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
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
|
restart
debug needsPackage "NumericalAlgebraicGeometry"
load "quadratic_tp_experiment.m2"
needs "example_2d.m2"
setRandomSeed 1
R = CC[x,y]
S = CC[x,y,t]
(d1,d2) = (3,3)
f = {sub(randomPolynomial(d1, RR[gens R]), R), sub(randomPolynomial(d2, RR[gens R]),R)}
f' = {sub(sub(randomPolynomial(d1, RR[gens R]), R),S), sub(sub(randomPolynomial(d2, RR[gens R]),R),S)}
ps = polySystem f
startSols = solveSystem polySystem ps
g = {sub(randomPolynomial(d1, RR[gens R]), R), sub(randomPolynomial(d2, RR[gens R]),R)}
g' = {sub(sub(randomPolynomial(d1, RR[gens R]), R),S), sub(sub(randomPolynomial(d2, RR[gens R]),R),S)}
fm = matrix {flatten f}
gm = matrix {flatten g}
S = CC[x,y,t]
fmm = sub(fm, S)
gmm = sub(gm, S)
h = matrix{{t*gmm + (1-t)*fmm}}
findTurningPoints track(f,g,startSols)
(t0, t1) = (0, 1)
sols = track(f,g, startSols)
netList sols
peek sols#0
coordinates sols#0
x0 = ((1/2) * (matrix sols#0 + matrix sols#3))_(0,0)
t0 = sub((sols#0).LastT,CC)
lli = sub(.05,CC)
approxi ={{x0,t0}}
deflationMethod = (H, approx, ll) -> (
ldimm := # gens R;
R'' := CC[x,t,l_1..l_ldimm];
H'' := sub(H,R'');
l' := matrix{drop (gens R'',{0,1})};
JJ := sub(submatrix'(jacobian H,{1},),R'');
JJ' := JJ*l';
vv := random(CC^1,CC^ldimm);
vv' := vv*transpose l'+1;
N' := polySystem{H'',JJ',vv'};
pp := point{append(flatten approx, ll)};
Approx := newton(N',pp)
)
deflationMethod(h, approxi, lli)
|
