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Figure 7. Single mass bubble graph.

Figure 7 Single mass bubble graph.

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Figure 1. Polytope of b(z) = 14 2, + z2 + cz, 22. Written as intersection of half planes, we have Ay = {a1 > 0} N {a2 > OF} N { 01 => inf 02> 1}. Let us now review the concept of a coamoeba of a variety. Consider the ideal J generated by some polynomials f;,..., f; C C[z1,...,2n]. The zero set of the ideal J = (fi,..., fj) defines the algebraic variety
Figure 1. Polytope of b(z) = 14 2, + z2 + cz, 22. Written as intersection of half planes, we have Ay = {a1 > 0} N {a2 > OF} N { 01 => inf 02> 1}. Let us now review the concept of a coamoeba of a variety. Consider the ideal J generated by some polynomials f;,..., f; C C[z1,...,2n]. The zero set of the ideal J = (fi,..., fj) defines the algebraic variety
Figure 2. Coamoeba (shaded) of b = 1+ 222 + 2123 + 2725 + caz7z drawn in the fundamental domain [—7,7] x [—7,7] of T? in R?. This case corresponds to c = (1,1,1,1,c4), with cy near 1. Here, we have three connected components, one of which contains (0,0) (center of the figure).
Figure 2. Coamoeba (shaded) of b = 1+ 222 + 2123 + 2725 + caz7z drawn in the fundamental domain [—7,7] x [—7,7] of T? in R?. This case corresponds to c = (1,1,1,1,c4), with cy near 1. Here, we have three connected components, one of which contains (0,0) (center of the figure).
Figure 3. A connected component of the coamoeba(shaded) of b(z) = 1+ 21 + zg + cz122 drawn it the fundamental domain [—7,7] x [—7,7] of T? in R?. The coefficient ¢ is near 1.
Figure 3. A connected component of the coamoeba(shaded) of b(z) = 1+ 21 + zg + cz122 drawn it the fundamental domain [—7,7] x [—7,7] of T? in R?. The coefficient ¢ is near 1.
along with its toric version I,(«). The vector « has the form
along with its toric version I,(«). The vector « has the form
Figure 6. Massless cantaloupe graph. 3.3.3. The massless L-loop cantaloupe graph
Figure 6. Massless cantaloupe graph. 3.3.3. The massless L-loop cantaloupe graph
The roots can be written as
The roots can be written as
Figure 10. On shell massless box. Let us consider the more general problem which lead to the roots
Figure 10. On shell massless box. Let us consider the more general problem which lead to the roots
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