Download or view functionUtilsTest.frink in plain text format
/** These are tests for the functionUtils.frink library. It demonstrates
how to find derivatives and integrals of functions, including functions
defined in Frink.
*/
use functionUtils.frink
use allTransforms.frink
symbolicMode[true]
showApproximations[false]
// Test with named function
squareFunc[x] := x^2
fSquare = getFunction["squareFunc", 1]
println["Function is: " + inputForm[fSquare]]
derivativeFunc1 = makeDerivative[fSquare]
println["Before solve: $derivativeFunc1"]
derivative1 = transformExpression[derivativeFunc1]
println["Derivative is: $derivative1"]
integral1 = transformExpression[makeIntegral[fSquare]]
println["Integral is: $integral1"]
println["-----------------------------------\n\n"]
// Test with named function (sin) which uses built-in function.
// This needs to recognize that there's no Frink-defined function
// body and use any defined transformations to calculate its derivative.
// For example, the derivative of sin[x] is defined in derivatives.frink.
fSin = getFunction["sin", 1]
println["Function is: " + inputForm[fSin]]
derivativeFunc1 = makeDerivative[fSin]
println["Before solve: $derivativeFunc1"]
derivative1 = transformExpression[derivativeFunc1]
println["Derivative is: $derivative1"]
integral1 = transformExpression[makeIntegral[fSin]]
println["Integral is: $integral1"]
println["-----------------------------------\n\n"]
// Test with anonymous function
anonFunc = { |x| x sin[x] }
println["Function is: " + inputForm[anonFunc]]
derivativeFunc2 = makeDerivative[anonFunc]
println["Before solve: $derivativeFunc2"]
derivative2 = transformExpression[derivativeFunc2]
println["Derivative is: $derivative2"]
println["-----------------------------------\n\n"]
// The following four lines are essentially equivalent because the === is a
// special form of expression that is used for symbolic transformations and
// does not evaluate either side of the expression by default.
//
// solve = makeSolve[noEval[x], noEval[y^3 + 2 y^2 + 3 y + 4], noEval[y]]
// solve = makeSolve[noEval[x === y^3 + 2 y^2 + 3 y + 4], noEval[y]]
// solve = makeSolve[x === y^3 + 2 y^2 + 3 y + 4, noEval[y]]
solve = noEval[solve[x === y^3 + 2 y^2 + 3 y + 4, y]]
println["Going to solve:\t$solve"]
solutions = transformExpression[solve]
for sol = solutions
{
// The solution comes back as something like x === 3 y + 2
// So the right-hand-side (child 1) = (3 y + 2) will be the solution
right = getChild[sol, 1]
println["Solution: $right\n"]
substituted = substituteExpression[right, noEval[x], 2] // Substitute x -> 2
println["Substituted: $substituted\n"]
retransformed = transformExpression[substituted]
if ! structureEquals[substituted, retransformed]
println["Re-Transformed: $retransformed\n"]
println["Evaluated solution: " + eval[retransformed] + "\n"]
println[]
}
Download or view functionUtilsTest.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19971 days, 20 hours, 23 minutes ago.