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Question: Why solution set is empty.

Question:Why solution set is empty.

Jef7823 15 Maple 2022
solvetools
September 19 2023
2

Hello. I am trying to solve the following polynomial system. Maple solution is empty but when I add the polynomial X4_4-2^(1/2)/10 to the list then maple gives me a set of solutions. What could I be doing wrong?

with(SolveTools):
F:=[
10*X4_4 + Y1_1,
10*X4_4*Y1_1 + 2,
20*X4_4*Y3_1,
2*Y3_1,
10*X4_4*Y1_2,
20*X4_4*Y3_2 + 2,
10*X4_4 + 2*Y3_2,
4*L2 - 7*L1 + 5*L3 - 6*L4 + 5*L5 + 9*L6 - 6*L7 - 1,
L1 + 10*L2*X4_4,
10*L5*X4_4,
2*L4 + 20*L3*X4_4,
2*L7 + 20*L6*X4_4
]:
V:=[X4_4, Y1_1, Y1_2, Y3_1, Y3_2, L1, L2, L3, L4, L5, L6, L7]:

Sols := PolynomialSystem(F, V);
Please Wait...