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diff --git a/benchmarks/newton_structured-8-3-5_all-paths_1/macaulay2/out.json b/benchmarks/newton/sumpowlin-8-3-5/1/macaulay2/out.json
similarity index 100%
rename from benchmarks/newton_structured-8-3-5_all-paths_1/macaulay2/out.json
rename to benchmarks/newton/sumpowlin-8-3-5/1/macaulay2/out.json
diff --git a/benchmarks/newton_structured-8-3-5_all-paths_1/macaulay2/perflog.txt b/benchmarks/newton/sumpowlin-8-3-5/1/macaulay2/perflog.txt
similarity index 100%
rename from benchmarks/newton_structured-8-3-5_all-paths_1/macaulay2/perflog.txt
rename to benchmarks/newton/sumpowlin-8-3-5/1/macaulay2/perflog.txt
diff --git a/benchmarks/newton_structured-8-3-5_all-paths_1/macaulay2/script.m2 b/benchmarks/newton/sumpowlin-8-3-5/1/macaulay2/script.m2
similarity index 100%
rename from benchmarks/newton_structured-8-3-5_all-paths_1/macaulay2/script.m2
rename to benchmarks/newton/sumpowlin-8-3-5/1/macaulay2/script.m2
diff --git a/data/linear_dense-10-10_all-paths_1.json b/data/linear/dense-10-10/all/1.json
similarity index 100%
rename from data/linear_dense-10-10_all-paths_1.json
rename to data/linear/dense-10-10/all/1.json
diff --git a/data/linear_dense-10_all-paths_1.json b/data/linear/dense-10/all/1.json
similarity index 100%
rename from data/linear_dense-10_all-paths_1.json
rename to data/linear/dense-10/all/1.json
diff --git a/data/linear_dense-100_all-paths_1.json b/data/linear/dense-100/all/1.json
similarity index 100%
rename from data/linear_dense-100_all-paths_1.json
rename to data/linear/dense-100/all/1.json
diff --git a/data/linear_dense-1000_all-paths_1.json b/data/linear/dense-1000/all/1.json
similarity index 100%
rename from data/linear_dense-1000_all-paths_1.json
rename to data/linear/dense-1000/all/1.json
diff --git a/data/linear_dense-20-20_all-paths_1.json b/data/linear/dense-20-20/all/1.json
similarity index 100%
rename from data/linear_dense-20-20_all-paths_1.json
rename to data/linear/dense-20-20/all/1.json
diff --git a/data/linear_dense-20_all-paths_1.json b/data/linear/dense-20/all/1.json
similarity index 100%
rename from data/linear_dense-20_all-paths_1.json
rename to data/linear/dense-20/all/1.json
diff --git a/data/linear_dense-3-3-3-3-3-3-3-3_100-paths_1.json b/data/linear/dense-3-3-3-3-3-3-3-3/random-100/1.json
similarity index 100%
rename from data/linear_dense-3-3-3-3-3-3-3-3_100-paths_1.json
rename to data/linear/dense-3-3-3-3-3-3-3-3/random-100/1.json
diff --git a/data/linear_dense-3-3-3-3-3-3_100-paths_1.json b/data/linear/dense-3-3-3-3-3-3/random-100/1.json
similarity index 100%
rename from data/linear_dense-3-3-3-3-3-3_100-paths_1.json
rename to data/linear/dense-3-3-3-3-3-3/random-100/1.json
diff --git a/data/linear_dense-3-3-3-3_100-paths_1.json b/data/linear/dense-3-3-3-3/random-100/1.json
similarity index 100%
rename from data/linear_dense-3-3-3-3_100-paths_1.json
rename to data/linear/dense-3-3-3-3/random-100/1.json
diff --git a/data/linear_dense-30-30_all-paths_1.json b/data/linear/dense-30-30/all/1.json
similarity index 100%
rename from data/linear_dense-30-30_all-paths_1.json
rename to data/linear/dense-30-30/all/1.json
diff --git a/data/linear_dense-30_all-paths_1.json b/data/linear/dense-30/all/1.json
similarity index 100%
rename from data/linear_dense-30_all-paths_1.json
rename to data/linear/dense-30/all/1.json
diff --git a/data/linear_dense-40-40_all-paths_1.json b/data/linear/dense-40-40/all/1.json
similarity index 100%
rename from data/linear_dense-40-40_all-paths_1.json
rename to data/linear/dense-40-40/all/1.json
diff --git a/data/linear_dense-40_all-paths_1.json b/data/linear/dense-40/all/1.json
similarity index 100%
rename from data/linear_dense-40_all-paths_1.json
rename to data/linear/dense-40/all/1.json
diff --git a/data/linear_dense-5-5_all-paths_1.json b/data/linear/dense-5-5/all/1.json
similarity index 100%
rename from data/linear_dense-5-5_all-paths_1.json
rename to data/linear/dense-5-5/all/1.json
diff --git a/data/linear_dense-50-50_all-paths_1.json b/data/linear/dense-50-50/all/1.json
similarity index 100%
rename from data/linear_dense-50-50_all-paths_1.json
rename to data/linear/dense-50-50/all/1.json
diff --git a/data/linear_dense-50_all-paths_1.json b/data/linear/dense-50/all/1.json
similarity index 100%
rename from data/linear_dense-50_all-paths_1.json
rename to data/linear/dense-50/all/1.json
diff --git a/data/linear_dense-500_all-paths_1.json b/data/linear/dense-500/all/1.json
similarity index 100%
rename from data/linear_dense-500_all-paths_1.json
rename to data/linear/dense-500/all/1.json
diff --git a/data/linear_katsura-10_all-paths_1.json b/data/linear/katsura-10/all/1.json
similarity index 100%
rename from data/linear_katsura-10_all-paths_1.json
rename to data/linear/katsura-10/all/1.json
diff --git a/data/linear_katsura-10_100-paths_1.json b/data/linear/katsura-10/random-100/1.json
similarity index 100%
rename from data/linear_katsura-10_100-paths_1.json
rename to data/linear/katsura-10/random-100/1.json
diff --git a/data/linear_katsura-15_all-paths_1.json b/data/linear/katsura-15/all/1.json
similarity index 100%
rename from data/linear_katsura-15_all-paths_1.json
rename to data/linear/katsura-15/all/1.json
diff --git a/data/linear_katsura-15_100-paths_1.json b/data/linear/katsura-15/random-100/1.json
similarity index 100%
rename from data/linear_katsura-15_100-paths_1.json
rename to data/linear/katsura-15/random-100/1.json
diff --git a/data/linear_katsura-20_all-paths_1.json b/data/linear/katsura-20/all/1.json
similarity index 100%
rename from data/linear_katsura-20_all-paths_1.json
rename to data/linear/katsura-20/all/1.json
diff --git a/data/linear_katsura-20_100-paths_1.json b/data/linear/katsura-20/random-100/1.json
similarity index 100%
rename from data/linear_katsura-20_100-paths_1.json
rename to data/linear/katsura-20/random-100/1.json
diff --git a/data/linear_katsura-25_100-paths_1.json b/data/linear/katsura-25/random-100/1.json
similarity index 100%
rename from data/linear_katsura-25_100-paths_1.json
rename to data/linear/katsura-25/random-100/1.json
diff --git a/data/linear_katsura-30_100-paths_1.json b/data/linear/katsura-30/random-100/1.json
similarity index 100%
rename from data/linear_katsura-30_100-paths_1.json
rename to data/linear/katsura-30/random-100/1.json
diff --git a/data/linear_katsura-4_all-paths_1.json b/data/linear/katsura-4/all/1.json
similarity index 100%
rename from data/linear_katsura-4_all-paths_1.json
rename to data/linear/katsura-4/all/1.json
diff --git a/data/linear_katsura-40_100-paths_1.json b/data/linear/katsura-40/random-100/1.json
similarity index 100%
rename from data/linear_katsura-40_100-paths_1.json
rename to data/linear/katsura-40/random-100/1.json
diff --git a/data/linear_katsura-6_all-paths_1.json b/data/linear/katsura-6/all/1.json
similarity index 100%
rename from data/linear_katsura-6_all-paths_1.json
rename to data/linear/katsura-6/all/1.json
diff --git a/data/linear_katsura-8_all-paths_1.json b/data/linear/katsura-8/all/1.json
similarity index 100%
rename from data/linear_katsura-8_all-paths_1.json
rename to data/linear/katsura-8/all/1.json
diff --git a/data/linear_katsura-8_100-paths_1.json b/data/linear/katsura-8/random-100/1.json
similarity index 100%
rename from data/linear_katsura-8_100-paths_1.json
rename to data/linear/katsura-8/random-100/1.json
diff --git a/data/linear_structured-4-3-5_100-paths_1.json b/data/linear/sumpowlin-4-3-5/random-100/1.json
similarity index 100%
rename from data/linear_structured-4-3-5_100-paths_1.json
rename to data/linear/sumpowlin-4-3-5/random-100/1.json
diff --git a/data/linear_structured-6-3-5_100-paths_1.json b/data/linear/sumpowlin-6-3-5/random-100/1.json
similarity index 100%
rename from data/linear_structured-6-3-5_100-paths_1.json
rename to data/linear/sumpowlin-6-3-5/random-100/1.json
diff --git a/data/linear_structured-8-3-5_100-paths_1.json b/data/linear/sumpowlin-8-3-5/random-100/1.json
similarity index 100%
rename from data/linear_structured-8-3-5_100-paths_1.json
rename to data/linear/sumpowlin-8-3-5/random-100/1.json
diff --git a/data/newton_dense-3-3-3-3-3-3-3-3_all-paths_1.json b/data/newton/dense-3-3-3-3-3-3-3-3/1.json
similarity index 100%
rename from data/newton_dense-3-3-3-3-3-3-3-3_all-paths_1.json
rename to data/newton/dense-3-3-3-3-3-3-3-3/1.json
diff --git a/data/newton_dense-3-3-3-3-3-3_all-paths_1.json b/data/newton/dense-3-3-3-3-3-3/1.json
similarity index 100%
rename from data/newton_dense-3-3-3-3-3-3_all-paths_1.json
rename to data/newton/dense-3-3-3-3-3-3/1.json
diff --git a/data/newton_dense-3-3-3-3_all-paths_1.json b/data/newton/dense-3-3-3-3/1.json
similarity index 100%
rename from data/newton_dense-3-3-3-3_all-paths_1.json
rename to data/newton/dense-3-3-3-3/1.json
diff --git a/data/newton_katsura-10_all-paths_1.json b/data/newton/katsura-10/1.json
similarity index 100%
rename from data/newton_katsura-10_all-paths_1.json
rename to data/newton/katsura-10/1.json
diff --git a/data/newton_katsura-20_all-paths_1.json b/data/newton/katsura-20/1.json
similarity index 100%
rename from data/newton_katsura-20_all-paths_1.json
rename to data/newton/katsura-20/1.json
diff --git a/data/newton_katsura-30_all-paths_1.json b/data/newton/katsura-30/1.json
similarity index 100%
rename from data/newton_katsura-30_all-paths_1.json
rename to data/newton/katsura-30/1.json
diff --git a/data/newton_katsura-40_all-paths_1.json b/data/newton/katsura-40/1.json
similarity index 100%
rename from data/newton_katsura-40_all-paths_1.json
rename to data/newton/katsura-40/1.json
diff --git a/data/newton_katsura-5_all-paths_1.json b/data/newton/katsura-5/1.json
similarity index 100%
rename from data/newton_katsura-5_all-paths_1.json
rename to data/newton/katsura-5/1.json
diff --git a/data/newton_structured-10-10-5_all-paths_1.json b/data/newton/sumpowlin-10-10-5/1.json
similarity index 100%
rename from data/newton_structured-10-10-5_all-paths_1.json
rename to data/newton/sumpowlin-10-10-5/1.json
diff --git a/data/newton_structured-15-15-5_all-paths_1.json b/data/newton/sumpowlin-15-15-5/1.json
similarity index 100%
rename from data/newton_structured-15-15-5_all-paths_1.json
rename to data/newton/sumpowlin-15-15-5/1.json
diff --git a/data/newton_structured-20-20-5_all-paths_1.json b/data/newton/sumpowlin-20-20-5/1.json
similarity index 100%
rename from data/newton_structured-20-20-5_all-paths_1.json
rename to data/newton/sumpowlin-20-20-5/1.json
diff --git a/data/newton_structured-25-25-5_all-paths_1.json b/data/newton/sumpowlin-25-25-5/1.json
similarity index 100%
rename from data/newton_structured-25-25-5_all-paths_1.json
rename to data/newton/sumpowlin-25-25-5/1.json
diff --git a/data/newton_structured-30-30-5_all-paths_1.json b/data/newton/sumpowlin-30-30-5/1.json
similarity index 100%
rename from data/newton_structured-30-30-5_all-paths_1.json
rename to data/newton/sumpowlin-30-30-5/1.json
diff --git a/data/newton_structured-4-3-5_all-paths_1.json b/data/newton/sumpowlin-4-3-5/1.json
similarity index 100%
rename from data/newton_structured-4-3-5_all-paths_1.json
rename to data/newton/sumpowlin-4-3-5/1.json
diff --git a/data/newton_structured-5-5-5_all-paths_1.json b/data/newton/sumpowlin-5-5-5/1.json
similarity index 100%
rename from data/newton_structured-5-5-5_all-paths_1.json
rename to data/newton/sumpowlin-5-5-5/1.json
diff --git a/data/newton_structured-6-3-5_all-paths_1.json b/data/newton/sumpowlin-6-3-5/1.json
similarity index 100%
rename from data/newton_structured-6-3-5_all-paths_1.json
rename to data/newton/sumpowlin-6-3-5/1.json
diff --git a/data/newton_structured-8-3-5_all-paths_1.json b/data/newton/sumpowlin-8-3-5/1.json
similarity index 100%
rename from data/newton_structured-8-3-5_all-paths_1.json
rename to data/newton/sumpowlin-8-3-5/1.json
diff --git a/gen.sage b/gen.sage
index af15c6cb23f6d752d19bc5d00e7b717c52cd40e7..3fb55899dc3b6e9ac25983b044408408fcb12253 100644
--- a/gen.sage
+++ b/gen.sage
@@ -1,97 +1,424 @@
-import argparse
-import json
-import os
 import itertools
+import json
+from pathlib import Path
+
+
+class Name:
+    name = None
+
+    def get_name(self):
+        pass
+
+
+class DegreesCtx(Name):
+    degrees = None
+
+    def __init__(self, degrees=None, default="factorized"):
+        if degrees is None:
+            try:
+                self.degrees = list(map(int, input(
+                    f"Input a comma separated list of degrees, e.g. 3, 7, 2. Bad/no input will be considered as default={default}").replace(" ", "").split(",")))
+            except:
+                self.degrees = default
+            self.name = Path(str(self.degrees).replace("[",
+                                                       "").replace("]", "").replace(", ", "-"))
+        else:
+            self.degrees = degrees
+
+
+class StructureCtx(Name):
+    structure = None
+
+    def __init__(self, structure=None, default="factorized"):
+        if structure is None:
+            try:
+                self.structure = input(
+                    f"Input a structure (developped, factorized). Bad/no input will be considered as default={default}")
+            except:
+                self.structure = default
+            self.name = Path(self.structure)
+        else:
+            self.structure = structure
+
+
+class IntegerCtx(Name):
+    value = None
+
+    def __init__(self, value=None, default=0, message="Input an integer."):
+        if value is None:
+            try:
+                self.value = int(input(
+                    f"{message} Bad/no input will be considered as default={default}"))
+            except:
+                self.value = default
+            self.name = Path(str(self.value))
+        else:
+            self.value = value
+
+
+class System:
+    ring = None
+    system = None
+
+    def get_degrees(self):
+        return [f.degree() for f in self.system]
+
+
+class StartSystem(System):
+    fiber = None
+
+    def compute_fiber(self):
+        pass
+
+
+class Problem:
+    system = None
+    variables = None
+    parameters = None
+    path = None
+    fiber = None
+
+    def to_json(self, target_path=Path("./data")):
+        index = 1
+        (target_path / self.name).mkdir(parents=True, exist_ok=True)
+        while (target_path / self.name / f"{str(index)}.json").exists():
+            index += 1
+
+        print("Writting on test data file ...")
+        data_file = (target_path / self.name / f"{str(index)}.json").open("w")
+        json.dump({"system": self.system,
+                   "variables": self.variables,
+                   "parameters": self.parameters,
+                   "path": self.path,
+                   "fiber": self.fiber},
+                  data_file,
+                  indent=2)
+        data_file.close()
+
+
+class DenseCtx(Name, System):
+    degrees_ctx = None
+
+    def __init__(self, degrees=None):
+        self.degrees_ctx = DegreesCtx(degrees=degrees)
+        self.ring = PolynomialRing(
+            CC, names=[f"x_{i}" for i in range(len(self.degrees_ctx.degrees))])
+        dictlist = [((1 + sum(self.ring.gens())) ^ di).dict()
+                    for di in self.degrees_ctx.degrees]
+        for dict in dictlist:
+            for k in dict:
+                dict[k] = normalvariate(0, 1) + I*normalvariate(0, 1)
+        self.system = [self.ring(dict) for dict in dictlist]
+        self.name = Path(
+            "dense" + f"-{self.degrees_ctx.name}"*(degrees is None))
+
+    def get_degrees(self):
+        return self.degrees_ctx.degrees
+
+
+class SumPowLinCtx(Name, System):
+    structure_ctx = None
+    n_ctx = None
+    d_ctx = None
+    l_ctx = None
+
+    def get_degrees(self):
+        return [self.d_ctx.value for _ in range(self.n_ctx.value)]
+
+    def __init__(self, n=None, d=None, l=None, structure=None):
+        self.structure_ctx = StructureCtx(structure=structure)
+        self.n_ctx = IntegerCtx(n, default=3, message="Dimension ?")
+        self.d_ctx = IntegerCtx(d, default=3, message="Degree ?")
+        self.l_ctx = IntegerCtx(l, default=3, message="Length ?")
+        self.ring = PolynomialRing(
+            CC, names=[f"x_{i}" for i in range(self.n_ctx.value)])
+        self.system = [f"{str(choice([-1, 1]))} + " + " + ".join(["(" + str(sum([normalvariate(-1, 1)*v for v in self.ring.gens()])
+                                                                            ) + f")^{self.d_ctx.value}" for _ in range(self.l_ctx.value)]) for _ in range(self.n_ctx.value)]
+        print(self.system)
+        if self.structure_ctx.structure == "developped":
+            self.system = list(map(self.ring, self.system))
+        self.name = Path("sumpowlin" + f"-{self.structure_ctx.name}"*(
+            structure is None) + f"-{self.n_ctx.name}-{self.d_ctx.name}-{self.l_ctx.name}")
+
+
+class ResultantsCtx(Name, System):
+    n_ctx: None
+    d_ctx: None
+    degrees: None
+
+    def get_degrees(self):
+        return self.degrees
+
+    def __init__(self, n=None, d=None):
+        self.n_ctx = IntegerCtx(n, default=3, message="Dimension ?")
+        self.d_ctx = IntegerCtx(d, default=3, message="Degree ?")
+
+        variables = [f"x_{i}" for i in range(self.n_ctx.value)]
+        self.ring = PolynomialRing(
+            CC, names=variables)
+        Cpy = PolynomialRing(CC, names=["y"] + variables)
+        self.system = []
+        for _ in range(self.n_ctx.value):
+            f = Cpy.random_element(degree=self.d_ctx.value, terms=1000)
+            g = Cpy.random_element(degree=self.d_ctx.value, terms=1000)
+            h = g.resultant(f, Cpy.gens()[0])
+            self.system.append(self.ring(h))
+        self.degrees = [f.degree() for f in self.system]
+        self.name = Path(
+            "resultants" + f"-{self.n_ctx.name}-{self.d_ctx.name}")
+
+
+class GradientCtx(Name, System):
+    nvars_ctx: None
+    d_ctx: None
+    structure_ctx = StructureCtx("factorized")
+
+    def __init__(self, nvars=None, d=None, l=None):
+        self.nvars_ctx = IntegerCtx(
+            nvars, default=3, message="Number of variables for the polynomial?")
+        self.d_ctx = IntegerCtx(nvars, default=3, message="Degree?")
+        n = self.nvars_ctx.value
+        self.ring = PolynomialRing(CC, names=[f"x_{i}" for i in range(n)])
+        coeffs = [[normalvariate(-1, 1) for _ in range(n)] for _ in range(n)]
+        self.system = [" + ".join([f"{self.d_ctx.value}*({coeffs[i][k]})*(" + str(sum([coeffs[i][j]*v for j, v in enumerate(self.ring.gens())])
+                                                                                  ) + f")^{self.d_ctx.value - 1}" for i in range(n)]) for k in range(n)]
+        self.name = Path(
+            f"gradient_{self.nvars_ctx.value}-{self.d_ctx.value}")
+
+    def get_degrees(self):
+        return [self.d_ctx.value - 1 for _ in range(self.nvars_ctx.value)]
+
+
+class KatsuraCtx(Name, System):
+    n_ctx: None
+
+    def __init__(self, n=None):
+        self.n_ctx = IntegerCtx(
+            n, default=5, message="Size of katsura system?")
+        n = self.n_ctx.value
+        self.ring = PolynomialRing(
+            CC, names=[f"x_{i}" for i in range(n + 1)])
+        self.system = sage.rings.ideal.Katsura(
+            self.ring, n + 1).gens()
+        self.name = Path(f"katsura_{n}")
+
+    def get_degrees(self):
+        return super().get_degrees()
+
+
+class URootsCtx(Name, System):
+    degrees_ctx = None
+    fiber = None
+    fiber_type = "random"
+    fiber_size = 100
+    fiber_name = ""
+    compute_fiber_bool = False
+
+    def __init__(self, degrees=None, compute_fiber=None):
+        self.degrees_ctx = DegreesCtx(degrees=degrees)
+        print(self.get_degrees())
+        self.fiber_init(compute_fiber=compute_fiber)
+        self.ring = PolynomialRing(
+            CC, names=[f"x_{i}" for i in range(len(self.degrees_ctx.degrees))])
+        self.system = [f"({normalvariate(0, 1)} + I*{normalvariate(0, 1)})*({v}^{d} - 1)" for v,
+                       d in zip(self.ring.gens(), self.degrees_ctx.degrees)]
+        self.name = Path("uroots" + f"-{self.degrees_ctx.name}"*(
+            degrees is None) + f"-{self.fiber_name}"*self.compute_fiber_bool)
+
+    def get_degrees(self):
+        return self.degrees_ctx.degrees
+
+    def fiber_init(self, compute_fiber=None):
+        if compute_fiber is None:
+            try:
+                self.compute_fiber_bool = bool(int(input(
+                    "Should the fiber be computed ? (Y/N)").replace("Y", "1").replace("y", "1").replace("N", "0").replace("n", "0")))
+            except:
+                pass
+        else:
+            self.compute_fiber_bool = compute_fiber
+
+        if self.compute_fiber_bool:
+            try:
+                self.fiber_type = input(
+                    "Which type of fiber? (all, random)")
+            except:
+                pass
+
+            self.fiber_name = self.fiber_type
+            if self.fiber_type == "random":
+                try:
+                    self.fiber_size = int(input("Fiber size? (int)"))
+                except:
+                    pass
+                self.fiber_name += f"-{self.fiber_size}"
+
+            self.compute_fiber()
+
+    def compute_fiber(self):
+        exps = [[str(CC(exp(k*2*CC.gen()*pi/di)))
+                 for k in range(di)] for di in self.get_degrees()]
+
+        if self.fiber_type == "all":
+            self.fiber = list(itertools.product(*exps))
+        else:
+            self.fiber = [[choice(exp) for exp in exps]
+                          for _ in range(self.fiber_size)]
+
+
+class TargetCtx(Name):
+    target_type = None
+    target = None
+
+    def __init__(self, target_type=None, default="dense", message="Input a kind of system."):
+        if target_type is None:
+            try:
+                self.target_type = input(
+                    f"{message} (dense, uroots, sumpowlin, resultants, gradient, katsura) Bad/no input will be considered as default={default}")
+            except:
+                self.target_type = default
+            self.name = Path(str(self.target_type))
+        else:
+            self.target_type = target_type
+
+        if self.target_type == "uroots":
+            self.target = URootsCtx(compute_fiber=False)
+        elif self.target_type == "sumpowlin":
+            self.target = SumPowLinCtx()
+        elif self.target_type == "resultants":
+            self.target = ResultantsCtx()
+        elif self.target_type == "gradient":
+            self.target = GradientCtx()
+        elif self.target_type == "katsura":
+            self.target = KatsuraCtx()
+        else:
+            self.target = DenseCtx()
+
+
+class LinearHomotopyCtx(Name, Problem):
+    target_ctx = None
+    start = None
+
+    def __init__(self, structure=None, target_type=None):
+        self.target_ctx = TargetCtx(target_type=target_type, default="dense")
+        self.start = URootsCtx(
+            degrees=self.target_ctx.target.get_degrees(), compute_fiber=True)
+        self.name = "linear" / self.target_ctx.target.name / Path(str(self.start.name).replace("uroots-", ""))
+
+        # compute homotopy
+        try:
+            structure = self.target_ctx.target.structure_ctx.structure
+        except:
+            structure = ""
+
+        if structure == "factorized":
+            self.system = [f"t*({ft}) + (1 - t)*({fs})" for ft,
+                           fs in zip(self.target_ctx.target.system, self.start.system)]
+        else:
+            CPt = PolynomialRing(
+                CC, names=['t'] + [str(v) for v in self.target_ctx.target.ring.gens()])
+            self.system = [str(CPt.gens()[0]*CPt(ft) + (1 - CPt.gens()[0])*CPt(fs))
+                           for ft, fs in zip(self.target_ctx.target.system, self.start.system)]
+
+        self.variables = [str(v) for v in self.target_ctx.target.ring.gens()]
+        self.parameters = ["t"]
+        self.path = [["0.0"], ["1.0"]]
+        self.fiber = self.start.fiber  # TODO: convert to strings
+
+    def to_json(self, target_path=Path("./data")):
+        return super().to_json(target_path)
+
+
+class NewtonHomotopyCtx(Name, Problem):
+    target_ctx = None
+
+    def __init__(self, target_type=None, start_type=None):
+        self.target_ctx = TargetCtx(target_type=target_type, default="dense")
+        self.name = "newton" / self.target_ctx.target.name
+
+        # homotopy
+        n = len(self.target_ctx.target.system)
+        z = vector(CC, [normalvariate(0, 1) + I*normalvariate(0, 1)
+                   for _ in range(n)])
+        fiber = [list(z/z.norm())]
+        Cpt = PolynomialRing(
+            CC, names=["t"] + list(map(str, self.target_ctx.target.ring.gens())))
+
+        D = {}
+        for z, v in zip(fiber[0], self.target_ctx.target.ring.gens()):
+            D[str(v)] = z
+
+        T_fiber = [sage_eval(str(f), D) for f in self.target_ctx.target.system]
+
+        try:
+            structure = self.target_ctx.target.structure_ctx.structure
+        except:
+            structure = ""
+        if structure == "factorized":
+            self.system = [f"{f} - (1 - t)*({c})" for f,
+                           c in zip(self.target_ctx.target.system, T_fiber)]
+        else:
+            self.system = [str(Cpt(f) - (1 - Cpt.gens()[0])*Cpt(c))
+                           for f, c in zip(self.target_ctx.target.system, T_fiber)]
+
+        fiber = [[str(zi) for zi in z] for z in fiber]
+
+        self.variables = list(map(str, self.target_ctx.target.ring.gens()))
+        self.parameters = ["t"]
+        self.path = [["0.0"], ["1.0"]]
+        self.fiber = fiber  # TODO: convert to strings
+
+
+class Problem:
+    system = None
+    variables = None
+    parameters = None
+    path = None
+    fiber = None
+
+    def to_json(self, target_path=Path("./data")):
+        index = 1
+        (target_path / self.name).mkdir(parents=True, exist_ok=True)
+        while (target_path / self.name / f"{str(index)}.json").exists():
+            index += 1
+
+        print("Writting on test data file ...")
+        data_file = (target_path / self.name / f"{str(index)}.json").open("w")
+        json.dump({"system": self.system,
+                   "variables": self.variables,
+                   "parameters": self.parameters,
+                   "path": self.path,
+                   "fiber": self.fiber},
+                  data_file,
+                  indent=2)
+        data_file.close()
+
+
+class ProblemCtx(Name):
+    problem_type = None
+    problem = None
+
+    def __init__(self, problem_type=None, default="linear", message="Input a kind of problem."):
+        if problem_type is None:
+            try:
+                self.problem_type = input(
+                    f"{message} (linear, newton) Bad/no input will be considered as default={default}")
+            except:
+                self.problem_type = default
+            self.name = Path(str(self.problem_type))
+        else:
+            self.problem_type = problem_type
+
+        if self.problem_type == "newton":
+            self.problem = NewtonHomotopyCtx()
+        else:
+            self.problem = LinearHomotopyCtx()
+
+        self.name = self.problem.name
+
+    def to_json(self):
+        self.problem.to_json()
+
 
-parser = argparse.ArgumentParser(description="A sage script that generates examples from different families.")
-parser.add_argument("h", choices = ["linear", "newton"], help = "Homotopy type")
-parser.add_argument("type", nargs = '+', help = "Type of target system, followed by its parameters. It can be dense <d1> ... <dn>, structured <n> <d> <l> or katsura <n>")
-parser.add_argument("--paths", nargs = '?', default = "all", help = "Number of paths tracked. Should be either an positive integer or all")
-args = parser.parse_args()
-
-h_type = args.h
-f_type = args.type[0]
-
-degrees = []
-n = 0
-d = 0
-l = 0
-if f_type == "dense":
-    degrees = [int(d) for d in args.type[1:]]
-    n = len(degrees)
-elif f_type == "structured":
-    n = int(args.type[1])
-    d = int(args.type[2])
-    l = int(args.type[3])
-elif f_type == "katsura":
-    n = int(args.type[1]) + 1
-
-variables = [f"x{i}" for i in range(n)]
-parameter = "t"
-
-CP = PolynomialRing(CC, names = variables)
-CPt = PolynomialRing(CC, names = ['t'] + variables)
-
-print("Generating target system ...")
-if f_type == "dense":
-    dictlist = [((1 + sum(CP.gens()))^di).dict() for di in degrees]
-    for dict in dictlist:
-        for k in dict:
-            dict[k] = normalvariate(0, 1) + I*normalvariate(0, 1)
-
-    T = [CP(dict) for dict in dictlist]
-
-elif f_type == "structured":
-    degrees = [d for _ in range(n)]
-    T = [str(choice([-1, 1])) + " + " + " + ".join(["(" + str(sum([randint(-1, 1)*v for v in CP.gens()])) + ")^" + str(d) for _ in range(l)]) for _ in range(n)]
-
-elif f_type == "katsura":
-    T = sage.rings.ideal.Katsura(CP, n).gens()
-    degrees = [f.degree() for f in T]
-
-system = []
-fiber = []
-
-print("Generating homotopy and fiber ...")
-if h_type == "linear":
-    S = [(normalvariate(0, 1) + I*normalvariate(0, 1))*(p^di - 1) for di, p in zip(degrees, CP.gens())]
-    if f_type == "structured":
-        system = [f"t*({ft}) + (1 - t)*({fs})" for ft, fs in zip(T, S)]
-    else:
-        system = [str(CPt.gens()[0]*CPt(ft) + (1 - CPt.gens()[0])*CPt(fs)) for ft, fs in zip(T, S)]
-
-    exps = [[str(CC(exp(k*2*CC.gen()*pi/di))) for k in range(di)] for di in degrees]
-    
-    if args.paths == "all":
-        fiber = list(itertools.product(*exps))
-    else:
-        n_paths = int(args.paths)
-        fiber = [[choice(exp) for exp in exps] for _ in range(n_paths)]
-
-elif h_type == "newton":
-    z = vector(CC, [normalvariate(0, 1) + I*normalvariate(0, 1) for _ in range(n)])
-    fiber = [list(z/z.norm())]
-    
-    D = {}
-    for z, v in zip(fiber[0], CP.gens()):
-        D[str(v)] = z
-    
-    T_fiber = [sage_eval(str(f), D) for f in T]
-
-    if f_type == "structured":
-        system = [f"{f} - (1 - t)*({c})" for f, c in zip(T, T_fiber)]
-    else:
-        system = [str(CPt(f) - (1 - CPt.gens()[0])*CPt(c)) for f, c in zip(T, T_fiber)]
-    fiber = [[str(zi) for zi in z] for z in fiber]
-
-name = h_type + "_" + '-'.join(args.type) + "_" + args.paths + "-paths"
-
-index = 1
-while os.path.exists(name + "_" + str(index) + ".json"):
-    index += 1
-
-print("Writting on test data file ...")
-
-data_file = open("data/" + name + "_" + str(index) + ".json", "w")
-json.dump({"system": system, "variables": variables, "parameters": [parameter], "path": [["0.0"], ["1.0"]], "fiber": fiber}, data_file, indent = 2)
-data_file.close()
\ No newline at end of file
+problem = ProblemCtx()
+problem.to_json()
diff --git a/runtest.py b/runtest.py
index 63c72f3183af404b855dadafb2f0e931163e3f20..eed04fc7147c6dad8f8f01536be5b502d0311e70 100644
--- a/runtest.py
+++ b/runtest.py
@@ -5,6 +5,7 @@ import json
 import signal
 import re
 from datetime import datetime
+from pathlib import Path
 
 parser = argparse.ArgumentParser(description = "A description")
 parser.add_argument("pkg", help = "The package which is tested. Should be packages/<pkg_name>.py e.g. packages/algpath.py")
@@ -15,26 +16,28 @@ parser.add_argument("-m", "--mem", nargs = "?", const = "8G", help = "Maximum am
 parser.add_argument("-n", "--norun", action = 'store_true', default = False, help = "To only generate script and command")
 args = parser.parse_args()
 
-pkg = args.pkg
-data = args.data
+pkg_path = Path(args.pkg)
+data_path = Path(args.data)
 
-assert os.path.exists(data)and os.path.exists(pkg), "Specify correct data and pkg file."
+assert data_path.exists() and pkg_path.exists(), "Specify correct data and pkg file."
 
-data_str = os.path.basename(os.path.splitext(data)[0])
-pkg_str = os.path.basename(os.path.splitext(pkg)[0])
+data = data_path.stem
+pkg = pkg_path.stem
+
+print(f"Benchmarking {pkg} on {data_path}" + args.perf*" (with perf stat)")
 
-print(f"Benchmarking {pkg_str} on {data_str}" + args.perf*" (with perf stat)")
 print("Creating benchmark folder...")
-subprocess.run(["mkdir", "-p", "benchmarks"])
-os.chdir("benchmarks")
-subprocess.run(["mkdir", "-p", data_str])
-os.chdir(data_str)
-subprocess.run(["mkdir", "-p", pkg_str])
-os.chdir(pkg_str)
-print("Generating script and command...")
-subprocess.run(["python3", f"../../../{pkg}", f"../../../{data}"])
-subprocess.run(["chmod", "+x", "command.sh"])
+bench_path = (Path("benchmarks").joinpath(*data_path.with_suffix("").parts[1:]) / pkg_path.with_suffix(""))
+bench_path.mkdir(parents=True, exist_ok=True)
 
+print("Generating script and command...")
+absolute_pkg_path = pkg_path.resolve()
+absolute_data_path = data_path.resolve()
+absolute_bench_path = bench_path.resolve()
+os.chdir(bench_path)
+subprocess.run(["python3", f"{absolute_pkg_path}", f"{absolute_data_path}"])
+subprocess.run(["chmod", "+x", str(absolute_bench_path / "command.sh")])
+# assert 1 == 0
 
 if not args.norun:
     print(f"Timeout: {args.timeout}")
diff --git a/synthesize.py b/synthesize.py
index ea574dcf55982aa3a9327c69b5af10195661a010..7b4d97c250d7ba5a797c6ce7b195cc83bba5a46e 100644
--- a/synthesize.py
+++ b/synthesize.py
@@ -3,6 +3,7 @@ import os
 import numpy
 import argparse
 import math
+from pathlib import Path
 
 parser = argparse.ArgumentParser(description = "A python script to generate a table of results out of given entries.")
 parser.add_argument("entries", help = "A JSON file containing entries.")
@@ -10,7 +11,7 @@ args = parser.parse_args()
 
 
 # Recovering data
-assert os.path.exists(args.entries), "Specify valid path"
+assert Path(args.entries), "Specify valid path"
 
 entries_file = open(args.entries, "r")
 try:
@@ -148,8 +149,8 @@ def degrees(data):
 
 #. Formulas for the different statistics to computes
 data_stats = {
-    "raw name": lambda data: data.replace("_", "\_"),
-    "name": lambda data: data.split("_")[1].split("-")[0] + " *"*(not "all" in data) + " \\textsuperscript{N}"*("newton" in data),
+    "raw name": lambda data: data.replace("/", "\_"),
+    "name": lambda data: data.split("/")[1].split("-")[0] + " *"*(not "all" in data) + " \\textsuperscript{N}"*("newton" in data),
     "dimension": lambda data: len(json.load(open(f"data/{data}.json", "r"))["system"]),
     "max deg": lambda data: int(max(degrees(data))),
     "paths": lambda data: len(json.load(open(f"data/{data}.json", "r"))["fiber"]),
diff --git a/tables/all/entries.json b/tables/all/entries.json
index d68ad9f23e217ef17a2d64f124a7901319d5c634..1f51623b7564b7c32e9a0c25015da9b87c89f053 100644
--- a/tables/all/entries.json
+++ b/tables/all/entries.json
@@ -1,46 +1,46 @@
 {
     "data_list": [
-        "linear_dense-10_all-paths_1",
-        "linear_dense-20_all-paths_1",
-        "linear_dense-30_all-paths_1",
-        "linear_dense-40_all-paths_1",
-        "linear_dense-50_all-paths_1",
-        "linear_dense-100_all-paths_1",
-        "linear_dense-500_all-paths_1",
-        "linear_dense-1000_all-paths_1",
-        "linear_dense-5-5_all-paths_1",
-        "linear_dense-10-10_all-paths_1",
-        "linear_dense-20-20_all-paths_1",
-        "linear_dense-30-30_all-paths_1",
-        "linear_dense-40-40_all-paths_1",
-        "linear_dense-50-50_all-paths_1",
-        "linear_katsura-4_all-paths_1",
-        "linear_katsura-6_all-paths_1",
-        "linear_katsura-8_all-paths_1",
-        "linear_katsura-10_all-paths_1",
-        "linear_katsura-15_all-paths_1",
-        "linear_katsura-20_all-paths_1",
-        "linear_katsura-25_100-paths_1",
-        "linear_katsura-30_100-paths_1",
-        "linear_katsura-40_100-paths_1",
-        "linear_dense-3-3-3-3_100-paths_1",
-        "linear_dense-3-3-3-3-3-3_100-paths_1",
-        "linear_dense-3-3-3-3-3-3-3-3_100-paths_1",
-        "linear_structured-4-3-5_100-paths_1",
-        "linear_structured-6-3-5_100-paths_1",
-        "linear_structured-8-3-5_100-paths_1",
-        "newton_structured-5-5-5_all-paths_1",
-        "newton_structured-10-10-5_all-paths_1",
-        "newton_structured-15-15-5_all-paths_1",
-        "newton_structured-20-20-5_all-paths_1",
-        "newton_structured-25-25-5_all-paths_1",
-        "newton_structured-30-30-5_all-paths_1",
-        "newton_dense-3-3-3-3_all-paths_1",
-        "newton_dense-3-3-3-3-3-3_all-paths_1",
-        "newton_dense-3-3-3-3-3-3-3-3_all-paths_1",
-        "newton_structured-4-3-5_all-paths_1",
-        "newton_structured-6-3-5_all-paths_1",
-        "newton_structured-8-3-5_all-paths_1"
+        "linear/dense-10/all/1",
+        "linear/dense-20/all/1",
+        "linear/dense-30/all/1",
+        "linear/dense-40/all/1",
+        "linear/dense-50/all/1",
+        "linear/dense-100/all/1",
+        "linear/dense-500/all/1",
+        "linear/dense-1000/all/1",
+        "linear/dense-5-5/all/1",
+        "linear/dense-10-10/all/1",
+        "linear/dense-20-20/all/1",
+        "linear/dense-30-30/all/1",
+        "linear/dense-40-40/all/1",
+        "linear/dense-50-50/all/1",
+        "linear/katsura-4/all/1",
+        "linear/katsura-6/all/1",
+        "linear/katsura-8/all/1",
+        "linear/katsura-10/all/1",
+        "linear/katsura-15/all/1",
+        "linear/katsura-20/all/1",
+        "linear/katsura-25/random-100/1",
+        "linear/katsura-30/random-100/1",
+        "linear/katsura-40/random-100/1",
+        "linear/dense-3-3-3-3/random-100/1",
+        "linear/dense-3-3-3-3-3-3/random-100/1",
+        "linear/dense-3-3-3-3-3-3-3-3/random-100/1",
+        "linear/sumpowlin-4-3-5/random-100/1",
+        "linear/sumpowlin-6-3-5/random-100/1",
+        "linear/sumpowlin-8-3-5/random-100/1",
+        "newton/sumpowlin-5-5-5/1",
+        "newton/sumpowlin-10-10-5/1",
+        "newton/sumpowlin-15-15-5/1",
+        "newton/sumpowlin-20-20-5/1",
+        "newton/sumpowlin-25-25-5/1",
+        "newton/sumpowlin-30-30-5/1",
+        "newton/dense-3-3-3-3/1",
+        "newton/dense-3-3-3-3-3-3/1",
+        "newton/dense-3-3-3-3-3-3-3-3/1",
+        "newton/sumpowlin-4-3-5/1",
+        "newton/sumpowlin-6-3-5/1",
+        "newton/sumpowlin-8-3-5/1"
     ],
     "header": {
         "val": "root",
diff --git a/tables/all/table.json b/tables/all/table.json
index 0de6ac1cabbc6f6d4444544ed0e6a40d967becc2..bff098b932341c8c7d99193e77d2530c6de6fd0d 100644
--- a/tables/all/table.json
+++ b/tables/all/table.json
@@ -132,7 +132,7 @@
         "w": 1
       },
       {
-        "str": 10,
+        "str": "",
         "w": 1
       },
       {
@@ -218,7 +218,7 @@
         "w": 1
       },
       {
-        "str": 20,
+        "str": "",
         "w": 1
       },
       {
@@ -304,7 +304,7 @@
         "w": 1
       },
       {
-        "str": 30,
+        "str": "",
         "w": 1
       },
       {
@@ -390,7 +390,7 @@
         "w": 1
       },
       {
-        "str": 40,
+        "str": "",
         "w": 1
       },
       {
@@ -460,7 +460,7 @@
         "w": 1
       },
       {
-        "str": 50,
+        "str": "",
         "w": 1
       },
       {
@@ -530,7 +530,7 @@
         "w": 1
       },
       {
-        "str": 100,
+        "str": "",
         "w": 1
       },
       {
@@ -600,7 +600,7 @@
         "w": 1
       },
       {
-        "str": 500,
+        "str": "",
         "w": 1
       },
       {
@@ -686,7 +686,7 @@
         "w": 1
       },
       {
-        "str": 1000,
+        "str": "",
         "w": 1
       },
       {
@@ -768,15 +768,15 @@
         "w": 1
       },
       {
-        "str": 2,
+        "str": "",
         "w": 1
       },
       {
-        "str": 5,
+        "str": "",
         "w": 1
       },
       {
-        "str": 25,
+        "str": "",
         "w": 1
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diff --git a/tables/katsura_20_all_paths/entries.json b/tables/katsura_20_all_paths/entries.json
index 6dfc9f346688bd0081e9c419c9c1c96f0c2e609a..d61019aa21e25fa85280d0ed897a086859fd10c2 100644
--- a/tables/katsura_20_all_paths/entries.json
+++ b/tables/katsura_20_all_paths/entries.json
@@ -1,6 +1,6 @@
 {
     "data_list": [
-        "linear_katsura-20_all-paths_1"
+        "linear/katsura-20/all/1"
     ],
     "header": {
         "val": "root",
diff --git a/tables/katsura_20_all_paths/table.json b/tables/katsura_20_all_paths/table.json
index 0e13a1492f532dcc603b9a03a2594a5548f20d02..b8182c8d9f3c04e1e51e2a11b12226672fee1a9d 100644
--- a/tables/katsura_20_all_paths/table.json
+++ b/tables/katsura_20_all_paths/table.json
@@ -100,7 +100,7 @@
   "table": [
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