diff --git a/data/clustered-10-10-1000/1.json b/data/clustered-10-10-1000/1.json
new file mode 100644
index 0000000000000000000000000000000000000000..4206449918aa0bd130f9cacec23af3c784c02dab
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+ "(1 - t)*(0.5 - t)*((-0.05484138409268325 + I*0.22140908720504787)*(x_0^25 - 1)) + (-0.363285536561863 + 0.135629969467119*I)*t*(1 - t)*((x_0 - 1.00644290972057)*(x_0 - 1.00199096859688 - 0.00612757127365022*I)*(x_0 - 0.994787576542835 - 0.00378704731560332*I)*(x_0 - 0.994787576542835 + 0.00378704731560332*I)*(x_0 - 1.00199096859688 + 0.00612757127365022*I)*(x_0 - 0.315459904095518 - 0.951056516295154*I)*(x_0 - 0.311007962971827 - 0.957184087568804*I)*(x_0 - 0.303804570917782 - 0.954843563610757*I)*(x_0 - 0.303804570917782 - 0.947269468979550*I)*(x_0 - 0.311007962971827 - 0.944928945021503*I)*(x_0 + 0.802574084654377 - 0.587785252292473*I)*(x_0 + 0.807026025778067 - 0.593912823566123*I)*(x_0 + 0.814229417832113 - 0.591572299608076*I)*(x_0 + 0.814229417832113 - 0.583998204976870*I)*(x_0 + 0.807026025778067 - 0.581657681018823*I)*(x_0 + 0.802574084654377 + 0.587785252292473*I)*(x_0 + 0.807026025778067 + 0.581657681018823*I)*(x_0 + 0.814229417832113 + 0.583998204976870*I)*(x_0 + 0.814229417832113 + 0.591572299608076*I)*(x_0 + 0.807026025778067 + 0.593912823566123*I)*(x_0 - 0.315459904095518 + 0.951056516295154*I)*(x_0 - 0.311007962971827 + 0.944928945021503*I)*(x_0 - 0.303804570917782 + 0.947269468979550*I)*(x_0 - 0.303804570917782 + 0.954843563610757*I)*(x_0 - 0.311007962971827 + 0.957184087568804*I)) + (-0.934390108822289 + 0.393884781458255*I)*t*(0.5 - t)*((-0.536361857202138 + 0.376494822439640*I)*x_0^25 + (0.172775498954363 + 0.656052469668845*I)*x_0^24 + (-1.16380530076153 + 1.33766638574610*I)*x_0^23 + (-0.724194831799946 - 0.190280452775855*I)*x_0^22 + (0.567444754221918 - 1.30735245146270*I)*x_0^21 + (1.80000725715302 - 0.806525535429073*I)*x_0^20 + (-0.0813919205491460 + 0.564312650763339*I)*x_0^19 + (-0.241048804101517 - 0.961486610174572*I)*x_0^18 + (0.241061770268707 + 0.817118702711186*I)*x_0^17 + (-0.0238251464844561 + 1.13507951458972*I)*x_0^16 + (-0.861928389171528 + 0.273515406291217*I)*x_0^15 + (0.0840499528852050 + 0.318083382154060*I)*x_0^14 + (-0.0120053778335397 + 1.42218898820601*I)*x_0^13 + (0.100807226655669 + 0.0721887387839017*I)*x_0^12 + (1.61003989540646 + 1.45541344286949*I)*x_0^11 + (0.326769629256696 + 0.960450273187808*I)*x_0^10 + (-0.265825743548194 + 0.188672358221237*I)*x_0^9 + (0.677449898816123 - 0.200920739699462*I)*x_0^8 + (-1.97130675682501 + 0.768962646405138*I)*x_0^7 + (0.165517317362689 + 0.691382742579433*I)*x_0^6 + (-1.87101159342088 - 0.346964059375008*I)*x_0^5 + (1.55029201820297 + 0.999577510533179*I)*x_0^4 + (-0.916821050846505 - 0.630048656979378*I)*x_0^3 + (0.120118216352754 + 0.816353462824002*I)*x_0^2 + (-0.334590436537096 + 0.979905941613524*I)*x_0 + 1.45765708595046 - 0.560705908087928*I)"
+ ],
+ "variables": [
+ "x_0"
+ ],
+ "parameters": [
+ "t"
+ ],
+ "path": [
+ [
+ "0.0"
+ ],
+ [
+ "1.0"
+ ]
+ ],
+ "fiber": [
+ [
+ "1.00000000000000"
+ ],
+ [
+ "0.968583161128631 + 0.248689887164855*I"
+ ],
+ [
+ "0.876306680043864 + 0.481753674101715*I"
+ ],
+ [
+ "0.728968627421412 + 0.684547105928689*I"
+ ],
+ [
+ "0.535826794978997 + 0.844327925502015*I"
+ ],
+ [
+ "0.309016994374947 + 0.951056516295154*I"
+ ],
+ [
+ "0.0627905195293135 + 0.998026728428272*I"
+ ],
+ [
+ "-0.187381314585725 + 0.982287250728689*I"
+ ],
+ [
+ "-0.425779291565073 + 0.904827052466019*I"
+ ],
+ [
+ "-0.637423989748690 + 0.770513242775789*I"
+ ],
+ [
+ "-0.809016994374947 + 0.587785252292473*I"
+ ],
+ [
+ "-0.929776485888251 + 0.368124552684678*I"
+ ],
+ [
+ "-0.992114701314478 + 0.125333233564305*I"
+ ],
+ [
+ "-0.992114701314478 - 0.125333233564304*I"
+ ],
+ [
+ "-0.929776485888251 - 0.368124552684678*I"
+ ],
+ [
+ "-0.809016994374948 - 0.587785252292473*I"
+ ],
+ [
+ "-0.637423989748690 - 0.770513242775789*I"
+ ],
+ [
+ "-0.425779291565072 - 0.904827052466020*I"
+ ],
+ [
+ "-0.187381314585725 - 0.982287250728689*I"
+ ],
+ [
+ "0.0627905195293128 - 0.998026728428272*I"
+ ],
+ [
+ "0.309016994374947 - 0.951056516295154*I"
+ ],
+ [
+ "0.535826794978996 - 0.844327925502016*I"
+ ],
+ [
+ "0.728968627421411 - 0.684547105928689*I"
+ ],
+ [
+ "0.876306680043864 - 0.481753674101715*I"
+ ],
+ [
+ "0.968583161128631 - 0.248689887164855*I"
+ ]
+ ]
+}
\ No newline at end of file
diff --git a/data/clustered-5-5-10/2.json b/data/clustered-5-5-10/2.json
new file mode 100644
index 0000000000000000000000000000000000000000..03a706a85a8bcabc9f63431e32b82b4cb6002241
--- /dev/null
+++ b/data/clustered-5-5-10/2.json
@@ -0,0 +1,96 @@
+{
+ "system": [
+ "(1 - t)*(0.5 - t)*((1.731879514095225 + I*0.1950249883145006)*(x_0^25 - 1)) + (-0.977529996021465 + 0.197042665529265*I)*t*(1 - t)*((x_0 - 1.00644290972057)*(x_0 - 1.00199096859688 - 0.00612757127365022*I)*(x_0 - 0.994787576542835 - 0.00378704731560332*I)*(x_0 - 0.994787576542835 + 0.00378704731560332*I)*(x_0 - 1.00199096859688 + 0.00612757127365022*I)*(x_0 - 0.315459904095518 - 0.951056516295154*I)*(x_0 - 0.311007962971827 - 0.957184087568804*I)*(x_0 - 0.303804570917782 - 0.954843563610757*I)*(x_0 - 0.303804570917782 - 0.947269468979550*I)*(x_0 - 0.311007962971827 - 0.944928945021503*I)*(x_0 + 0.802574084654377 - 0.587785252292473*I)*(x_0 + 0.807026025778067 - 0.593912823566123*I)*(x_0 + 0.814229417832113 - 0.591572299608076*I)*(x_0 + 0.814229417832113 - 0.583998204976870*I)*(x_0 + 0.807026025778067 - 0.581657681018823*I)*(x_0 + 0.802574084654377 + 0.587785252292473*I)*(x_0 + 0.807026025778067 + 0.581657681018823*I)*(x_0 + 0.814229417832113 + 0.583998204976870*I)*(x_0 + 0.814229417832113 + 0.591572299608076*I)*(x_0 + 0.807026025778067 + 0.593912823566123*I)*(x_0 - 0.315459904095518 + 0.951056516295154*I)*(x_0 - 0.311007962971827 + 0.944928945021503*I)*(x_0 - 0.303804570917782 + 0.947269468979550*I)*(x_0 - 0.303804570917782 + 0.954843563610757*I)*(x_0 - 0.311007962971827 + 0.957184087568804*I)) + (0.331797434135044 + 0.0436117666512064*I)*t*(0.5 - t)*((-1.93804869107709 - 0.183058556497742*I)*x_0^25 + (-0.139006988553487 + 1.97914490559594*I)*x_0^24 + (-0.203472125448455 + 0.197574026020356*I)*x_0^23 + (0.541497661162171 + 0.423979161738556*I)*x_0^22 + (-0.939810138224372 - 0.348172024840656*I)*x_0^21 + (-1.35058804851982 - 1.67933265757800*I)*x_0^20 + (0.608474333195177 - 0.812856825374798*I)*x_0^19 + (-0.630457073285557 - 1.01986618173779*I)*x_0^18 + (-1.19896538249218 + 0.568595378197705*I)*x_0^17 + (0.908417043362670 + 1.30341867145903*I)*x_0^16 + (1.58678072748441 - 0.939537631865288*I)*x_0^15 + (-1.48969316275242 + 0.711643162808153*I)*x_0^14 + (0.548838806422178 - 0.434482316371346*I)*x_0^13 + (2.50049529693627 + 0.487790584903777*I)*x_0^12 + (-0.639108278034850 - 0.450624555274172*I)*x_0^11 + (-0.627292696500845 + 0.489363033016822*I)*x_0^10 + (-0.728921174898087 - 0.544713296600824*I)*x_0^9 + (3.70465606398291 + 1.18138379054559*I)*x_0^8 + (0.194503093790548 - 1.36655285500566*I)*x_0^7 + (-0.113570081905217 + 0.413205822648875*I)*x_0^6 + (0.0934716476546580 + 0.780593951577257*I)*x_0^5 + (-0.825728817477181 - 0.428689477847869*I)*x_0^4 + (-0.514290838230882 - 0.969828577931728*I)*x_0^3 + (0.978411455786260 + 1.01778400310490*I)*x_0^2 + (-0.779531529602297 - 1.28831197665067*I)*x_0 - 0.795575931175836 + 1.33916190957638*I)"
+ ],
+ "variables": [
+ "x_0"
+ ],
+ "parameters": [
+ "t"
+ ],
+ "path": [
+ [
+ "0.0"
+ ],
+ [
+ "1.0"
+ ]
+ ],
+ "fiber": [
+ [
+ "1.00000000000000"
+ ],
+ [
+ "0.968583161128631 + 0.248689887164855*I"
+ ],
+ [
+ "0.876306680043864 + 0.481753674101715*I"
+ ],
+ [
+ "0.728968627421412 + 0.684547105928689*I"
+ ],
+ [
+ "0.535826794978997 + 0.844327925502015*I"
+ ],
+ [
+ "0.309016994374947 + 0.951056516295154*I"
+ ],
+ [
+ "0.0627905195293135 + 0.998026728428272*I"
+ ],
+ [
+ "-0.187381314585725 + 0.982287250728689*I"
+ ],
+ [
+ "-0.425779291565073 + 0.904827052466019*I"
+ ],
+ [
+ "-0.637423989748690 + 0.770513242775789*I"
+ ],
+ [
+ "-0.809016994374947 + 0.587785252292473*I"
+ ],
+ [
+ "-0.929776485888251 + 0.368124552684678*I"
+ ],
+ [
+ "-0.992114701314478 + 0.125333233564305*I"
+ ],
+ [
+ "-0.992114701314478 - 0.125333233564304*I"
+ ],
+ [
+ "-0.929776485888251 - 0.368124552684678*I"
+ ],
+ [
+ "-0.809016994374948 - 0.587785252292473*I"
+ ],
+ [
+ "-0.637423989748690 - 0.770513242775789*I"
+ ],
+ [
+ "-0.425779291565072 - 0.904827052466020*I"
+ ],
+ [
+ "-0.187381314585725 - 0.982287250728689*I"
+ ],
+ [
+ "0.0627905195293128 - 0.998026728428272*I"
+ ],
+ [
+ "0.309016994374947 - 0.951056516295154*I"
+ ],
+ [
+ "0.535826794978996 - 0.844327925502016*I"
+ ],
+ [
+ "0.728968627421411 - 0.684547105928689*I"
+ ],
+ [
+ "0.876306680043864 - 0.481753674101715*I"
+ ],
+ [
+ "0.968583161128631 - 0.248689887164855*I"
+ ]
+ ]
+}
\ No newline at end of file
diff --git a/gen.sage b/gen.sage
index 4f29afdaeb5d7de40bff7115aeba45ec977e8f89..a32e15ca442a41a82d3d9051741ebafdc2a937d7 100644
--- a/gen.sage
+++ b/gen.sage
@@ -194,10 +194,11 @@ class Wilkinson(Name, System):
self.name = Path("wilkinson" + f"-{self.structure_ctx.name}"*(
structure is None) + f"-{self.d_ctx.name}")
-
+
def get_degrees(self):
return [self.d_ctx.value]
+
class GradientCtx(Name, System):
nvars_ctx: None
d_ctx: None
@@ -331,7 +332,7 @@ class TargetCtx(Name):
if target_type is None:
try:
self.target_type = input(
- f"{message} (dense, uroots, sumpowlin, resultants, gradient, katsura, spl-gradient) Bad/no input will be considered as default={default}")
+ f"{message} (dense, uroots, sumpowlin, resultants, gradient, katsura, spl-gradient, wilkinson) Bad/no input will be considered as default={default}")
except:
self.target_type = default
self.name = Path(str(self.target_type))
@@ -431,6 +432,40 @@ class NewtonHomotopyCtx(Name, Problem):
self.fiber = fiber # TODO: convert to strings
+class ClusteredHomotopy(Name, Problem):
+ nc_ctx = None
+ cs_ctx = None
+ α_ctx = None
+
+ def __init__(self, nc=None, cs=None, α=None):
+ self.nc_ctx = IntegerCtx(nc, default=5, message="Number of clusters")
+ self.cs_ctx = IntegerCtx(
+ cs, default=3, message="Number of roots per cluster")
+ self.α_ctx = IntegerCtx(
+ α, default=100, message="Clustering factor (small α leads to close roots in a cluster, default is 100).")
+ nc, cs, α = self.nc_ctx.value, self.cs_ctx.value, self.α_ctx.value
+ d = nc*cs
+ A = PolynomialRing(CC, names="x_0")
+ self.name = Path(f"clustered-{nc}-{cs}-{α}")
+ start_ctx = URootsCtx([d], True)
+ c = [CC(exp(2*I*pi*k/nc)) for k in range(nc)]
+ u = CC(2 ^ (-53))
+ z = [[CC(c[k] + α*u ^ (1/cs)*exp(2*I*pi*l/cs))
+ for l in range(cs)] for k in range(nc)]
+ x_0 = var("x_0")
+ E = "*".join([f"({x_0 - zij})" for zi in z for zij in zi])
+ γ1 = CC.random_element()
+ γ2 = CC.random_element()
+ target_ctx = DenseCtx([d])
+
+ self.system = [
+ f"(1 - t)*(0.5 - t)*({start_ctx.system[0]}) + ({γ1})*t*(1 - t)*({E}) + ({γ2})*t*(0.5 - t)*({target_ctx.system[0]})"]
+ self.variables = ["x_0"]
+ self.parameters = ["t"]
+ self.path = [["0.0"], ["1.0"]]
+ self.fiber = start_ctx.fiber # TODO: convert to strings
+
+
class Problem:
system = None
variables = None
@@ -465,7 +500,7 @@ class ProblemCtx(Name):
if problem_type is None:
try:
self.problem_type = input(
- f"{message} (linear, newton) Bad/no input will be considered as default={default}")
+ f"{message} (linear, newton, clustered) Bad/no input will be considered as default={default}")
except:
self.problem_type = default
self.name = Path(str(self.problem_type))
@@ -474,6 +509,8 @@ class ProblemCtx(Name):
if self.problem_type == "newton":
self.problem = NewtonHomotopyCtx()
+ elif self.problem_type == "clustered":
+ self.problem = ClusteredHomotopy()
else:
self.problem = LinearHomotopyCtx()