γράψτε τον αριθμό: α =

  Ανάλυση φυσικού αριθμού σε
 γινόμενο πρώτων παραγόντων 

α = 6272 (slider from 2 to 25000, step 1)
Lα1 = ΠρώτοιΠαράγοντεςΑριθμού(α)
Lα2 = Sequence(α / If[n ≟ 0, 1, Product[Lα1, n]], n, 0, Length[Lα1])
Εισ1 = Textfield(α)
Lα3 = Unique(Lα1)
α1 = Element(Lα3, 1)
α2 = Element(Lα3, 2)
α3 = Element(Lα3, 3)
α4 = Element(Lα3, 4)
α5 = Element(Lα3, 5)
α6 = Element(Lα3, 6)
α7 = Element(Lα3, 7)
α8 = Element(Lα3, 8)
α9 = Element(Lα3, 9)
α1ν = Length(KeepIf[x ≟ α1, Lα1])
α2ν = Length(KeepIf[x ≟ α2, Lα1])
α3ν = Length(KeepIf[x ≟ α3, Lα1])
α4ν = Length(KeepIf[x ≟ α4, Lα1])
α5ν = Length(KeepIf[x ≟ α5, Lα1])
α6ν = Length(KeepIf[x ≟ α6, Lα1])
α7ν = Length(KeepIf[x ≟ α7, Lα1])
α8ν = Length(KeepIf[x ≟ α8, Lα1])
α9ν = Length(KeepIf[x ≟ α9, Lα1])
A1: "" + (LaTeX[α]) + " = " + (LaTeX[((α1 * "^") * α1ν)]) + " " + (LaTeX[If[α2 > 1, "·" + (((α2 * "^") * α2ν)), ""]]) + " " + (LaTeX[If[α3 > 1, "·" + (((α3 * "^") * α3ν)), ""]]) + " " + (LaTeX[If[α4 > 1, "·" + (((α4 * "^") * α4ν)), ""]]) + " " + (LaTeX[If[α5 > 1, "·" + (((α5 * "^") * α5ν)), ""]]) + " " + (LaTeX[If[α6 > 1, "·" + (((α6 * "^") * α6ν)), ""]]) + " " + (LaTeX[If[α7 > 1, "·" + (((α7 * "^") * α7ν)), ""]]) + " " + (LaTeX[If[α8 > 1, "·" + (((α8 * "^") * α8ν)), ""]]) + " " + (LaTeX[If[α9 > 1, "·" + (((α9 * "^") * α9ν)), ""]]) + ""
β = 90
Lx = Sequence("διαιρώ με το " + (Element[Lα1, n]), n, 1, Length[Lα1])
A2 = TableText({Lα2, Lα1, Lx}, "|_vc")
κείμενο2: "Ο αριθμός είναι " + (If[Length[Lα1] ≟ 1, "πρώτος", "σύνθετος"]) + ""

Tool: Πρώτοι Παράγοντες Αριθμού (command ΠρώτοιΠαράγοντεςΑριθμού)
Δώστε ένα δρομέα α με τιμές μεγαλύτερες του 2 ή έναν αριθμό β
Input: a
Output: κα1

λ11 = Sequence(If[Mod[a, k] ≟ 0, Div[a, k], 0], k, 1, a, 1)
λ12 = Sort(λ11)
λ13 = KeepIf((x ≥ 1) ∧ (x ≤ a), λ12)
μ1 = Length(λ13)
α_1 = Element(λ13, 2)
β_1 = Element(λ13, μ1 - 1)
λ21 = Sequence(If[Mod[β_1, k] ≟ 0, Div[β_1, k], 0], k, 1, β_1, 1)
λ22 = Sort(λ21)
λ23 = KeepIf((x ≥ 1) ∧ (x ≤ β_1), λ22)
α_2 = Element(λ23, 2)
μ2 = Length(λ23)
β_2 = Element(λ23, μ2 - 1)
λ31 = Sequence(If[Mod[β_2, k] ≟ 0, Div[β_2, k], 0], k, 1, β_2, 1)
λ32 = Sort(λ31)
λ33 = KeepIf((x ≥ 1) ∧ (x ≤ β_2), λ32)
α_3 = Element(λ33, 2)
μ3 = Length(λ33)
β_3 = Element(λ33, μ3 - 1)
λ41 = Sequence(If[Mod[β_3, k] ≟ 0, Div[β_3, k], 0], k, 1, β_3, 1)
λ42 = Sort(λ41)
λ43 = KeepIf((x ≥ 1) ∧ (x ≤ β_3), λ42)
μ4 = Length(λ43)
α_4 = Element(λ43, 2)
β_4 = Element(λ43, μ4 - 1)
λ51 = Sequence(If[Mod[β_4, k] ≟ 0, Div[β_4, k], 0], k, 1, β_4, 1)
λ52 = Sort(λ51)
λ53 = KeepIf((x ≥ 1) ∧ (x ≤ β_4), λ52)
μ5 = Length(λ53)
α_5 = Element(λ53, 2)
β_5 = Element(λ53, μ5 - 1)
λ61 = Sequence(If[Mod[β_5, k] ≟ 0, Div[β_5, k], 0], k, 1, β_5, 1)
λ62 = Sort(λ61)
λ63 = KeepIf((x ≥ 1) ∧ (x ≤ β_5), λ62)
μ6 = Length(λ63)
α_6 = Element(λ63, 2)
β_6 = Element(λ63, μ6 - 1)
λ71 = Sequence(If[Mod[β_6, k] ≟ 0, Div[β_6, k], 0], k, 1, β_6, 1)
λ72 = Sort(λ71)
λ73 = KeepIf((x ≥ 1) ∧ (x ≤ β_6), λ72)
μ7 = Length(λ73)
α_7 = Element(λ73, 2)
β_7 = Element(λ73, μ7 - 1)
λ81 = Sequence(If[Mod[β_7, k] ≟ 0, Div[β_7, k], 0], k, 1, β_7, 1)
λ82 = Sort(λ81)
λ83 = KeepIf((x ≥ 1) ∧ (x ≤ β_7), λ82)
α_8 = Element(λ83, 2)
κα: {α_1, α_2, α_3, α_4, α_5, α_6, α_7, α_8}
κα1 = RemoveUndefined(κα)

Tool: Ανάλυση Πρώτων Παραγόντων Αριθμού (command ΑνάλυσηΠρώτωνΠαραγόντωνΑριθμού)
Δώστε έναν φυσικό αριθμό >= 2
Input: α
Output: A1, A2, Lα1

Lα1 = ΠρώτοιΠαράγοντεςΑριθμού(α)
Lα2 = Sequence(α / If[n ≟ 0, 1, Product[Lα1, n]], n, 0, Length[Lα1])
A2 = TableText({Lα2, Lα1}, "vr|")
Lα3 = Unique(Lα1)
α1 = Element(Lα3, 1)
α2 = Element(Lα3, 2)
α3 = Element(Lα3, 3)
α4 = Element(Lα3, 4)
α5 = Element(Lα3, 5)
α6 = Element(Lα3, 6)
α7 = Element(Lα3, 7)
α8 = Element(Lα3, 8)
α9 = Element(Lα3, 9)
α1ν = Length(KeepIf[x ≟ α1, Lα1])
α2ν = Length(KeepIf[x ≟ α2, Lα1])
α3ν = Length(KeepIf[x ≟ α3, Lα1])
α4ν = Length(KeepIf[x ≟ α4, Lα1])
α5ν = Length(KeepIf[x ≟ α5, Lα1])
α6ν = Length(KeepIf[x ≟ α6, Lα1])
α7ν = Length(KeepIf[x ≟ α7, Lα1])
α8ν = Length(KeepIf[x ≟ α8, Lα1])
α9ν = Length(KeepIf[x ≟ α9, Lα1])
A1: "" + (LaTeX[α]) + " = " + (LaTeX[((α1 * "^") * α1ν)]) + " " + (LaTeX[If[α2 > 1, "·" + (((α2 * "^") * α2ν)), ""]]) + " " + (LaTeX[If[α3 > 1, "·" + (((α3 * "^") * α3ν)), ""]]) + " " + (LaTeX[If[α4 > 1, "·" + (((α4 * "^") * α4ν)), ""]]) + " " + (LaTeX[If[α5 > 1, "·" + (((α5 * "^") * α5ν)), ""]]) + " " + (LaTeX[If[α6 > 1, "·" + (((α6 * "^") * α6ν)), ""]]) + " " + (LaTeX[If[α7 > 1, "·" + (((α7 * "^") * α7ν)), ""]]) + " " + (LaTeX[If[α8 > 1, "·" + (((α8 * "^") * α8ν)), ""]]) + " " + (LaTeX[If[α9 > 1, "·" + (((α9 * "^") * α9ν)), ""]]) + ""