## test-symbols.lua

    require 'pl'
    -- force us to look in the script's directory when requiring...
    app.require_here()
    require 'symbols'

    local MT = getmetatable(_1)

    add = MT.__add
    mul = MT.__mul
    pow = MT.__pow

    function testeq (e1,e2)
        if not equals(e1,e2) then
            print ('Not equal',repr(e1),repr(e2))
        end
    end

    sin = register(math.sin,'sin')

    f = register(function(x,y,z) end)

    --[[
    testeq (_1,_1)
    testeq (_1+_2,_1+_2)
    testeq (_1 + 3*_2,_1 + 3*_2)
    testeq (_2+_1,_1+_2)
    testeq (sin(_1),sin(_1))
    testeq (1+f(10,20,'ok'),f(10,20,'ok')+1)
    --]]

    function testexpand (e)
        print(repr(fold(expand(e)))) --fold
    end

    --[[
    testexpand (a*(a+1))

    testexpand ((x+2)*(b+1))
    ]]--

    function testfold (e)
        print(repr(fold(e)))
    end

    a,b,c,x,y = Var 'a,b,c,x,y'

    --~ testfold(_1 + _2)
    --~ testfold(add(10,20))
    --~ testfold(add(mul(2,_1),mul(3,_2)))
    --[[
    testfold(sin(a))
    e = a^(b+2)
    testfold(e)
    bindval(b,1)
    testfold(e)
    bindval(a,2)
    testfold(e)

    bindval(a)
    bindval(b)
    ]]

    function testdiff (e)
        balance(e)
        e = diff(e,x)
        balance(e)
        print('+ ',e)
        e = fold(e)
        print('- ',e)
    end

    testdiff(x^2+1)
    testdiff(3*x^2)
    testdiff(x^2 + 2*x^3)
    testdiff(x^2 + 2*a*x^3 + x^4)
    testdiff(2*a*x^3)
    testdiff(x*x*x)

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