### Table 2. Elimination lemmas

2004

"... In PAGE 3: ... Note that the de- pendency graph of the constructions must be cycle free. To eliminate a point from the goal we need to apply one of the elimination lem- mas shown on Table2 on page 5. This table can be read as follows: To eliminate a point Y , choose the line corresponding to the way Y has been constructed, and apply the formula given in the column corresponding to the geometric quantity in which Y is used.... In PAGE 4: ... We rst translate the goal (A0B0 k AB) into its equivalent using the signed area: SA0B0A = SA0B0B Then we eliminate compound points from the goal starting by the last point in the order of their construction. The geometric quantities containing an oc- currence of B0 are SA0B0B and SA0B0A, B0 has been constructed using the rst construction on Table2 with = 1 2: SA0B0A = SAA0B0 = 1 2SAA0A + 1 2SAA0C = 1 2SAA0C and SA0B0B = SBA0B0 = 1 2SBA0A + 1 2SBA0C The new goal is SAA0C = SBA0A + SBA0C Now we eliminate A0 using: SCAA0 = 1 2SCAB + 1 2SCAC = 1 2SCAB SABA0 = 1 2SABB + 1 2SABC = 1... In PAGE 11: ... This tactic (called eliminate_all) rst searches the con- text for a point which is not used to build another point (a leaf in the dependency graph). Then for each occurrence of the point in the goal, it applies the right lemma from Table2 by nding in the context how the point has been constructed and which geometric quantity it appears in. Finally it removes the hypotheses stating how the point has been constructed from the context.... In PAGE 12: ...this classical reasoning step. As noted before, the elimination lemmas given in Table2 on page 5, do eliminate an occurrence of a point Y only if Y appears only one time in the geometric quantity (A,B,C and D must be di erent from Y ). If Y appears twice in S, this is not a problem because then the geometric quantity is zero, and so already eliminated by the simpli cation phase.... ..."

Cited by 4

### Table 5. Factorization of the eliminant

1998

"... In PAGE 28: ...his happens in Conjecture 1.1, Theorem 2.3, Theorem 3.9(i) and (iv), and in other cases. Table5 lists the degrees of the factors in the case of Conjecture 1.1.... ..."

Cited by 10

### Table 5. Factorization of the eliminant

1998

"... In PAGE 26: ...he integers. This happens in Conjecture 1.1, Theorem 2.3, Theorem 3.9(i) and (iv), and in other cases. Table5 lists the degrees of the factors in the case of Conjecture 1.1.... ..."

Cited by 10

### Table 5. Factorization of the eliminant

1998

"... In PAGE 28: ...his happens in Conjecture 1.1, Theorem 2.3, Theorem 3.9(i) and (iv), and in other cases. Table5 lists the degrees of the factors in the case of Conjecture 1.1.... ..."

Cited by 10