1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
|
levelSet1= {x | f(x) <= 1} with f=
[x,y]->[x^4 + y^4]
levelSet1 contains [-0.5, -0.5] ? True
levelSet1 contains [0.5, 0.0] ? True
levelSet1 contains [1.5, 0.0] ? False
levelSet2= {x | f(x) <= 1} with f=
[x,y]->[(x-1)^2 + y^2]
levelSet2 contains [-0.5, -0.5] ? False
levelSet2 contains [0.5, 0.0] ? True
levelSet2 contains [1.5, 0.0] ? True
intersection of {x | f(x) <= 1} with f=
[x,y]->[x^4 + y^4] and {x | f(x) <= 1} with f=
[x,y]->[(x-1)^2 + y^2] equals {x | f(x) <= 0} with f=
[x,y]->[x^4 + y^4] <= 1 and [x,y]->[(x-1)^2 + y^2] <= 1
intersection contains [-0.5, -0.5] ? False
intersection contains [0.5, 0.0] ? True
intersection contains [1.5, 0.0] ? False
join of {x | f(x) <= 1} with f=
[x,y]->[x^4 + y^4] and {x | f(x) <= 1} with f=
[x,y]->[(x-1)^2 + y^2] equals {x | f(x) <= 0} with f=
[x,y]->[x^4 + y^4] <= 1 or [x,y]->[(x-1)^2 + y^2] <= 1
join contains [-0.5, -0.5] ? True
join contains [0.5, 0.0] ? True
join contains [1.5, 0.0] ? True
union x3 {x | f(x) < 0} with f=
[x]->[x] < 0 or [x]->[x+1] < 0 or [x]->[x+2] < 0
intersection 3x {x | f(x) < 0} with f=
[x]->[x] < 0 and [x]->[x+1] < 0 and [x]->[x+2] < 0
|
