^9 b^2 c^7 x^2 y^4 z^2 - 432 a^8 b^3 c^7 x^2 y^4 z^2 +
3952 a^7 b^4 c^7 x^2 y^4 z^2 + 5776 a^6 b^5 c^7 x^2 y^4 z^2 +
1552 a^5 b^6 c^7 x^2 y^4 z^2 + 624 a^4 b^7 c^7 x^2 y^4 z^2 -
84 a^10 c^8 x^2 y^4 z^2 + 168 a^9 b c^8 x^2 y^4 z^2 +
276 a^8 b^2 c^8 x^2 y^4 z^2 - 432 a^7 b^3 c^8 x^2 y^4 z^2 -
876 a^6 b^4 c^8 x^2 y^4 z^2 + 1032 a^5 b^5 c^8 x^2 y^4 z^2 -
916 a^4 b^6 c^8 x^2 y^4 z^2 + 168 a^9 c^9 x^2 y^4 z^2 +
168 a^8 b c^9 x^2 y^4 z^2 - 336 a^7 b^2 c^9 x^2 y^4 z^2 +
1104 a^6 b^3 c^9 x^2 y^4 z^2 - 1592 a^5 b^4 c^9 x^2 y^4 z^2 -
664 a^4 b^5 c^9 x^2 y^4 z^2 - 84 a^8 c^10 x^2 y^4 z^2 -
336 a^7 b c^10 x^2 y^4 z^2 + 264 a^6 b^2 c^10 x^2 y^4 z^2 -
976 a^5 b^3 c^10 x^2 y^4 z^2 + 492 a^4 b^4 c^10 x^2 y^4 z^2 -
48 a^7 c^11 x^2 y^4 z^2 + 240 a^6 b c^11 x^2 y^4 z^2 -
48 a^5 b^2 c^11 x^2 y^4 z^2 + 304 a^4 b^3 c^11 x^2 y^4 z^2 +
78 a^6 c^12 x^2 y^4 z^2 - 84 a^5 b c^12 x^2 y^4 z^2 -
18 a^4 b^2 c^12 x^2 y^4 z^2 - 36 a^5 c^13 x^2 y^4 z^2 +
12 a^4 b c^13 x^2 y^4 z^2 + 6 a^4 c^14 x^2 y^4 z^2 +
48 a^13 b c^4 x y^5 z^2 - 48 a^12 b^2 c^4 x y^5 z^2 +
272 a^11 b^3 c^4 x y^5 z^2 + 48 a^10 b^4 c^4 x y^5 z^2 -
560 a^9 b^5 c^4 x y^5 z^2 - 80 a^8 b^6 c^4 x y^5 z^2 +
240 a^7 b^7 c^4 x y^5 z^2 + 80 a^6 b^8 c^4 x y^5 z^2 -
240 a^12 b c^5 x y^5 z^2 - 848 a^10 b^3 c^5 x y^5 z^2 -
1024 a^9 b^4 c^5 x y^5 z^2 + 1520 a^8 b^5 c^5 x y^5 z^2 +
768 a^7 b^6 c^5 x y^5 z^2 - 176 a^6 b^7 c^5 x y^5 z^2 +
432 a^11 b c^6 x y^5 z^2 + 528 a^10 b^2 c^6 x y^5 z^2 +
416 a^9 b^3 c^6 x y^5 z^2 + 352 a^8 b^4 c^6 x y^5 z^2 +
2480 a^7 b^5 c^6 x y^5 z^2 + 1424 a^6 b^6 c^6 x y^5 z^2 -
240 a^10 b c^7 x y^5 z^2 - 1152 a^9 b^2 c^7 x y^5 z^2 +
352 a^8 b^3 c^7 x y^5 z^2 + 2176 a^7 b^4 c^7 x y^5 z^2 +
400 a^6 b^5 c^7 x y^5 z^2 - 240 a^9 b c^8 x y^5 z^2 +
1008 a^8 b^2 c^8 x y^5 z^2 + 80 a^7 b^3 c^8 x y^5 z^2 -
1552 a^6 b^4 c^8 x y^5 z^2 + 432 a^8 b c^9 x y^5 z^2 -
384 a^7 b^2 c^9 x y^5 z^2 - 272 a^6 b^3 c^9 x y^5 z^2 -
240 a^7 b c^10 x y^5 z^2 + 48 a^6 b^2 c^10 x y^5 z^2 +
48 a^6 b c^11 x y^5 z^2 + 64 a^12 b^2 c^4 y^6 z^2 -
128 a^10 b^4 c^4 y^6 z^2 + 64 a^8 b^6 c^4 y^6 z^2 -
256 a^11 b^2 c^5 y^6 z^2 - 256 a^10 b^3 c^5 y^6 z^2 +
256 a^9 b^4 c^5 y^6 z^2 + 256 a^8 b^5 c^5 y^6 z^2 +
384 a^10 b^2 c^6 y^6 z^2 + 512 a^9 b^3 c^6 y^6 z^2 -
128 a^8 b^4 c^6 y^6 z^2 - 256 a^9 b^2 c^7 y^6 z^2 -
256 a^8 b^3 c^7 y^6 z^2 + 64 a^8 b^2 c^8 y^6 z^2 -
16 a^8 b^8 c^2 x^5 z^3 + 48 a^7 b^9 c^2 x^5 z^3 -
16 a^6 b^10 c^2 x^5 z^3 - 80 a^5 b^11 c^2 x^5 z^3 +
80 a^4 b^12 c^2 x^5 z^3 + 16 a^3 b^13 c^2 x^5 z^3 -
48 a^2 b^14 c^2 x^5 z^3 + 16 a b^15 c^2 x^5 z^3 -
112 a^7 b^8 c^3 x^5 z^3 + 256 a^6 b^9 c^3 x^5 z^3 +
16 a^5 b^10 c^3 x^5 z^3 - 384 a^4 b^11 c^3 x^5 z^3 +
176 a^3 b^12 c^3 x^5 z^3 + 128 a^2 b^13 c^3 x^5 z^3 -
80 a b^14 c^3 x^5 z^3 - 48 a^6 b^8 c^4 x^5 z^3 +
208 a^5 b^9 c^4 x^5 z^3 + 32 a^4 b^10 c^4 x^5 z^3 -
352 a^3 b^11 c^4 x^5 z^3 + 16 a^2 b^12 c^4 x^5 z^3 +
144 a b^13 c^4 x^5 z^3 + 1136 a^5 b^8 c^5 x^5 z^3 +
768 a^4 b^9 c^5 x^5 z^3 - 416 a^3 b^10 c^5 x^5 z^3 -
384 a^2 b^11 c^5 x^5 z^3 - 80 a b^12 c^5 x^5 z^3 -
496 a^4 b^8 c^6 x^5 z^3 + 1104 a^3 b^9 c^6 x^5 z^3 +
496 a^2 b^10 c^6 x^5 z^3 - 80 a b^11 c^6 x^5 z^3 -
528 a^3 b^8 c^7 x^5 z^3 - 256 a^2 b^9 c^7 x^5 z^3 +
144 a b^10 c^7 x^5 z^3 + 48 a^2 b^8 c^8 x^5 z^3 -
80 a b^9 c^8 x^5 z^3 + 16 a b^8 c^9 x^5 z^3 -
12 a^10 b^6 c^2 x^4 y z^3 + 8 a^9 b^7 c^2 x^4 y z^3 +
68 a^8 b^8 c^2 x^4 y z^3 - 80 a^7 b^9 c^2 x^4 y z^3 -
72 a^6 b^10 c^2 x^4 y z^3 + 128 a^5 b^11 c^2 x^4 y z^3 -
8 a^4 b^12 c^2 x^4 y z^3 - 48 a^3 b^13 c^2 x^4 y z^3 +
20 a^2 b^14 c^2 x^4 y z^3 - 8 a b^15 c^2 x^4 y z^3 +
4 b^16 c^2 x^4 y z^3 - 24 a^9 b^6 c^3 x^4 y z^3 -
120 a^8 b^7 c^3 x^4 y z^3 + 368 a^7 b^8 c^3 x^4 y z^3 -
512 a^5 b^10 c^3 x^4 y z^3 + 208 a^4 b^11 c^3 x^4 y z^3 +
144 a^3 b^12 c^3 x^4 y z^3 - 64 a^2 b^13 c^3 x^4 y z^3 +
24 a b^14 c^3 x^4 y z^3 - 24 b^15 c^3 x^4 y z^3 -
316 a^8 b^6 c^4 x^4 y z^3 + 1072 a^7 b^7 c^4 x^4 y z^3 +
144 a^6 b^8 c^4 x^4 y z^3 - 1536 a^5 b^9 c^4 x^4 y z^3 +
136 a^4 b^10 c^4 x^4 y z^3 + 432 a^3 b^11 c^4 x^4 y z^3 -
16 a^2 b^12 c^4 x^4 y z^3 + 32 a b^13 c^4 x^4 y z^3 +
52 b^14 c^4 x^4 y z^3 - 208 a^7 b^6 c^5 x^4 y z^3 +
3136 a^6 b^7 c^5 x^4 y z^3 + 5376 a^5 b^8 c^5 x^4 y z^3 -
1824 a^4 b^9 c^5 x^4 y z^3 - 1232 a^3 b^10 c^5 x^4 y z^3 +
128 a^2 b^11 c^5 x^4 y z^3 - 224 a b^12 c^5 x^4 y z^3 -
32 b^13 c^5 x^4 y z^3 + 1912 a^6 b^6 c^6 x^4 y z^3 +
4480 a^5 b^7 c^6 x^4 y z^3 + 904 a^4 b^8 c^6 x^4 y z^3 +
432 a^3 b^9 c^6 x^4 y z^3 + 184 a^2 b^10 c^6 x^4 y z^3 +
336 a b^11 c^6 x^4 y z^3 - 56 b^12 c^6 x^4 y z^3 +
256 a^5 b^6 c^7 x^4 y z^3 + 2128 a^4 b^7 c^7 x^4 y z^3 +
624 a^3 b^8 c^7 x^4 y z^3 - 576 a^2 b^9 c^7 x^4 y z^3 -
112 a b^10 c^7 x^4 y z^3 + 112 b^11 c^7 x^4 y z^3 -
1544 a^4 b^6 c^8 x^4 y z^3 - 304 a^3 b^7 c^8 x^4 y z^3 +
368 a^2 b^8 c^8 x^4 y z^3 - 224 a b^9 c^8 x^4 y z^3 -
56 b^10 c^8 x^4 y z^3 - 48 a^3 b^6 c^9 x^4 y z^3 +
288 a b^8 c^9 x^4 y z^3 - 32 b^9 c^9 x^4 y z^3 -
44 a^2 b^6 c^10 x^4 y z^3 - 136 a b^7 c^10 x^4 y z^3 +
52 b^8 c^10 x^4 y z^3 + 24 a b^6 c^11 x^4 y z^3 -
24 b^7 c^11 x^4 y z^3 + 4 b^6 c^12 x^4 y z^3 +
28 a^12 b^4 c^2 x^3 y^2 z^3 - 136 a^11 b^5 c^2 x^3 y^2 z^3 +
204 a^10 b^6 c^2 x^3 y^2 z^3 - 296 a^8 b^8 c^2 x^3 y^2 z^3 +
304 a^7 b^9 c^2 x^3 y^2 z^3 - 104 a^6 b^10 c^2 x^3 y^2 z^3 -
64 a^5 b^11 c^2 x^3 y^2 z^3 + 140 a^4 b^12 c^2 x^3 y^2 z^3 -
104 a^3 b^13 c^2 x^3 y^2 z^3 + 28 a^2 b^14 c^2 x^3 y^2 z^3 +
8 a^11 b^4 c^3 x^3 y^2 z^3 - 216 a^10 b^5 c^3 x^3 y^2 z^3 +
624 a^9 b^6 c^3 x^3 y^2 z^3 - 592 a^8 b^7 c^3 x^3 y^2 z^3 -
64 a^7 b^8 c^3 x^3 y^2 z^3 + 704 a^6 b^9 c^3 x^3 y^2 z^3 -
752 a^5 b^10 c^3 x^3 y^2 z^3 + 208 a^4 b^11 c^3 x^3 y^2 z^3 +
184 a^3 b^12 c^3 x^3 y^2 z^3 - 104 a^2 b^13 c^3 x^3 y^2 z^3 +
844 a^10 b^4 c^4 x^3 y^2 z^3 - 1008 a^9 b^5 c^4 x^3 y^2 z^3 -
848 a^8 b^6 c^4 x^3 y^2 z^3 + 2736 a^7 b^7 c^4 x^3 y^2 z^3 -
1208 a^6 b^8 c^4 x^3 y^2 z^3 - 1936 a^5 b^9 c^4 x^3 y^2 z^3 +
1072 a^4 b^10 c^4 x^3 y^2 z^3 + 208 a^3 b^11 c^4 x^3 y^2 z^3 +
140 a^2 b^12 c^4 x^3 y^2 z^3 - 608 a^9 b^4 c^5 x^3 y^2 z^3 -
464 a^8 b^5 c^5 x^3 y^2 z^3 + 4496 a^7 b^6 c^5 x^3 y^2 z^3 +
6560 a^6 b^7 c^5 x^3 y^2 z^3 + 3008 a^5 b^8 c^5 x^3 y^2 z^3 -
1936 a^4 b^9 c^5 x^3 y^2 z^3 - 752 a^3 b^10 c^5 x^3 y^2 z^3 -
64 a^2 b^11 c^5 x^3 y^2 z^3 - 872 a^8 b^4 c^6 x^3 y^2 z^3 +
1824 a^7 b^5 c^6 x^3 y^2 z^3 + 12552 a^6 b^6 c^6 x^3 y^2 z^3 +
6560 a^5 b^7 c^6 x^3 y^2 z^3 - 1208 a^4 b^8 c^6 x^3 y^2 z^3 +
704 a^3 b^9 c^6 x^3 y^2 z^3 - 104 a^2 b^10 c^6 x^3 y^2 z^3 +
1200 a^7 b^4 c^7 x^3 y^2 z^3 + 1824 a^6 b^5 c^7 x^3 y^2 z^3 +
4496 a^5 b^6 c^7 x^3 y^2 z^3 + 2736 a^4 b^7 c^7 x^3 y^2 z^3 -
64 a^3 b^8 c^7 x^3 y^2 z^3 + 304 a^2 b^9 c^7 x^3 y^2 z^3 -
872 a^6 b^4 c^8 x^3 y^2 z^3 - 464 a^5 b^5 c^8 x^3 y^2 z^3 -
848 a^4 b^6 c^8 x^3 y^2 z^3 - 592 a^3 b^7 c^8 x^3 y^2 z^3 -
296 a^2 b^8 c^8 x^3 y^2 z^3 - 608 a^5 b^4 c^9 x^3 y^2 z^3 -
1008 a^4 b^5 c^9 x^3 y^2 z^3 + 624 a^3 b^6 c^9 x^3 y^2 z^3 +
844 a^4 b^4 c^10 x^3 y^2 z^3 - 216 a^3 b^5 c^10 x^3 y^2 z^3 +
204 a^2 b^6 c^10 x^3 y^2 z^3 + 8 a^3 b^4 c^11 x^3 y^2 z^3 -
136 a^2 b^5 c^11 x^3 y^2 z^3 + 28 a^2 b^4 c^12 x^3 y^2 z^3 +
28 a^14 b^2 c^2 x^2 y^3 z^3 - 104 a^13 b^3 c^2 x^2 y^3 z^3 +
140 a^12 b^4 c^2 x^2 y^3 z^3 - 64 a^11 b^5 c^2 x^2 y^3 z^3 -
104 a^10 b^6 c^2 x^2 y^3 z^3 + 304 a^9 b^7 c^2 x^2 y^3 z^3 -
296 a^8 b^8 c^2 x^2 y^3 z^3 + 204 a^6 b^10 c^2 x^2 y^3 z^3 -
136 a^5 b^11 c^2 x^2 y^3 z^3 + 28 a^4 b^12 c^2 x^2 y^3 z^3 -
104 a^13 b^2 c^3 x^2 y^3 z^3 + 184 a^12 b^3 c^3 x^2 y^3 z^3 +
208 a^11 b^4 c^3 x^2 y^3 z^3 - 752 a^10 b^5 c^3 x^2 y^3 z^3 +
704 a^9 b^6 c^3 x^2 y^3 z^3 - 64 a^8 b^7 c^3 x^2 y^3 z^3 -
592 a^7 b^8 c^3 x^2 y^3 z^3 + 624 a^6 b^9 c^3 x^2 y^3 z^3 -
216 a^5 b^10 c^3 x^2 y^3 z^3 + 8 a^4 b^11 c^3 x^2 y^3 z^3 +
140 a^12 b^2 c^4 x^2 y^3 z^3 + 208 a^11 b^3 c^4 x^2 y^3 z^3 +
1072 a^10 b^4 c^4 x^2 y^3 z^3 - 1936 a^9 b^5 c^4 x^2 y^3 z^3 -
1208 a^8 b^6 c^4 x^2 y^3 z^3 + 2736 a^7 b^7 c^4 x^2 y^3 z^3 -
848 a^6 b^8 c^4 x^2 y^3 z^3 - 1008 a^5 b^9 c^4 x^2 y^3 z^3 +
844 a^4 b^10 c^4 x^2 y^3 z^3 - 64 a^11 b^2 c^5 x^2 y^3 z^3 -
752 a^10 b^3 c^5 x^2 y^3 z^3 - 1936 a^9 b^4 c^5 x^2 y^3 z^3 +
3008 a^8 b^5 c^5 x^2 y^3 z^3 + 6560 a^7 b^6 c^5 x^2 y^3 z^3 +
4496 a^6 b^7 c^5 x^2 y^3 z^3 - 464 a^5 b^8 c^5 x^2 y^3 z^3 -
608 a^4 b^9 c^5 x^2 y^3 z^3 - 104 a^10 b^2 c^6 x^2 y^3 z^3 +
704 a^9 b^3 c^6 x^2 y^3 z^3 - 1208 a^8 b^4 c^6 x^2 y^3 z^3 +
6560 a^7 b^5 c^6 x^2 y^3 z^3 + 12552 a^6 b^6 c^6 x^2 y^3 z^3 +
1824 a^5 b^7 c^6 x^2 y^3 z^3 - 872 a^4 b^8 c^6 x^2 y^3 z^3 +
304 a^9 b^2 c^7 x^2 y^3 z^3 - 64 a^8 b^3 c^7 x^2 y^3 z^3 +
2736 a^7 b^4 c^7 x^2 y^3 z^3 + 4496 a^6 b^5 c^7 x^2 y^3 z^3 +
1824 a^5 b^6 c^7 x^2 y^3 z^3 + 1200 a^4 b^7 c^7 x^2 y^3 z^3 -
296 a^8 b^2 c^8 x^2 y^3 z^3 - 592 a^7 b^3 c^8 x^2 y^3 z^3 -
848 a^6 b^4 c^8 x^2 y^3 z^3 - 464 a^5 b^5 c^8 x^2 y^3 z^3 -
872 a^4 b^6 c^8 x^2 y^3 z^3 + 624 a^6 b^3 c^9 x^2 y^3 z^3 -
1008 a^5 b^4 c^9 x^2 y^3 z^3 - 608 a^4 b^5 c^9 x^2 y^3 z^3 +
204 a^6 b^2 c^10 x^2 y^3 z^3 - 216 a^5 b^3 c^10 x^2 y^3 z^3 +
844 a^4 b^4 c^10 x^2 y^3 z^3 - 136 a^5 b^2 c^11 x^2 y^3 z^3 +
8 a^4 b^3 c^11 x^2 y^3 z^3 + 28 a^4 b^2 c^12 x^2 y^3 z^3 +
4 a^16 c^2 x y^4 z^3 - 8 a^15 b c^2 x y^4 z^3 +
20 a^14 b^2 c^2 x y^4 z^3 - 48 a^13 b^3 c^2 x y^4 z^3 -
8 a^12 b^4 c^2 x y^4 z^3 + 128 a^11 b^5 c^2 x y^4 z^3 -
72 a^10 b^6 c^2 x y^4 z^3 - 80 a^9 b^7 c^2 x y^4 z^3 +
68 a^8 b^8 c^2 x y^4 z^3 + 8 a^7 b^9 c^2 x y^4 z^3 -
12 a^6 b^10 c^2 x y^4 z^3 - 24 a^15 c^3 x y^4 z^3 +
24 a^14 b c^3 x y^4 z^3 - 64 a^13 b^2 c^3 x y^4 z^3 +
144 a^12 b^3 c^3 x y^4 z^3 + 208 a^11 b^4 c^3 x y^4 z^3 -
512 a^10 b^5 c^3 x y^4 z^3 + 368 a^8 b^7 c^3 x y^4 z^3 -
120 a^7 b^8 c^3 x y^4 z^3 - 24 a^6 b^9 c^3 x y^4 z^3 +
52 a^14 c^4 x y^4 z^3 + 32 a^13 b c^4 x y^4 z^3 -
16 a^12 b^2 c^4 x y^4 z^3 + 432 a^11 b^3 c^4 x y^4 z^3 +
136 a^10 b^4 c^4 x y^4 z^3 - 1536 a^9 b^5 c^4 x y^4 z^3 +
144 a^8 b^6 c^4 x y^4 z^3 + 1072 a^7 b^7 c^4 x y^4 z^3 -
316 a^6 b^8 c^4 x y^4 z^3 - 32 a^13 c^5 x y^4 z^3 -
224 a^12 b c^5 x y^4 z^3 + 128 a^11 b^2 c^5 x y^4 z^3 -
1232 a^10 b^3 c^5 x y^4 z^3 - 1824 a^9 b^4 c^5 x y^4 z^3 +
5376 a^8 b^5 c^5 x y^4 z^3 + 3136 a^7 b^6 c^5 x y^4 z^3 -
208 a^6 b^7 c^5 x y^4 z^3 - 56 a^12 c^6 x y^4 z^3 +
336 a^11 b c^6 x y^4 z^3 + 184 a^10 b^2 c^6 x y^4 z^3 +
432 a^9 b^3 c^6 x y^4 z^3 + 904 a^8 b^4 c^6 x y^4 z^3 +
4480 a^7 b^5 c^6 x y^4 z^3 + 1912 a^6 b^6 c^6 x y^4 z^3 +
112 a^11 c^7 x y^4 z^3 - 112 a^10 b c^7 x y^4 z^3 -
576 a^9 b^2 c^7 x y^4 z^3 + 624 a^8 b^3 c^7 x y^4 z^3 +
2128 a^7 b^4 c^7 x y^4 z^3 + 256 a^6 b^5 c^7 x y^4 z^3 -
56 a^10 c^8 x y^4 z^3 - 224 a^9 b c^8 x y^4 z^3 +
368 a^8 b^2 c^8 x y^4 z^3 - 304 a^7 b^3 c^8 x y^4 z^3 -
1544 a^6 b^4 c^8 x y^4 z^3 - 32 a^9 c^9 x y^4 z^3 +
288 a^8 b c^9 x y^4 z^3 - 48 a^6 b^3 c^9 x y^4 z^3 +
52 a^8 c^10 x y^4 z^3 - 136 a^7 b c^10 x y^4 z^3 -
44 a^6 b^2 c^10 x y^4 z^3 - 24 a^7 c^11 x y^4 z^3 +
24 a^6 b c^11 x y^4 z^3 + 4 a^6 c^12 x y^4 z^3 +
16 a^15 b c^2 y^5 z^3 - 48 a^14 b^2 c^2 y^5 z^3 +
16 a^13 b^3 c^2 y^5 z^3 + 80 a^12 b^4 c^2 y^5 z^3 -
80 a^11 b^5 c^2 y^5 z^3 - 16 a^10 b^6 c^2 y^5 z^3 +
48 a^9 b^7 c^2 y^5 z^3 - 16 a^8 b^8 c^2 y^5 z^3 -
80 a^14 b c^3 y^5 z^3 + 128 a^13 b^2 c^3 y^5 z^3 +
176 a^12 b^3 c^3 y^5 z^3 - 384 a^11 b^4 c^3 y^5 z^3 +
16 a^10 b^5 c^3 y^5 z^3 + 256 a^9 b^6 c^3 y^5 z^3 -
112 a^8 b^7 c^3 y^5 z^3 + 144 a^13 b c^4 y^5 z^3 +
16 a^12 b^2 c^4 y^5 z^3 - 352 a^11 b^3 c^4 y^5 z^3 +
32 a^10 b^4 c^4 y^5 z^3 + 208 a^9 b^5 c^4 y^5 z^3 -
48 a^8 b^6 c^4 y^5 z^3 - 80 a^12 b c^5 y^5 z^3 -
384 a^11 b^2 c^5 y^5 z^3 - 416 a^10 b^3 c^5 y^5 z^3 +
768 a^9 b^4 c^5 y^5 z^3 + 1136 a^8 b^5 c^5 y^5 z^3 -
80 a^11 b c^6 y^5 z^3 + 496 a^10 b^2 c^6 y^5 z^3 +
1104 a^9 b^3 c^6 y^5 z^3 - 496 a^8 b^4 c^6 y^5 z^3 +
144 a^10 b c^7 y^5 z^3 - 256 a^9 b^2 c^7 y^5 z^3 -
528 a^8 b^3 c^7 y^5 z^3 - 80 a^9 b c^8 y^5 z^3 +
48 a^8 b^2 c^8 y^5 z^3 + 16 a^8 b c^9 y^5 z^3 + a^10 b^8 x^4 z^4 -
6 a^9 b^9 x^4 z^4 + 13 a^8 b^10 x^4 z^4 - 8 a^7 b^11 x^4 z^4 -
14 a^6 b^12 x^4 z^4 + 28 a^5 b^13 x^4 z^4 - 14 a^4 b^14 x^4 z^4 -
8 a^3 b^15 x^4 z^4 + 13 a^2 b^16 x^4 z^4 - 6 a b^17 x^4 z^4 +
b^18 x^4 z^4 + 10 a^9 b^8 c x^4 z^4 - 54 a^8 b^9 c x^4 z^4 +
104 a^7 b^10 c x^4 z^4 - 56 a^6 b^11 c x^4 z^4 -
84 a^5 b^12 c x^4 z^4 + 140 a^4 b^13 c x^4 z^4 -
56 a^3 b^14 c x^4 z^4 - 24 a^2 b^15 c x^4 z^4 +
26 a b^16 c x^4 z^4 - 6 b^17 c x^4 z^4 - 19 a^8 b^8 c^2 x^4 z^4 +
8 a^7 b^9 c^2 x^4 z^4 + 140 a^6 b^10 c^2 x^4 z^4 -
232 a^5 b^11 c^2 x^4 z^4 + 46 a^4 b^12 c^2 x^4 z^4 +
120 a^3 b^13 c^2 x^4 z^4 - 52 a^2 b^14 c^2 x^4 z^4 -
24 a b^15 c^2 x^4 z^4 + 13 b^16 c^2 x^4 z^4 -
392 a^7 b^8 c^3 x^4 z^4 + 872 a^6 b^9 c^3 x^4 z^4 -
168 a^5 b^10 c^3 x^4 z^4 - 728 a^4 b^11 c^3 x^4 z^4 +
360 a^3 b^12 c^3 x^4 z^4 + 120 a^2 b^13 c^3 x^4 z^4 -
56 a b^14 c^3 x^4 z^4 - 8 b^15 c^3 x^4 z^4 -
494 a^6 b^8 c^4 x^4 z^4 + 716 a^5 b^9 c^4 x^4 z^4 +
334 a^4 b^10 c^4 x^4 z^4 - 728 a^3 b^11 c^4 x^4 z^4 +
46 a^2 b^12 c^4 x^4 z^4 + 140 a b^13 c^4 x^4 z^4 -
14 b^14 c^4 x^4 z^4 + 1788 a^5 b^8 c^5 x^4 z^4 +
716 a^4 b^9 c^5 x^4 z^4 - 168 a^3 b^10 c^5 x^4 z^4 -
232 a^2 b^11 c^5 x^4 z^4 - 84 a b^12 c^5 x^4 z^4 +
28 b^13 c^5 x^4 z^4 - 494 a^4 b^8 c^6 x^4 z^4 +
872 a^3 b^9 c^6 x^4 z^4 + 140 a^2 b^10 c^6 x^4 z^4 -
56 a b^11 c^6 x^4 z^4 - 14 b^12 c^6 x^4 z^4 -
392 a^3 b^8 c^7 x^4 z^4 + 8 a^2 b^9 c^7 x^4 z^4 +
104 a b^10 c^7 x^4 z^4 - 8 b^11 c^7 x^4 z^4 -
19 a^2 b^8 c^8 x^4 z^4 - 54 a b^9 c^8 x^4 z^4 +
13 b^10 c^8 x^4 z^4 + 10 a b^8 c^9 x^4 z^4 - 6 b^9 c^9 x^4 z^4 +
b^8 c^10 x^4 z^4 + 4 a^12 b^6 x^3 y z^4 - 24 a^11 b^7 x^3 y z^4 +
52 a^10 b^8 x^3 y z^4 - 32 a^9 b^9 x^3 y z^4 -
56 a^8 b^10 x^3 y z^4 + 112 a^7 b^11 x^3 y z^4 -
56 a^6 b^12 x^3 y z^4 - 32 a^5 b^13 x^3 y z^4 +
52 a^4 b^14 x^3 y z^4 - 24 a^3 b^15 x^3 y z^4 +
4 a^2 b^16 x^3 y z^4 + 24 a^11 b^6 c x^3 y z^4 -
136 a^10 b^7 c x^3 y z^4 + 288 a^9 b^8 c x^3 y z^4 -
224 a^8 b^9 c x^3 y z^4 - 112 a^7 b^10 c x^3 y z^4 +
336 a^6 b^11 c x^3 y z^4 - 224 a^5 b^12 c x^3 y z^4 +
32 a^4 b^13 c x^3 y z^4 + 24 a^3 b^14 c x^3 y z^4 -
8 a^2 b^15 c x^3 y z^4 - 44 a^10 b^6 c^2 x^3 y z^4 +
368 a^8 b^8 c^2 x^3 y z^4 - 576 a^7 b^9 c^2 x^3 y z^4 +
184 a^6 b^10 c^2 x^3 y z^4 + 128 a^5 b^11 c^2 x^3 y z^4 -
16 a^4 b^12 c^2 x^3 y z^4 - 64 a^3 b^13 c^2 x^3 y z^4 +
20 a^2 b^14 c^2 x^3 y z^4 - 48 a^9 b^6 c^3 x^3 y z^4 -
304 a^8 b^7 c^3 x^3 y z^4 + 624 a^7 b^8 c^3 x^3 y z^4 +
432 a^6 b^9 c^3 x^3 y z^4 - 1232 a^5 b^10 c^3 x^3 y z^4 +
432 a^4 b^11 c^3 x^3 y z^4 + 144 a^3 b^12 c^3 x^3 y z^4 -
48 a^2 b^13 c^3 x^3 y z^4 - 1544 a^8 b^6 c^4 x^3 y z^4 +
2128 a^7 b^7 c^4 x^3 y z^4 + 904 a^6 b^8 c^4 x^3 y z^4 -
1824 a^5 b^9 c^4 x^3 y z^4 + 136 a^4 b^10 c^4 x^3 y z^4 +
208 a^3 b^11 c^4 x^3 y z^4 - 8 a^2 b^12 c^4 x^3 y z^4 +
256 a^7 b^6 c^5 x^3 y z^4 + 4480 a^6 b^7 c^5 x^3 y z^4 +
5376 a^5 b^8 c^5 x^3 y z^4 - 1536 a^4 b^9 c^5 x^3 y z^4 -
512 a^3 b^10 c^5 x^3 y z^4 + 128 a^2 b^11 c^5 x^3 y z^4 +
1912 a^6 b^6 c^6 x^3 y z^4 + 3136 a^5 b^7 c^6 x^3 y z^4 +
144 a^4 b^8 c^6 x^3 y z^4 - 72 a^2 b^10 c^6 x^3 y z^4 -
208 a^5 b^6 c^7 x^3 y z^4 + 1072 a^4 b^7 c^7 x^3 y z^4 +
368 a^3 b^8 c^7 x^3 y z^4 - 80 a^2 b^9 c^7 x^3 y z^4 -
316 a^4 b^6 c^8 x^3 y z^4 - 120 a^3 b^7 c^8 x^3 y z^4 +
68 a^2 b^8 c^8 x^3 y z^4 - 24 a^3 b^6 c^9 x^3 y z^4 +
8 a^2 b^7 c^9 x^3 y z^4 - 12 a^2 b^6 c^10 x^3 y z^4 +
6 a^14 b^4 x^2 y^2 z^4 - 36 a^13 b^5 x^2 y^2 z^4 +
78 a^12 b^6 x^2 y^2 z^4 - 48 a^11 b^7 x^2 y^2 z^4 -
84 a^10 b^8 x^2 y^2 z^4 + 168 a^9 b^9 x^2 y^2 z^4 -
84 a^8 b^10 x^2 y^2 z^4 - 48 a^7 b^11 x^2 y^2 z^4 +
78 a^6 b^12 x^2 y^2 z^4 - 36 a^5 b^13 x^2 y^2 z^4 +
6 a^4 b^14 x^2 y^2 z^4 + 12 a^13 b^4 c x^2 y^2 z^4 -
84 a^12 b^5 c x^2 y^2 z^4 + 240 a^11 b^6 c x^2 y^2 z^4 -
336 a^10 b^7 c x^2 y^2 z^4 + 168 a^9 b^8 c x^2 y^2 z^4 +
168 a^8 b^9 c x^2 y^2 z^4 - 336 a^7 b^10 c x^2 y^2 z^4 +
240 a^6 b^11 c x^2 y^2 z^4 - 84 a^5 b^12 c x^2 y^2 z^4 +
12 a^4 b^13 c x^2 y^2 z^4 - 18 a^12 b^4 c^2 x^2 y^2 z^4 -
48 a^11 b^5 c^2 x^2 y^2 z^4 + 264 a^10 b^6 c^2 x^2 y^2 z^4 -
336 a^9 b^7 c^2 x^2 y^2 z^4 + 276 a^8 b^8 c^2 x^2 y^2 z^4 -
336 a^7 b^9 c^2 x^2 y^2 z^4 + 264 a^6 b^10 c^2 x^2 y^2 z^4 -
48 a^5 b^11 c^2 x^2 y^2 z^4 - 18 a^4 b^12 c^2 x^2 y^2 z^4 +
304 a^11 b^4 c^3 x^2 y^2 z^4 - 976 a^10 b^5 c^3 x^2 y^2 z^4 +
1104 a^9 b^6 c^3 x^2 y^2 z^4 - 432 a^8 b^7 c^3 x^2 y^2 z^4 -
432 a^7 b^8 c^3 x^2 y^2 z^4 + 1104 a^6 b^9 c^3 x^2 y^2 z^4 -
976 a^5 b^10 c^3 x^2 y^2 z^4 + 304 a^4 b^11 c^3 x^2 y^2 z^4 +
492 a^10 b^4 c^4 x^2 y^2 z^4 - 1592 a^9 b^5 c^4 x^2 y^2 z^4 -
876 a^8 b^6 c^4 x^2 y^2 z^4 + 3952 a^7 b^7 c^4 x^2 y^2 z^4 -
876 a^6 b^8 c^4 x^2 y^2 z^4 - 1592 a^5 b^9 c^4 x^2 y^2 z^4 +
492 a^4 b^10 c^4 x^2 y^2 z^4 - 664 a^9 b^4 c^5 x^2 y^2 z^4 +
1032 a^8 b^5 c^5 x^2 y^2 z^4 + 5776 a^7 b^6 c^5 x^2 y^2 z^4 +
5776 a^6 b^7 c^5 x^2 y^2 z^4 + 1032 a^5 b^8 c^5 x^2 y^2 z^4 -
664 a^4 b^9 c^5 x^2 y^2 z^4 - 916 a^8 b^4 c^6 x^2 y^2 z^4 +
1552 a^7 b^5 c^6 x^2 y^2 z^4 + 8072 a^6 b^6 c^6 x^2 y^2 z^4 +
1552 a^5 b^7 c^6 x^2 y^2 z^4 - 916 a^4 b^8 c^6 x^2 y^2 z^4 +
624 a^7 b^4 c^7 x^2 y^2 z^4 + 816 a^6 b^5 c^7 x^2 y^2 z^4 +
816 a^5 b^6 c^7 x^2 y^2 z^4 + 624 a^4 b^7 c^7 x^2 y^2 z^4 +
142 a^6 b^4 c^8 x^2 y^2 z^4 - 388 a^5 b^5 c^8 x^2 y^2 z^4 +
142 a^4 b^6 c^8 x^2 y^2 z^4 - 276 a^5 b^4 c^9 x^2 y^2 z^4 -
276 a^4 b^5 c^9 x^2 y^2 z^4 + 294 a^4 b^4 c^10 x^2 y^2 z^4 +
4 a^16 b^2 x y^3 z^4 - 24 a^15 b^3 x y^3 z^4 +
52 a^14 b^4 x y^3 z^4 - 32 a^13 b^5 x y^3 z^4 -
56 a^12 b^6 x y^3 z^4 + 112 a^11 b^7 x y^3 z^4 -
56 a^10 b^8 x y^3 z^4 - 32 a^9 b^9 x y^3 z^4 +
52 a^8 b^10 x y^3 z^4 - 24 a^7 b^11 x y^3 z^4 +
4 a^6 b^12 x y^3 z^4 - 8 a^15 b^2 c x y^3 z^4 +
24 a^14 b^3 c x y^3 z^4 + 32 a^13 b^4 c x y^3 z^4 -
224 a^12 b^5 c x y^3 z^4 + 336 a^11 b^6 c x y^3 z^4 -
112 a^10 b^7 c x y^3 z^4 - 224 a^9 b^8 c x y^3 z^4 +
288 a^8 b^9 c x y^3 z^4 - 136 a^7 b^10 c x y^3 z^4 +
24 a^6 b^11 c x y^3 z^4 + 20 a^14 b^2 c^2 x y^3 z^4 -
64 a^13 b^3 c^2 x y^3 z^4 - 16 a^12 b^4 c^2 x y^3 z^4 +
128 a^11 b^5 c^2 x y^3 z^4 + 184 a^10 b^6 c^2 x y^3 z^4 -
576 a^9 b^7 c^2 x y^3 z^4 + 368 a^8 b^8 c^2 x y^3 z^4 -
44 a^6 b^10 c^2 x y^3 z^4 - 48 a^13 b^2 c^3 x y^3 z^4 +
144 a^12 b^3 c^3 x y^3 z^4 + 432 a^11 b^4 c^3 x y^3 z^4 -
1232 a^10 b^5 c^3 x y^3 z^4 + 432 a^9 b^6 c^3 x y^3 z^4 +
624 a^8 b^7 c^3 x y^3 z^4 - 304 a^7 b^8 c^3 x y^3 z^4 -
48 a^6 b^9 c^3 x y^3 z^4 - 8 a^12 b^2 c^4 x y^3 z^4 +
208 a^11 b^3 c^4 x y^3 z^4 + 136 a^10 b^4 c^4 x y^3 z^4 -
1824 a^9 b^5 c^4 x y^3 z^4 + 904 a^8 b^6 c^4 x y^3 z^4 +
2128 a^7 b^7 c^4 x y^3 z^4 - 1544 a^6 b^8 c^4 x y^3 z^4 +
128 a^11 b^2 c^5 x y^3 z^4 - 512 a^10 b^3 c^5 x y^3 z^4 -
1536 a^9 b^4 c^5 x y^3 z^4 + 5376 a^8 b^5 c^5 x y^3 z^4 +
4480 a^7 b^6 c^5 x y^3 z^4 + 256 a^6 b^7 c^5 x y^3 z^4 -
72 a^10 b^2 c^6 x y^3 z^4 + 144 a^8 b^4 c^6 x y^3 z^4 +
3136 a^7 b^5 c^6 x y^3 z^4 + 1912 a^6 b^6 c^6 x y^3 z^4 -
80 a^9 b^2 c^7 x y^3 z^4 + 368 a^8 b^3 c^7 x y^3 z^4 +
1072 a^7 b^4 c^7 x y^3 z^4 - 208 a^6 b^5 c^7 x y^3 z^4 +
68 a^8 b^2 c^8 x y^3 z^4 - 120 a^7 b^3 c^8 x y^3 z^4 -
316 a^6 b^4 c^8 x y^3 z^4 + 8 a^7 b^2 c^9 x y^3 z^4 -
24 a^6 b^3 c^9 x y^3 z^4 - 12 a^6 b^2 c^10 x y^3 z^4 +
a^18 y^4 z^4 - 6 a^17 b y^4 z^4 + 13 a^16 b^2 y^4 z^4 -
8 a^15 b^3 y^4 z^4 - 14 a^14 b^4 y^4 z^4 + 28 a^13 b^5 y^4 z^4 -
14 a^12 b^6 y^4 z^4 - 8 a^11 b^7 y^4 z^4 + 13 a^10 b^8 y^4 z^4 -
6 a^9 b^9 y^4 z^4 + a^8 b^10 y^4 z^4 - 6 a^17 c y^4 z^4 +
26 a^16 b c y^4 z^4 - 24 a^15 b^2 c y^4 z^4 -
56 a^14 b^3 c y^4 z^4 + 140 a^13 b^4 c y^4 z^4 -
84 a^12 b^5 c y^4 z^4 - 56 a^11 b^6 c y^4 z^4 +
104 a^10 b^7 c y^4 z^4 - 54 a^9 b^8 c y^4 z^4 +
10 a^8 b^9 c y^4 z^4 + 13 a^16 c^2 y^4 z^4 - 24 a^15 b c^2 y^4 z^4 -
52 a^14 b^2 c^2 y^4 z^4 + 120 a^13 b^3 c^2 y^4 z^4 +
46 a^12 b^4 c^2 y^4 z^4 - 232 a^11 b^5 c^2 y^4 z^4 +
140 a^10 b^6 c^2 y^4 z^4 + 8 a^9 b^7 c^2 y^4 z^4 -
19 a^8 b^8 c^2 y^4 z^4 - 8 a^15 c^3 y^4 z^4 -
56 a^14 b c^3 y^4 z^4 + 120 a^13 b^2 c^3 y^4 z^4 +
360 a^12 b^3 c^3 y^4 z^4 - 728 a^11 b^4 c^3 y^4 z^4 -
168 a^10 b^5 c^3 y^4 z^4 + 872 a^9 b^6 c^3 y^4 z^4 -
392 a^8 b^7 c^3 y^4 z^4 - 14 a^14 c^4 y^4 z^4 +
140 a^13 b c^4 y^4 z^4 + 46 a^12 b^2 c^4 y^4 z^4 -
728 a^11 b^3 c^4 y^4 z^4 + 334 a^10 b^4 c^4 y^4 z^4 +
716 a^9 b^5 c^4 y^4 z^4 - 494 a^8 b^6 c^4 y^4 z^4 +
28 a^13 c^5 y^4 z^4 - 84 a^12 b c^5 y^4 z^4 -
232 a^11 b^2 c^5 y^4 z^4 - 168 a^10 b^3 c^5 y^4 z^4 +
716 a^9 b^4 c^5 y^4 z^4 + 1788 a^8 b^5 c^5 y^4 z^4 -
14 a^12 c^6 y^4 z^4 - 56 a^11 b c^6 y^4 z^4 +
140 a^10 b^2 c^6 y^4 z^4 + 872 a^9 b^3 c^6 y^4 z^4 -
494 a^8 b^4 c^6 y^4 z^4 - 8 a^11 c^7 y^4 z^4 +
104 a^10 b c^7 y^4 z^4 + 8 a^9 b^2 c^7 y^4 z^4 -
392 a^8 b^3 c^7 y^4 z^4 + 13 a^10 c^8 y^4 z^4 -
54 a^9 b c^8 y^4 z^4 - 19 a^8 b^2 c^8 y^4 z^4 - 6 a^9 c^9 y^4 z^4 +
10 a^8 b c^9 y^4 z^4 + a^8 c^10 y^4 z^4 + 16 a^9 b^8 c x^3 z^5 -
80 a^8 b^9 c x^3 z^5 + 144 a^7 b^10 c x^3 z^5 -
80 a^6 b^11 c x^3 z^5 - 80 a^5 b^12 c x^3 z^5 +
144 a^4 b^13 c x^3 z^5 - 80 a^3 b^14 c x^3 z^5 +
16 a^2 b^15 c x^3 z^5 + 48 a^8 b^8 c^2 x^3 z^5 -
256 a^7 b^9 c^2 x^3 z^5 + 496 a^6 b^10 c^2 x^3 z^5 -
384 a^5 b^11 c^2 x^3 z^5 + 16 a^4 b^12 c^2 x^3 z^5 +
128 a^3 b^13 c^2 x^3 z^5 - 48 a^2 b^14 c^2 x^3 z^5 -
528 a^7 b^8 c^3 x^3 z^5 + 1104 a^6 b^9 c^3 x^3 z^5 -
416 a^5 b^10 c^3 x^3 z^5 - 352 a^4 b^11 c^3 x^3 z^5 +
176 a^3 b^12 c^3 x^3 z^5 + 16 a^2 b^13 c^3 x^3 z^5 -
496 a^6 b^8 c^4 x^3 z^5 + 768 a^5 b^9 c^4 x^3 z^5 +
32 a^4 b^10 c^4 x^3 z^5 - 384 a^3 b^11 c^4 x^3 z^5 +
80 a^2 b^12 c^4 x^3 z^5 + 1136 a^5 b^8 c^5 x^3 z^5 +
208 a^4 b^9 c^5 x^3 z^5 + 16 a^3 b^10 c^5 x^3 z^5 -
80 a^2 b^11 c^5 x^3 z^5 - 48 a^4 b^8 c^6 x^3 z^5 +
256 a^3 b^9 c^6 x^3 z^5 - 16 a^2 b^10 c^6 x^3 z^5 -
112 a^3 b^8 c^7 x^3 z^5 + 48 a^2 b^9 c^7 x^3 z^5 -
16 a^2 b^8 c^8 x^3 z^5 + 48 a^11 b^6 c x^2 y z^5 -
240 a^10 b^7 c x^2 y z^5 + 432 a^9 b^8 c x^2 y z^5 -
240 a^8 b^9 c x^2 y z^5 - 240 a^7 b^10 c x^2 y z^5 +
432 a^6 b^11 c x^2 y z^5 - 240 a^5 b^12 c x^2 y z^5 +
48 a^4 b^13 c x^2 y z^5 + 48 a^10 b^6 c^2 x^2 y z^5 -
384 a^9 b^7 c^2 x^2 y z^5 + 1008 a^8 b^8 c^2 x^2 y z^5 -
1152 a^7 b^9 c^2 x^2 y z^5 + 528 a^6 b^10 c^2 x^2 y z^5 -
48 a^4 b^12 c^2 x^2 y z^5 - 272 a^9 b^6 c^3 x^2 y z^5 +
80 a^8 b^7 c^3 x^2 y z^5 + 352 a^7 b^8 c^3 x^2 y z^5 +
416 a^6 b^9 c^3 x^2 y z^5 - 848 a^5 b^10 c^3 x^2 y z^5 +
272 a^4 b^11 c^3 x^2 y z^5 - 1552 a^8 b^6 c^4 x^2 y z^5 +
2176 a^7 b^7 c^4 x^2 y z^5 + 352 a^6 b^8 c^4 x^2 y z^5 -
1024 a^5 b^9 c^4 x^2 y z^5 + 48 a^4 b^10 c^4 x^2 y z^5 +
400 a^7 b^6 c^5 x^2 y z^5 + 2480 a^6 b^7 c^5 x^2 y z^5 +
1520 a^5 b^8 c^5 x^2 y z^5 - 560 a^4 b^9 c^5 x^2 y z^5 +
1424 a^6 b^6 c^6 x^2 y z^5 + 768 a^5 b^7 c^6 x^2 y z^5 -
80 a^4 b^8 c^6 x^2 y z^5 - 176 a^5 b^6 c^7 x^2 y z^5 +
240 a^4 b^7 c^7 x^2 y z^5 + 80 a^4 b^6 c^8 x^2 y z^5 +
48 a^13 b^4 c x y^2 z^5 - 240 a^12 b^5 c x y^2 z^5 +
432 a^11 b^6 c x y^2 z^5 - 240 a^10 b^7 c x y^2 z^5 -
240 a^9 b^8 c x y^2 z^5 + 432 a^8 b^9 c x y^2 z^5 -
240 a^7 b^10 c x y^2 z^5 + 48 a^6 b^11 c x y^2 z^5 -
48 a^12 b^4 c^2 x y^2 z^5 + 528 a^10 b^6 c^2 x y^2 z^5 -
1152 a^9 b^7 c^2 x y^2 z^5 + 1008 a^8 b^8 c^2 x y^2 z^5 -
384 a^7 b^9 c^2 x y^2 z^5 + 48 a^6 b^10 c^2 x y^2 z^5 +
272 a^11 b^4 c^3 x y^2 z^5 - 848 a^10 b^5 c^3 x y^2 z^5 +
416 a^9 b^6 c^3 x y^2 z^5 + 352 a^8 b^7 c^3 x y^2 z^5 +
80 a^7 b^8 c^3 x y^2 z^5 - 272 a^6 b^9 c^3 x y^2 z^5 +
48 a^10 b^4 c^4 x y^2 z^5 - 1024 a^9 b^5 c^4 x y^2 z^5 +
352 a^8 b^6 c^4 x y^2 z^5 + 2176 a^7 b^7 c^4 x y^2 z^5 -
1552 a^6 b^8 c^4 x y^2 z^5 - 560 a^9 b^4 c^5 x y^2 z^5 +
1520 a^8 b^5 c^5 x y^2 z^5 + 2480 a^7 b^6 c^5 x y^2 z^5 +
400 a^6 b^7 c^5 x y^2 z^5 - 80 a^8 b^4 c^6 x y^2 z^5 +
768 a^7 b^5 c^6 x y^2 z^5 + 1424 a^6 b^6 c^6 x y^2 z^5 +
240 a^7 b^4 c^7 x y^2 z^5 - 176 a^6 b^5 c^7 x y^2 z^5 +
80 a^6 b^4 c^8 x y^2 z^5 + 16 a^15 b^2 c y^3 z^5 -
80 a^14 b^3 c y^3 z^5 + 144 a^13 b^4 c y^3 z^5 -
80 a^12 b^5 c y^3 z^5 - 80 a^11 b^6 c y^3 z^5 +
144 a^10 b^7 c y^3 z^5 - 80 a^9 b^8 c y^3 z^5 +
16 a^8 b^9 c y^3 z^5 - 48 a^14 b^2 c^2 y^3 z^5 +
128 a^13 b^3 c^2 y^3 z^5 + 16 a^12 b^4 c^2 y^3 z^5 -
384 a^11 b^5 c^2 y^3 z^5 + 496 a^10 b^6 c^2 y^3 z^5 -
256 a^9 b^7 c^2 y^3 z^5 + 48 a^8 b^8 c^2 y^3 z^5 +
16 a^13 b^2 c^3 y^3 z^5 + 176 a^12 b^3 c^3 y^3 z^5 -
352 a^11 b^4 c^3 y^3 z^5 - 416 a^10 b^5 c^3 y^3 z^5 +
1104 a^9 b^6 c^3 y^3 z^5 - 528 a^8 b^7 c^3 y^3 z^5 +
80 a^12 b^2 c^4 y^3 z^5 - 384 a^11 b^3 c^4 y^3 z^5 +
32 a^10 b^4 c^4 y^3 z^5 + 768 a^9 b^5 c^4 y^3 z^5 -
496 a^8 b^6 c^4 y^3 z^5 - 80 a^11 b^2 c^5 y^3 z^5 +
16 a^10 b^3 c^5 y^3 z^5 + 208 a^9 b^4 c^5 y^3 z^5 +
1136 a^8 b^5 c^5 y^3 z^5 - 16 a^10 b^2 c^6 y^3 z^5 +
256 a^9 b^3 c^6 y^3 z^5 - 48 a^8 b^4 c^6 y^3 z^5 +
48 a^9 b^2 c^7 y^3 z^5 - 112 a^8 b^3 c^7 y^3 z^5 -
16 a^8 b^2 c^8 y^3 z^5 + 64 a^8 b^8 c^2 x^2 z^6 -
256 a^7 b^9 c^2 x^2 z^6 + 384 a^6 b^10 c^2 x^2 z^6 -
256 a^5 b^11 c^2 x^2 z^6 + 64 a^4 b^12 c^2 x^2 z^6 -
256 a^7 b^8 c^3 x^2 z^6 + 512 a^6 b^9 c^3 x^2 z^6 -
256 a^5 b^10 c^3 x^2 z^6 - 128 a^6 b^8 c^4 x^2 z^6 +
256 a^5 b^9 c^4 x^2 z^6 - 128 a^4 b^10 c^4 x^2 z^6 +
256 a^5 b^8 c^5 x^2 z^6 + 64 a^4 b^8 c^6 x^2 z^6 +
128 a^10 b^6 c^2 x y z^6 - 512 a^9 b^7 c^2 x y z^6 +
768 a^8 b^8 c^2 x y z^6 - 512 a^7 b^9 c^2 x y z^6 +
128 a^6 b^10 c^2 x y z^6 - 256 a^9 b^6 c^3 x y z^6 +
256 a^8 b^7 c^3 x y z^6 + 256 a^7 b^8 c^3 x y z^6 -
256 a^6 b^9 c^3 x y z^6 - 512 a^8 b^6 c^4 x y z^6 +
1024 a^7 b^7 c^4 x y z^6 - 512 a^6 b^8 c^4 x y z^6 +
256 a^7 b^6 c^5 x y z^6 + 256 a^6 b^7 c^5 x y z^6 +
384 a^6 b^6 c^6 x y z^6 + 64 a^12 b^4 c^2 y^2 z^6 -
256 a^11 b^5 c^2 y^2 z^6 + 384 a^10 b^6 c^2 y^2 z^6 -
256 a^9 b^7 c^2 y^2 z^6 + 64 a^8 b^8 c^2 y^2 z^6 -
256 a^10 b^5 c^3 y^2 z^6 + 512 a^9 b^6 c^3 y^2 z^6 -
256 a^8 b^7 c^3 y^2 z^6 - 128 a^10 b^4 c^4 y^2 z^6 +
256 a^9 b^5 c^4 y^2 z^6 - 128 a^8 b^6 c^4 y^2 z^6 +
256 a^8 b^5 c^5 y^2 z^6 + 64 a^8 b^4 c^6 y^2 z^6

Points on the Locus:

The circumcenter O is on the locus.
The barycentrics of the perspector are:

{a (a^4 - 2 a^2 b^2 + b^4 - a^2 b c + b^3 c - 2 a^2 c^2 - 4 b^2 c^2 + b c^3 + c^4 + 2 a b S - 2 b^2 S + 2 a c S + 4 b c S - 2 c^2 S),
b (a^4 - 2 a^2 b^2 + b^4 + a^3 c - a b^2 c - 4 a^2 c^2 - 2 b^2 c^2 + a c^3 + c^4 - 2 a^2 S + 2 a b S + 4 a c S + 2 b c S - 2 c^2 S),
c (a^4 + a^3 b - 4 a^2 b^2 + a b^3 + b^4 - 2 a^2 c^2 - a b c^2 - 2 b^2 c^2 + c^4 - 2 a^2 S + 4 a b S - 2 b^2 S + 2 a c S +
2 b c S)}

where S is twice the area of ABC, not in ETC, perhaps a simpler form is possible.