ideas-0.6: src/Domain/Math/Examples/DWO2.hs
-----------------------------------------------------------------------------
-- Copyright 2010, Open Universiteit Nederland. This file is distributed
-- under the terms of the GNU General Public License. For more information,
-- see the file "LICENSE.txt", which is included in the distribution.
-----------------------------------------------------------------------------
-- |
-- Maintainer : bastiaan.heeren@ou.nl
-- Stability : provisional
-- Portability : portable (depends on ghc)
--
-- Example exercises from the Digital Mathematics Environment (DWO)
--
-----------------------------------------------------------------------------
module Domain.Math.Examples.DWO2 where
import Prelude hiding ((^))
import Domain.Math.Expr
import Domain.Math.Data.Relation
--------------------------------------------------------------------
-- Algemene applet
higherDegreeEquations :: [Equation Expr]
higherDegreeEquations =
let x = variable "x" in
[ x^3 + x^2 :==: 0
, x^3 - 5*x :==: 0
, x^3 - 11*x^2 + 18*x :==: 0
, x^3 + 36*x :==: 13*x^2
, x^3 + 2*x^2 :==: 24*x
, 7*x^3 :==: 8*x^2
, x^4 :==: 9*x^2
, 64*x^7 :==: x^5
, x^3 - 4*x^2 - 9*x :==: 0
, (x-1)*(x^3 - 6*x) :==: 3*x^3 - 3*x^2
]
--------------------------------------------------------------------
-- Havo applets
-- Havo B Voorkennis: lineaire ongelijkheden
ineqLin1 :: [[Inequality Expr]]
ineqLin1 =
let a = Var "a" in
let x = Var "x" in
[ [ 7*x - 12 :<: 5*x + 3
, 4*(x-3) :>: 3*(x-4)
, 6*(a+1) :<: 3*(a-2)+4
, 5 - 2*(a-3) :>: 5*(3-a)
]
, [ 4*x+5 :<: 5*x - 3
, (1/3)*x+10 :>: (1/2)*x
, 3*x+1 :<: 7*x + 5
, x+6 :>: 2 - (3/4)*x
]
, [ 5*(x-1) :<: 7*x - 1
, -3*(4*x-1) :>: 2-(x-1)
, 2*(3*x-1) :<: 5-(2-9*x)
, 2*(x-1)-3*(x-2) :>: 6
]
]
-- Havo B Voorkennis: kwadratische ongelijkheden
-- (door eerst gelijkheid op te lossen)
-- (level 2 uit Hoofdstuk 3)
ineqQuad1 :: [[Inequality Expr]]
ineqQuad1 =
let x = Var "x" in
[ [ x^2 +3*x-4 :<: 0
, x^2-4*x-12 :>: 0
, -x^2 - 4*x + 5 :<: 0
, -x^2 + 3*x + 18 :>: 0
, (1/2)*x^2 - 3*x - 8 :<: 0
, -2*x^2 + 10*x :>: 0
]
, [ x^2 + 9*x :<: 3*x - 5
, x^2 - x :>: 12
, x^2 - 4.5*x :<: 7-3*x
, 2*x^2 - 10*x :>: x^2 - 3*x
, 4*x^2 + 6*x :<: x^2 + 3*x + 18
, 2*x^2 + 6*x - 10 :>: x^2 + 2*x - 5
]
]
-- Havo B hoofdstuk 3, hogeregraadsongelijkheid exact
-- (door eerst gelijkheid op te lossen)
ineqHigh :: [Inequality Expr]
ineqHigh =
let x = Var "x" in
[ 2*x^3 :>: 54
, -0.5*x^4 :<: -40.5
, 1 - 2*x^5 :<: -485
, (2*x-3)^4 :>: 1
, -(0.5*x+2)^3 :<: -1
, 0.25*(0.5*x-2)^4 :<: 4
]
-- Havo B hoofdstuk 3, Hogeregraadsvgl.
higherEq1 :: [[Equation Expr]]
higherEq1 =
let x = Var "x" in
[ [ (1/3)*x^3 :==: 9
, x^5 - 12 :==: 20
, 1 - 8*x^3 :==: -124
, 16 - 32*x^5 :==: - 227
]
, [ 3*x^4 :==: 48
, (1/9)*x^6 + 12 :==: 93
, 39 - 8*x^2 :==: 21
, (1/2)*x^4 - 13 :==: 27.5
]
, [ 3*(2*x-1)^3 + 11 :==: 659
, 0.5*(3*x-4)^5 + 7 :==: 23
, 2*(0.5*x+3)^7 - 11 :==: -9
, 5*(1-4*x)^3 + 4 :==: -621
]
, [ 3*(2*x + 5)^2 + 9 :==: 21
, 2*(3*x-6)^6 - 24 :==: -22
, -2*(4*x-5)^4 + 192 :==: -8000
, (3-2*x)^4 + 23 :==: 279
]
]
--------------------------------------------------------------------
-- VWO A/C applets
-- hoofdstuk 2
ineqQuad2 :: [Inequality Expr]
ineqQuad2 =
let x = Var "x" in
[ x^2 + 9*x :<: 3*x - 5
, x^2 - x :>: 12
, x^2 - 4.5*x :<: 7 - 3*x
, 2*x^2 - 10*x :>: x^2 - 3*x
, 4*x^2 + 6*x :<: x^2 + 3*x + 18
, 2*x^2 + 6*x - 10 :>: x^2 +2*x - 5
]
--------------------------------------------------------------------
-- VWO B applets
-- hoofdstuk 1
higherEq2 :: [[Equation Expr]]
higherEq2 =
let x = Var "x" in
[ [ 2*x^3 + 9 :==: 19
, 4*x^5 - 17 :==: 27
, 3*x^7 + 9 :==: 62
, 5*x^3 - 1 :==: 9
, 6 - 5*x^3 :==: 76
, 11 - 7*x^5 :==: 53
, 4 - 0.2*x^7 :==: 9
, 18 - 11*x^7 :==: 62
]
, [ 0.5*x^4 + 5 :==: 12
, 5*x^6 - 37 :==: 68
, 4*x^8 - 19 :==: 9
, 5*x^6 + 7 :==: 97
, 18 - 7*x^4 :==: -38
, 3 + (1/3)*x^6 :==: 7
, 1 - (1/9)*x^8 :==: -4
, 47 + 15*x^8 :==: 77
]
, [ 18*x^8 - 11 :==: 7
, (1/4)*x^6 + 14 :==: 30
, 5*x^4 + 67 :==: 472
, 5*x^4 - 1 :==: 4
, (1/8)*x^7 + 24 :==: 40
, 0.2*x^3 + 27 :==: 52
, 32*x^3 + 18 :==: 22
, 4*x^3 - 8 :==: 100
]
, [ 14 -2*x^3 :==: 700
, 4-3*x^5 :==: 100
, 14 - 11*x^7 :==: 25
, 1 - 3*x^5 :==: 97
, 3*(x-2)^4 + 7 :==: 37
, 6 - (2*x-1)^3 :==: 1
, (1/3)*(x+5)^6 - 4 :==: 3
, 6 - 0.5*(x-1)^5 :==: 10
]
, [ (1/2)*(3*x-1)^4 :==: 8
, 100-(1/3)*(4*x-3)^5 :==: 19
, 4*(0.5*x+2)^6 + 5 :==: 9
, 3*(2*x + 7)^3 + 11 :==: 35
]
-- (Ontbinden applet)
, [ x^3 - 5*x^2 + 4*x :==: 0
, x^3 :==: 3*x^2 + 10*x
, 14*x :==: x^3 + 5*x^2
, (1/2)*x^3 + 3*x^2 + 4*x :==: 0
, x^3 + 6*x^2 + 9*x :==: 0
, 5*x^2 :==: x^3 + 6*x
, x^3 - 5*x^2 :==: 6*x
, x^3 :==: 4*x^2 + 12*x
]
, [ x^4 + 36 :==: 13*x^2
, x^4 - 9*x^2 + 20 :==: 0
, x^4 :==: 2*x^2 + 3
, x^4 + 2*x^2 :==: 24
, 7*x^2 + 18 :==: x^4
, x^4 :==: x^2 + 12
, 29*x^2 :==: x^4 + 100
, 2*x^4 + 2*x^2 :==: 12
]
-- (abc-form applet)
, [ 4*x^4 + 4 :==: 17*x^2
, 16*x^4 + 225 :==: 136*x^2
, 2*x^4 - 15*x^2 + 25 :==: 0
, 9*x^4 - 28*x^2 + 3 :==: 0
, 3*x^4 - 14*x^2 - 5 :==: 0
, 2*x^4 :==: x^2 + 3
, 9*x^4 + 14*x^2 :==: 8
, 4*x^4 - 29*x^2 - 24 :==: 0
]
, [ 8*x^6 - 9*x^3 + 1 :==: 0
, 27*x^6 + 8 :==: 217*x^3
, 2*x^6 + x^3 - 1 :==: 0
, 8*x^6 + 31*x^3 :==: 4
, 3*x^6 - 80*x^3 - 27 :==: 0
, 5*x^6 :==: 39*x^3 + 8
, 7*x^6 + 8*x^3 + 1 :==: 0
, 4*x^6 + 2 :==: -9*x^3
]
]
--------------------------------------------------------------------
-- Extra test cases
extraIneqQuad :: [Inequality Expr]
extraIneqQuad =
let x = Var "x" in
[ x^2-x-7 :>: -100, x^2-x-7 :<: -100, x^2 :<: x^2, x :>=: x
, x^2 :>=: 0, x^2 :>: 0, x^2 :<: 0, x^2 :<=: 0
]