diff --git a/elm-stuff/0.19.1/Fractions.elmi b/elm-stuff/0.19.1/Fractions.elmi
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diff --git a/elm-stuff/0.19.1/Fractions.elmo b/elm-stuff/0.19.1/Fractions.elmo
new file mode 100644
index 0000000..dda0638
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diff --git a/elm-stuff/0.19.1/OverloadTest.elmi b/elm-stuff/0.19.1/OverloadTest.elmi
new file mode 100644
index 0000000..3c47a81
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diff --git a/elm-stuff/0.19.1/OverloadTest.elmo b/elm-stuff/0.19.1/OverloadTest.elmo
new file mode 100644
index 0000000..c3e157c
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diff --git a/elm-stuff/0.19.1/ParserMaths.elmi b/elm-stuff/0.19.1/ParserMaths.elmi
new file mode 100644
index 0000000..acd12a3
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new file mode 100644
index 0000000..f4dd32b
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diff --git a/elm-stuff/0.19.1/QCM.elmo b/elm-stuff/0.19.1/QCM.elmo
index 027b78e..7a15134 100644
Binary files a/elm-stuff/0.19.1/QCM.elmo and b/elm-stuff/0.19.1/QCM.elmo differ
diff --git a/elm-stuff/0.19.1/d.dat b/elm-stuff/0.19.1/d.dat
index 29f9b58..5432b3b 100644
Binary files a/elm-stuff/0.19.1/d.dat and b/elm-stuff/0.19.1/d.dat differ
diff --git a/elm-stuff/0.19.1/i.dat b/elm-stuff/0.19.1/i.dat
index f94a490..3f1cca2 100644
Binary files a/elm-stuff/0.19.1/i.dat and b/elm-stuff/0.19.1/i.dat differ
diff --git a/elm-stuff/0.19.1/o.dat b/elm-stuff/0.19.1/o.dat
index 5e931e4..c6edbbe 100644
Binary files a/elm-stuff/0.19.1/o.dat and b/elm-stuff/0.19.1/o.dat differ
diff --git a/elm.json b/elm.json
index 70e6ec9..3acf662 100644
--- a/elm.json
+++ b/elm.json
@@ -9,7 +9,8 @@
             "elm/browser": "1.0.2",
             "elm/core": "1.0.5",
             "elm/html": "1.0.0",
-            "elm/parser": "1.1.0"
+            "elm/parser": "1.1.0",
+            "lynn/elm-arithmetic": "3.0.0"
         },
         "indirect": {
             "elm/json": "1.1.3",
diff --git a/src/Fractions.elm b/src/Fractions.elm
new file mode 100644
index 0000000..6396b80
--- /dev/null
+++ b/src/Fractions.elm
@@ -0,0 +1,56 @@
+module Fractions exposing (..)
+
+import Arithmetic exposing (gcd)
+
+type alias Frac = { num : Int, den : Int }
+
+simplifier a =
+  let
+    pgcd = gcd a.num a.den
+    sgnDuDen =
+      if a.den < 0 then -1 else 1
+  in
+  Frac (sgnDuDen*a.num // pgcd) (sgnDuDen*a.den // pgcd)
+  --{ a | num = a.num // pgcd, den = a.den // pgcd }
+
+estEntier a = .den (simplifier a) == 1
+
+add a b =
+  simplifier <| Frac (a.num*b.den + a.den*b.num) (a.den*b.den)
+
+neg a = simplifier <| Frac (-a.num) a.den
+
+sub a b = simplifier <| add a (neg b)
+
+mul a b = simplifier <| Frac (a.num*b.num) (a.den*b.den)
+
+inv a = simplifier <| Frac a.den a.num
+
+div a b = simplifier <| mul a (inv b)
+
+exp : Frac -> Frac -> Maybe Frac
+exp a b =
+  let
+    aa = simplifier a
+    bb = simplifier b
+    sgnDeA =
+      if aa.num < 0 then -1 else 1
+    sgnDeB =
+      if bb.num < 0 then -1 else 1
+  in
+  if bb.den == 1 && bb.num < 0 then
+    Just <| Frac ((sgnDeA*aa.den)^(sgnDeB*bb.num)) ((sgnDeA*aa.num)^(sgnDeB*bb.num))
+  else if bb.den == 1 then
+    Just <| Frac (aa.num^bb.num) (aa.den^bb.num)
+  else
+    Nothing
+
+-- À utiliser sur une fraction simplifier !
+teX a
+  = case a.den of
+    1 -> String.fromInt a.num
+    _ ->
+      if a.num < 0 then
+        "-\\frac{" ++ String.fromInt (-a.num) ++ "}{" ++ String.fromInt a.den ++ "}"
+      else
+        "\\frac{" ++ String.fromInt a.num ++ "}{" ++ String.fromInt a.den ++ "}"
diff --git a/src/ParserMaths.elm b/src/ParserMaths.elm
new file mode 100644
index 0000000..c8d6d4a
--- /dev/null
+++ b/src/ParserMaths.elm
@@ -0,0 +1,236 @@
+module ParserMaths exposing (parseMaths, evaluer, montrerErreurs)
+
+import Fractions as F
+import Maybe as M
+import Parser exposing (..)
+
+montrerErreurs : String -> List DeadEnd -> String
+montrerErreurs source errs =
+    case List.head errs of
+        Nothing ->
+            ""
+
+        Just firstErr ->
+            source
+                ++ "\n"
+                ++ String.repeat (firstErr.col - 1) " "
+                ++ "^"
+                ++ "\nL'algorithme attendait :"
+                ++ String.join
+                    " ou "
+                    (List.map displayExpected errs)
+
+
+displayExpected : DeadEnd -> String
+displayExpected err =
+    case err.problem of
+        ExpectingNumber ->
+            "un nombre entier"
+        ExpectingSymbol s ->
+            "un \"" ++ s ++ "\""
+        _ ->
+            "une expression"
+
+
+evaluer : Expr -> Maybe F.Frac
+evaluer expression =
+    case expression of
+        Add a b ->
+            M.map2 F.add (evaluer a) (evaluer b)
+
+        Sub a b ->
+            M.map2 F.sub (evaluer a) (evaluer b)
+
+        Mul a b ->
+            M.map2 F.mul (evaluer a) (evaluer b)
+
+        Div a b ->
+            M.map2 F.div (evaluer a) (evaluer b)
+
+        Exp a b ->
+            case M.map2 F.exp (evaluer a) (evaluer b) of
+                Nothing -> Nothing
+                Just p -> p
+
+        Neg a ->
+            M.map F.neg (evaluer a)
+
+        Grouping l ->
+            evaluer l
+
+        Entier n ->
+            Just <| F.Frac n 1
+
+
+type Expr
+    = Add Expr Expr
+    | Sub Expr Expr
+    | Mul Expr Expr
+    | Div Expr Expr
+    | Exp Expr Expr
+    | Neg Expr
+    | Entier Int
+    | Grouping Expr
+
+
+parseMaths : String -> Result (List DeadEnd) Expr
+parseMaths source =
+    run expr source
+
+
+expr : Parser Expr
+expr =
+    add
+
+
+type Operator
+    = MulOp
+    | DivOp
+    | AddOp
+    | SubOp
+    | ExpOp
+
+
+type Operand
+    = NoOperand
+    | Operand Operator Expr
+
+
+binary : Expr -> Operand -> Expr
+binary a b =
+    case b of
+        NoOperand ->
+            a
+
+        Operand op e ->
+            case op of
+                MulOp ->
+                    Mul a e
+
+                DivOp ->
+                    Div a e
+
+                AddOp ->
+                    Add a e
+
+                SubOp ->
+                    Sub a e
+
+                ExpOp ->
+                    Exp a e
+
+
+add : Parser Expr
+add =
+    succeed
+        foldBinary
+        |= mul
+        |. spaces
+        |= loop [] addHelper
+
+
+foldBinary : Expr -> List Operand -> Expr
+foldBinary left operands =
+    List.foldr
+    (\operand expression -> binary expression operand)
+    left
+    operands
+
+
+addHelper : List Operand -> Parser (Step (List Operand) (List Operand))
+addHelper operands =
+    oneOf
+        [ succeed (\right -> Loop (Operand AddOp right :: operands))
+            |. symbol "+"
+            |. spaces
+            |= lazy (\_ -> mul)
+        , succeed (\right -> Loop (Operand SubOp right :: operands))
+            |. symbol "-"
+            |. spaces
+            |= lazy (\_ -> mul)
+        , succeed ()
+            |> map (\_ -> Done operands)
+        ]
+
+
+mul : Parser Expr
+mul =
+    succeed
+        foldBinary
+        |= exp
+        |. spaces
+        |= loop [] mulHelper
+
+
+mulHelper : List Operand -> Parser (Step (List Operand) (List Operand))
+mulHelper operands =
+    oneOf
+        [ succeed (\right -> Loop (Operand MulOp right :: operands))
+            |. symbol "*"
+            |. spaces
+            |= lazy (\_ -> exp)
+        , succeed (\right -> Loop (Operand DivOp right :: operands))
+            |. symbol "/"
+            |. spaces
+            |= lazy (\_ -> exp)
+        , succeed ()
+            |> map (\_ -> Done operands)
+        ]
+
+
+exp : Parser Expr
+exp =
+    succeed
+        binary
+        |= primary
+        |. spaces
+        |= oneOf
+            [ succeed (Operand ExpOp)
+                |. symbol "^"
+                |. spaces
+                |= lazy (\_ -> exp)
+            , succeed NoOperand
+            ]
+
+
+primary : Parser Expr
+primary =
+    succeed (\op literal ->
+            case op of
+                Nothing ->
+                    literal
+
+                Just _ ->
+                    Neg literal
+        )
+    |= oneOf
+        [ succeed Just
+            |= symbol "-"
+        , succeed Nothing
+        ]
+    |= oneOf
+        [ grouping
+        , nombre
+        ]
+
+
+nombre : Parser Expr
+nombre =
+    succeed Entier
+        |= number
+            { int = Just identity
+            , hex = Nothing
+            , octal = Nothing
+            , binary = Nothing
+            , float = Nothing
+            }
+
+
+grouping : Parser Expr
+grouping =
+    succeed Grouping
+        |. symbol "("
+        |. spaces
+        |= lazy (\_ -> expr)
+        |. spaces
+        |. symbol ")"
\ No newline at end of file
diff --git a/src/QCM.elm b/src/QCM.elm
index 185fab2..eaae4a9 100644
--- a/src/QCM.elm
+++ b/src/QCM.elm
@@ -3,7 +3,9 @@ module QCM exposing (..)
 import Browser
 import Parser as P exposing (Parser, (|.), (|=), succeed, symbol, float, spaces)
 import List as L
+import ParserMaths as PM
 import String as S
+import Fractions as F exposing (Frac)
 import Html exposing (Html, Attribute, button, div, input, text, p)
 import Html.Attributes exposing (..)
 import Html.Events exposing (onInput, onClick)
@@ -81,6 +83,17 @@ view model =
     <| input [ placeholder "Format de la question", value model.question, onInput Question ] []
     :: button [ onClick GenererQuestion ] [ text "Générer les questions" ]
     :: ( p [] <| L.map text model.questions )
+    :: [ text
+      (
+        let expressionParseePotentielle = PM.parseMaths "3+(2/3)^-2/3"
+        in
+        case expressionParseePotentielle of
+          Err erreur -> "L'expression est mal formée."
+          Ok expressionParsee ->
+            case Maybe.map F.teX <| PM.evaluer <| expressionParsee of
+              Just a -> a
+              Nothing -> "Les puissances non-entières ne sont pas acceptées."
+      ) ]
 
     {-
     , [ dl05 [0, 4, 2] 5 ]
@@ -109,8 +122,8 @@ view model =
     , List.map dl04 ( mix [ [-5,-3,-1,1,3,5], [-6,-4,-2,2,4,6], [0], [-9,-8,-7,-6,-5,-4,-3,-2,-1] ] )  --324 possibilités Ok
     , List.concat <| List.map ( mapTwist [3,5,9] ) ( List.map dl05 ( mix [ [0], [2,4,7,8,11,13,16,17], [2,4,7,8,11,13,16,17] ] ) )  -- 192 possibilités OK
     , d3 -- 512 possibilités OK
-    -}
     :: ( List.map primitPoly01 <| mix [ List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3, List.range -3 -2 ++ List.range 2 3 ] ) -- 256 possibilités OK
+    -}
 
 
 {-
@@ -161,10 +174,9 @@ texteSansVariables
 expressionVariable : Parser TexteVariable
 expressionVariable
   = succeed Variable
-  |. symbol "#("
-  |= (P.getChompedString <|
-    succeed ()
-    |. P.chompUntil "#")
+  |. symbol "#"
+  |= P.getChompedString ( P.chompUntil "#" )
+  |. symbol "#"
 
 {--
 testDeChomp
diff --git a/src/QCMbis.elm b/src/QCMbis.elm
deleted file mode 100644
index a806beb..0000000
--- a/src/QCMbis.elm
+++ /dev/null
@@ -1,583 +0,0 @@
-module QCMbis exposing (..)
-
--- Press buttons to increment and decrement a counter.
---
--- Read how it works:
---   https://guide.elm-lang.org/architecture/buttons.html
---
-
-
-import Browser
-import Html exposing (Html, button, div, text, p)
-import Html.Events exposing (onClick)
-
-
-
--- MAIN
-
-
-main =
-  Browser.sandbox { init = init, update = update, view = view }
-
-
-
--- MODEL
-
-
-type alias Model = Int
-
-
-init : Model
-init =
-  0
-
-
-
--- UPDATE
-
-
-type Msg
-  = Increment
-  | Decrement
-
-
-update : Msg -> Model -> Model
-update msg model =
-  case msg of
-    Increment ->
-      model + 1
-
-    Decrement ->
-      model - 1
-
-
-
--- VIEW
-
-
-view : Model -> Html Msg
-view model =
-  div [] ( List.concat
-    [
-    {--
-    , [ dl10 [0, 4, 2] 5 ]
-    , [ text ( poly [0, 0, 7, -3, 0 , 2, 1 , -1 , 3 , 1, 1, 1, 5] ) ]
-    , [ primitPoly02 [2,-5,1,7] ]
-    , [ primitLn02 [-5,-6] ]
-    , [ equaDiff04 -5 ]
-    , [ equaDiff05 [4, -5] ]
-    , [ equaDiff06 [4, -5] ]
-    , [ derivPoly03 [4, -5, 3, 5, 13] ]
-    , [ derivPoly04 [-3, -4, 2, 7, -13] ]
-    , [ dl06 [-5, -2, 2, -1] ]
-    , [ dl07 [-5, 0, -2, -1] ]
-    , [ dl08 [0, -8, 0, 7] ]
-    , [ dl09 [-1, 2, 0, -3] ]
-    --}
-      List.map equaDiff04 <| List.range -9 -2 -- 98 possibilités
-    , List.map equaDiff05 ( mix [ [3,5,7], [-2,-4,-7,-8] ] )  -- 99 possibilités
-    , List.map equaDiff06 ( mix [ [3,5,7], [-2,-4,-7,-8] ] )  -- 99 possibilités
-    , List.map derivPoly03 ( mix [ [4,6], List.range -7 -6, List.range 2 3, List.range 11 12 ] )  -- 576 possibilités
-    , List.map derivPoly04 ( mix [ [-5,-3], [-4,-2], [2,6], List.range -14 -13 ] )  -- 256 possibilités
-    , List.map primitLn02 ( mix [ List.range -3 -2 ++ List.range 2 3, List.range -5 -4 ++ List.range 5 6 ] )  -- 256 possibilités
-    , List.map primitPoly02 ( mix [ List.range -3 -2 , List.range 2 3, List.range -5 -4 , List.range 6 7 ] )  -- 256 possibilités
-    , List.map dl06 ( mix [ [-3,5], [-2,6], [2,3], [-2,3] ] )  -- 648 possibilités
-    , List.map dl07 ( mix [ [-5,-2,2], [0], [-3,-4], [-2,3] ] )  -- 300 possibilités
-    , List.map dl08 ( mix [ [0], [-3,-2,2,3], [0], [2,3,4,5] ] )  -- 162 possibilités
-    , List.map dl09 ( mix [ [-5,3,5], [-6,4], [0], [-5,-3] ] )  --324 possibilités
-    , List.concat <| List.map ( mapTwist [3,5,9] ) ( List.map dl10 ( mix [ [0], [2,4], [7,8] ] ) )  -- 192 possibilités
-    , d3 -- 729 possibilités
-    ] 
-  )
-
-{--
-type Fonction num
-  = Const num
-  | X
-  | Poly List num
-  | Exp Fonction
-  | Ln Fonction
-  | Sin Fonction
-  | Cos Fonction
---}
-
-
-mathTeX a = "$" ++ a ++ "$"
-
-fonction a = "x\\mapsto " ++ a
-
-affineExp a b c
-  = if (a,b) == (0,0) then "0"
-    else if (a,c) == (0,1) then String.fromInt b ++ "e^x"
-    else if a == 0 then String.fromInt b ++ "e^{" ++ (String.fromInt c) ++ "x}"
-    else if (a,b,c) == (1,0,1) then "xe^x"
-    else if (b,c) == (0,1) then (String.fromInt a) ++ "x" ++ "e^x"
-    else if b == 0 then (String.fromInt a) ++ "x" ++ "e^{" ++ (String.fromInt c) ++ "x}"
-    else if c == 1 then "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^x"
-    else "\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}"
-
-derivExp02 a b c =
-  let
-    f aa bb cc = mathTeX ( fonction ( affineExp aa bb cc ) )
-    vr aa bb cc = p [] [ text ( "+" ++ ( f aa bb cc) ) ]
-    fx aa bb cc = p [] [ text ( "-" ++ ( f aa bb cc) ) ]
-  in
-  div []
-    [ p [] [ text ("Donner la dérivée de la fonction " ++ f a b c) ]
-    , vr (a*c) (a+b*c) c
-    , fx (a+b) a c
-    , fx (a+b) a c
-    , fx (a+b*c) (a*c) c
-    , fx (a-b*c) (a*c) c
-    , fx (a-b*c) (a*c) c
-    , fx a 0 c
-    , fx (a*c) 0 c
-    , fx a 0 1
-    , fx (a*c) 0 1
-    {--
-    , p [] [ text ("----") ]
-    , p [] [ text ("Avant toute chose, il faut bien voir que $\\left(" ++ (String.fromInt a) ++ "x+" ++ (String.fromInt b) ++ "\\right)e^{" ++ (String.fromInt c) ++ "x}$ est de la forme $uv$ avec $u=ax+b$ et $v=e^{cx}$.") ],
-    , p [] [ text ("Ensuite, il faut savoir que la dérivée de $uv$ est donnée par $u'v+uv'$, et que la dérivée de $e^{u}$ est donnée par $e^{u}\\cdot u'$, ce qui dans notre cas nous donne que la dérivée de $e^{" ++ (String.fromInt c) ++ "x}$ est donnée par $" ++ (String.fromInt c) ++ "e^{" ++ (String.fromInt c) ++ "x}$.") ]
-    , p [] [ text ("Nous avons donc que la dérivée de la fonction est :") ]
-    , p [] [ text ("$\\begin{array}{rl} x\\mapsto & " ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt c) ++ "x}+\\left(" ++ (String.fromInt (a)) ++ "x+" ++ (String.fromInt (b)) ++ "\\right)ce^{" ++ (String.fromInt (c)) ++ "x}\\\\& =" ++ (String.fromInt (a)) ++ "e^{" ++ (String.fromInt (c)) ++ "x}+\\left(" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a)) ++ "+" ++ (String.fromInt (a*c)) ++ "x+" ++ (String.fromInt (b*c)) ++ "\\right)e^{" ++ (String.fromInt (c)) ++ "x}\\\\ & =\\left(" ++ (String.fromInt (a+b*c)) ++ "+" ++ (String.fromInt (a*c)) ++ "x\\right)e^{" ++ (String.fromInt (c)) ++ "x} \\end{array}$") ]
-    --}
-    , p [] [ text ("==== Dérivées, Exponentielle, derivExp02") ]
-    ]
-
-
-
--- Des DL
-
-monome a n =
-  if a == 0 then ""
-  else if n == 0 then ( String.fromInt a )
-  else if (n,a) == (1,1) then "x"
-  else if (n,a) == (1,-1) then "-x"
-  else if n == 1 then ( String.fromInt a ) ++ "x"
-  else if a == 1 then "x^{" ++ ( String.fromInt n ) ++ "}"
-  else if a == -1 then "-x^{" ++ ( String.fromInt n ) ++ "}"
-  else ( String.fromInt a ) ++ "x^{" ++ ( String.fromInt n ) ++ "}"
-
-poly a_ks =
-  if a_ks == [] then "0"
-  else polyBis a_ks ( List.length a_ks - 1 )
-
-polyBis a_ks n =
-  case a_ks of
-    [] -> ""
-    a_n :: a_kss ->
-      if a_n == 0 then polyBis a_kss ( n - 1 )
-      else ( monome a_n n ) ++ ( polyGen a_kss ( n - 1 ) )
-
-polyGen a_ks n =
-  case a_ks of
-    [] -> ""
-    a_i :: a_is ->
-      if a_i <= 0 then ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) )
-      else "+" ++ ( monome a_i n ) ++ ( polyGen a_is ( n - 1 ) )
-
-dl a_ks =
-  if a_ks == [] then "0"
-  else dlBis a_ks 0
-
-dlBis a_ks n =
-  case a_ks of
-    [] -> ""
-    premierCoef :: suite ->
-      if premierCoef == 0 then dlBis suite ( n + 1 )
-      else ( monome premierCoef n ) ++ ( dlGen suite ( n + 1 ) )
-
-dlGen a_ks n =
-  case a_ks of
-    [] -> ""
-    a_i :: a_is ->
-      if a_i <= 0 then ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) )
-      else "+" ++ ( monome a_i n ) ++ ( dlGen a_is ( n + 1 ) )
-
-dl06 a_k =
-  let
-    vr texte = p [] [ text ( "+" ++ texte ) ]
-    fx texte = p [] [ text ( "-" ++ texte ) ]
-  in
-  div []
-    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
-    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
-    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
-    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
-    , vr "$C$ est au-dessus de $T_0$."
-    , fx "$C$ est au-dessous de $T_0$."
-    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
-    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Développements limités, Tangentes, dl06") ]
-    ]
-
-
-dl07 a_k =
-  let
-    vr texte = p [] [ text ( "+" ++ texte ) ]
-    fx texte = p [] [ text ( "-" ++ texte ) ]
-  in
-  div []
-    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
-    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
-    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
-    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 3 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 3 a_k ) ++"x$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx "$C$ est au-dessus de $T_0$."
-    , vr "$C$ est au-dessous de $T_0$."
-    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
-    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Développements limités, Tangentes, dl07") ]
-    ]
-
-
-dl08 a_k =
-  let
-    vr texte = p [] [ text ( "+" ++ texte ) ]
-    fx texte = p [] [ text ( "-" ++ texte ) ]
-  in
-  div []
-    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
-    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
-    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
-    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx "$C$ est au-dessus de $T_0$."
-    , fx "$C$ est au-dessous de $T_0$."
-    , vr "$C$ est au-dessous puis au-dessus de $T_0$."
-    , fx "$C$ est au-dessus puis au-dessous de $T_0$."
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Développements limités, Tangentes, dl08") ]
-    ]
-
-
-dl09 a_k =
-  let
-    vr texte = p [] [ text ( "+" ++ texte ) ]
-    fx texte = p [] [ text ( "-" ++ texte ) ]
-  in
-  div []
-    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 3 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
-    , p [] [ text ( "On note $C$ la courbe représentative de $f$ et $T_0$ sa tangente en son point d'abscisse $0$." ) ]
-    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
-    , vr <| "L'équation de $T_0$ est $y=" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $y=" ++ poly ( List.take 2 a_k ) ++"$" -- ATTENTION à éviter les cas où a_0 = a_1
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.reverse <| List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $f\\left(x\\right)\\approx" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx <| "L'équation de $T_0$ est $" ++ poly ( List.take 2 a_k ) ++"$"
-    , fx "$C$ est au-dessus de $T_0$."
-    , fx "$C$ est au-dessous de $T_0$."
-    , fx "$C$ est au-dessous puis au-dessus de $T_0$."
-    , vr "$C$ est au-dessus puis au-dessous de $T_0$."
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Développements limités, Tangentes, dl09") ]
-    ]
-
-
-dl10 a_k k = -- À n'utiliser qu'avec a_0 = 0 !!!
-  let
-    coefLin =
-      case a_k of
-        [] -> 0
-        a_0 :: [] -> 0
-        a_0 :: a_1 :: a_ks -> a_1
-    coefQuad =
-      case a_k of
-        [] -> 0
-        a_0 :: [] -> 0
-        a_0 :: a_1 :: [] -> 0
-        a_0 :: a_1 :: a_2 :: a_ks -> a_2
-    vr a b = p [] [ text <| "+$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ]
-    ffx a b = p [] [ text <| "-$\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt b ++ "}$" ]
-    fx a = p [] [ text <| "-$" ++ String.fromInt a ++ "$" ]
-  in
-  div []
-    [ p [] [ text ( "On considère une fonction $f$ dont le développement limité à l'ordre 2 au voisinage de $0$ est " ++ mathTeX ( dl a_k ) ++ "." ) ]
-    , p [] [ text <| "Que vaut $\\lim\\limits_{x\\to0}\\frac{f\\left(x\\right)}{" ++ (String.fromInt k) ++ "x}$" ]
-    , vr coefLin k
-    , ffx 1 coefLin
-    , ffx 1 coefQuad
-    , ffx 1 k
-    , ffx coefQuad k
-    , ffx k coefQuad
-    , fx coefLin
-    , fx coefQuad
-    , fx k
-    , fx 1
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Développements limités, Tangentes, dl10") ]
-    ]
-
-
-mapTwist a b = List.map b a
-
-entiers = List.range 2 4
-
-d1 = List.map derivExp02 entiers
-
-d2 = List.concat ( List.map (mapTwist entiers) d1 )
-
-d3 = List.concat ( List.map (mapTwist entiers) d2 )
-
-mix lls =
-  case lls of
-    [] -> []
-    [] :: llss -> []
-    l :: [] -> List.map List.singleton l
-    (a :: ls) :: llss -> ( List.map ( (::) a ) ( mix llss ) ) ++ mix ( ls :: llss )
-
-derivPoly03 param = -- on donne a pair et positif, les deux racines x_1 < x_2, d, et m > x_2
-  case param of
-    [] -> div [] []
-    a :: [] -> div [] []
-    a :: b :: [] -> div [] []
-    a :: b :: c :: [] -> div [] []
-    a :: b :: c :: d :: [] -> div [] []
-    a :: b :: c :: d :: e :: a_ks -> derivPoly03Bis a b c d e
-
-derivPoly03Bis a x_1 x_2 d m =
-  let
-    b = 0 - 3*a*(x_1 + x_2)//2
-    c = 3*a*x_1*x_2
-    a_k = [a,b,c,d]
-    vr texte = p [] [ text ( "+" ++ texte ) ]
-    fx texte = p [] [ text ( "-" ++ texte ) ]
-  in
-  div []
-    [ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ]
-    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
-    , vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$."
-    , fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$."
-    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
-    , vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
-    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$"
-    , vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt m ++ ";+\\infty\\right[$"
-    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
-    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Dérivée, Polynômes, derivPoly03") ]
-    ]
-
-derivPoly04 param = -- on donne a impair et négatif, les deux racines x_1 < x_2 pairs distincs, d, et m < x_1
-  case param of
-    [] -> div [] []
-    a :: [] -> div [] []
-    a :: b :: [] -> div [] []
-    a :: b :: c :: [] -> div [] []
-    a :: b :: c :: d :: [] -> div [] []
-    a :: b :: c :: d :: e :: a_ks -> derivPoly04Bis a b c d e
-
-derivPoly04Bis a x_1 x_2 d m =
-  let
-    b = 0 - 3*a*(x_1 + x_2)//2
-    c = 3*a*x_1*x_2
-    a_k = [a,b,c,d]
-    vr texte = p [] [ text ( "+" ++ texte ) ]
-    fx texte = p [] [ text ( "-" ++ texte ) ]
-  in
-  div []
-    [ p [] [ text ( "On considère la fonction $f:x\\mapsto " ++ ( poly a_k ) ++ "$." ) ]
-    , p [] [ text ( "Cocher la ou les réponses correctes." ) ]
-    , vr <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly <| polyD a_k ) ++ "$."
-    , fx <| "La dérivée de $f$ est la fonction $f\\prime:x\\mapsto " ++ ( poly [3*a, 2*b, c + d] ) ++ "$."
-    , vr <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
-    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";" ++ String.fromInt x_2 ++ "\\right]$"
-    , vr <| "la fonction $f$ est décroissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right]$"
-    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left]-\\infty;" ++ String.fromInt m ++ "\\right[$"
-    , fx <| "la fonction $f$ est croissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
-    , fx <| "la fonction $f$ est décroissante sur l'intervalle $\\left[" ++ String.fromInt x_1 ++ ";+\\infty\\right[$"
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Dérivée, Polynômes, derivPoly04") ]
-    ]
-
-polyD a_ks = polyDbis a_ks ( List.length a_ks - 1 )
-
-polyDbis a_ks n =
-  case a_ks of
-    [] -> []
-    a_0 :: [] -> []
-    a_k :: a_kss -> ( n*a_k ) :: polyDbis a_kss ( n - 1 ) 
-
-equaDiff04 a = -- a négatif
-  let
-    f aa = mathTeX ( fonction ( aa ) )
-    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
-    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
-  in
-  div []
-    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y$ ?" ]
-    , vr <| String.fromInt ( a - 1 ) ++ "e^{" ++ String.fromInt a ++ "x}"
-    , vr <| String.fromInt ( a + 4 ) ++ "e^{" ++ String.fromInt a ++ "x}"
-    , vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}"
-    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt (a-1) ++ "x}"
-    , fx <| String.fromInt ( a - 3 ) ++ "e^x"
-    , fx <| String.fromInt ( a + 7 ) ++ "e^x" ++ String.fromInt a
-    , fx <| String.fromInt a ++ "e^x"
-    , fx <| String.fromInt a ++ "e^x+" ++ String.fromInt ( a + 100)
-    , fx <| String.fromInt ( a - 1 ) ++ "e^x+" ++ String.fromInt ( a + 100)
-    , fx <| String.fromInt ( a - 8 ) ++ "e^{" ++ String.fromInt (a-1) ++ "x}" ++ String.fromInt a
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Équations différentielles, equaDiff04") ]
-    ]
-
-equaDiff05 param =
-  case param of
-    [] -> div [] []
-    a :: [] -> div [] []
-    a :: b :: c -> equaDiff05Bis a b
-
-equaDiff05Bis a b = -- a positif, b négatif, pas de simplification
-  let
-    f aa = mathTeX ( fonction ( aa ) )
-    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
-    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
-  in
-  div []
-    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $" ++ String.fromInt a ++"y'=" ++ String.fromInt b ++ "y$ ?" ]
-    , vr <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
-    , vr <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
-    , fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
-    , fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
-    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
-    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt b ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Équations différentielles, equaDiff05") ]
-    ]
-
-equaDiff06 param =
-  case param of
-    [] -> div [] []
-    a :: [] -> div [] []
-    a :: b :: c -> equaDiff06Bis a b
-
-equaDiff06Bis a b = -- a positif, b négatif, pas de simplification
-  let
-    f aa = mathTeX ( fonction ( aa ) )
-    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
-    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
-  in
-  div []
-    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des solutions de l'équation différentielle $y'=" ++ String.fromInt a ++ "y" ++ String.fromInt b ++"$ ?" ]
-    , fx <| String.fromInt ( a - 17 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
-    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
-    , fx <| String.fromInt ( a + 3 ) ++ "e^{\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}x}"
-    , fx <| String.fromInt ( a - 17 ) ++ "e^{\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
-    , fx <| String.fromInt ( a + 23 ) ++ "e^{-\\frac{" ++ String.fromInt a ++ "}{" ++ String.fromInt (0 - b) ++ "}x}"
-    , fx <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , vr <| String.fromInt a ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , fx <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}-\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , vr <| String.fromInt b ++ "e^{" ++ String.fromInt a ++ "x}+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    , fx <| "e^x+\\frac{" ++ String.fromInt (0 - b) ++ "}{" ++ String.fromInt a ++ "}"
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Équations différentielles, equaDiff06") ]
-    ]
-
-primitLn02 a_k =
-  case a_k of
-    [] -> div [] []
-    a :: [] -> div [] []
-    a :: b :: c -> primitLn02Bis a b
-
-primitLn02Bis a b =
-  let
-    f aa = mathTeX ( fonction ( aa ) )
-    vr aa = p [] [ text ( "+" ++ ( f aa ) ) ]
-    fx aa = p [] [ text ( "-" ++ ( f aa ) ) ]
-    axpb = poly [a,b]
-  in
-  div []
-    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f <| "\\frac{" ++ String.fromInt a ++ "}{" ++ axpb ++ "}" ) ++ " ?" ]
-    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)"
-    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)+" ++ String.fromInt ( b + 30 )
-    , vr <| "\\ln\\left(" ++ axpb ++ "\\right)" ++ String.fromInt ( a - 20)
-    , fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
-    , fx <| "\\frac{" ++ String.fromInt (a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 )
-    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
-    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( b + 30 )
-    , fx <| "\\frac{" ++ String.fromInt (0 - a*a) ++ "}{" ++ axpb ++ "}" ++ String.fromInt ( a - 20)
-    , fx <| "\\frac{" ++ poly [a*a, a*b+a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
-    , fx <| "\\frac{" ++ poly [a*a, a*b-a*a] ++ "}{\\left(" ++ axpb ++ "\\right)^2}"
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Primitives, Logarithme, primitLn02") ]
-    ]
-
-primitPoly02 a_k =
-  case a_k of
-    [] -> div [] []
-    a :: [] -> div [] []
-    a :: b :: [] -> div [] []
-    a :: b :: c :: [] -> div [] []
-    a :: b :: c :: d :: e -> primitPoly02Bis a b c d
-
-primitPoly02Bis a b c d =
-  let
-    pol = [a,b,c,d,0]
-    polD = polyD pol
-    polDD = polyD polD
-    f a_k = mathTeX ( fonction ( poly a_k ) )
-    vr a_k = p [] [ text ( "+" ++ ( f a_k ) ) ]
-    fx a_k = p [] [ text ( "-" ++ ( f a_k ) ) ]
-  in
-  div []
-    [ p [] [ text <| "Parmi les fonctions ci-dessous, lesquelles sont des primitives de la fonction " ++ ( f polD ) ++ " ?" ]
-    , vr <| List.map2 (+) pol [0,0,0,0,5]
-    , vr <| List.map2 (+) pol [0,0,0,0,-8]
-    , vr <| List.map2 (+) pol [0,0,0,0,8]
-    , fx <| List.map2 (+) polD [0,0,0,8]
-    , fx <| List.map2 (+) polD [0,0,0,-5]
-    , fx <| List.map2 (+) polD [0,0,0,-8]
-    , fx <| List.map2 (+) polDD [0,0,8]
-    , fx <| List.map2 (+) polDD [0,0,-5]
-    , fx <| List.map2 (+) polDD [0,0,-8]
-    {--
-    , p [] [ text ("----") ]
-    --}
-    , p [] [ text ("==== Primitives, Polynômes, primitPoly02") ]
-    ]
-
-
-
-