# 2021.12.16
# AmirHosein Sadeghimanesh
# 
# The goal is to apply Lemma 5.2 of the superlevel set paper to conclude
# that with probability one, the rectangle [2, 2.5] * [2.5, 3] in Figure
# 3c of the Kac-Rice paper (the arXiv version) which has average number
# of solutions equal to 2 is not a rectangle that almost all of it is
# inside the region with 2 solutions, but instead has non-zero measure 
# intersections with regions of different number of solutions.
#
# The first step is to generate the example using 
# MCKR generate example 
#
Task: MCKR generate example
Save_location: ./
Save_name: File_20211216_testing_Lemma_5_2_output_1
Example_name: Kac_Rice_Example_2_3_normal
Number_of_variables: 1
Number_of_parameters: 2
Determinant_expression: 100*(5*x1^4+4*(-k2-9/2)*x1^3+3*((9*k2)/2+21/4)*x1^2+2*(-(23*k2)/4+3/8)*x1+(15*k2)/8-23/8)
g_expression: 25/4-100*x1^5+100*x1^4*k2+450*x1^4-450*x1^3*k2-525*x1^3+575*x1^2*k2-75/2*x1^2-375/2*k2*x1+575/2*x1
summand_expression: s(x1,k2,B)+s(1/x1,k2,B)/x1^2
Distribution: Normal
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