test_that("Miscellaneous wedge functionality", {

        dx <- as.kform(1)
        dy <- as.kform(2)
        dz <- as.kform(3)

        expect_true(is.empty(dx ^  0))
        expect_true(is.empty(0  ^ dx))

        expect_true(arity(dx)               ==1)
        expect_true(arity(dx ^ dx)          ==2)
        expect_true(arity(dx ^ dx ^ dx)     ==3)
        expect_true(arity(dx ^ dx ^ dx ^ dx)==4)
        
        expect_true(is.empty(Alt(0  ^ dx)))
        expect_true(is.empty(Alt(dx ^  0)))

        expect_true(is.empty(dx ^ dx))
        expect_true(is.empty(dy ^ dy))
        expect_true(is.empty(dz ^ dz))
      
        expect_true(dx ^ dy ^ dz == dy ^ dz ^ dx)
        expect_true(dx ^ dy ^ dz == dz ^ dx ^ dy)

        expect_true(is.empty((dx ^ dx) ^ (dy ^ dz)))
        expect_true(is.empty((dy ^ dz) ^ (dx ^ dx)))

        expect_true(is.empty(dx ^ dy ^ dz - dy ^ dz ^ dx))
        expect_true(is.empty(dx ^ dy ^ dz - dz ^ dx ^ dy))
        expect_true(is.empty(dx ^ dy ^ dz + dx ^ dz ^ dy))

        expect_true(is.empty(dx ^ dy ^ dz ^ dx))

        expect_true( (dx ^ dy) ^ dz == dx ^ (dy ^ dz))

        expect_true(dx ^ dy ^ dz + dx ^ dy ^ dx == dx ^ dy ^ dz)

        expect_true(nrow(index(kform_general(4,2))) == 6)
        expect_true(kform_general(4,2) + dx ^ dx == kform_general(4,2))

        expect_true(is.empty(grad(1:5) ^ grad(1:5)))
        expect_false(is.empty(grad(1:5) ^ grad(1:6)))


        expect_true(as.function(0*rtensor(k=3,n=7))(matrix(rnorm(21),ncol=3))==0)
        expect_true(as.function(as.ktensor(0*rform(k=3,n=7)))(matrix(rnorm(21),ncol=3))==0)

        expect_true(is.volume(dx))
        expect_true(is.volume(dx,1))
        expect_false(is.volume(dx,2))

        expect_false(is.volume(dy))
        expect_false(is.volume(dy,1))
        expect_false(is.volume(dy,2))

        expect_true(is.volume(dx ^ dy))

        expect_false(is.volume(dy ^ dx,1))
        expect_true (is.volume(dy ^ dx,2))
        expect_false(is.volume(dy ^ dx,3))

        expect_true(all(sapply(1:10,function(n){is.volume(d(seq_len(n)))})))

        expect_true(hodge(dx,3) == dy^dz)
        expect_true(is.scalar(hodge(dx,lose=FALSE)))
        expect_true(hodge(dx,lose=TRUE) == 1)

        expect_true(hodge(dx,2) == dy)
        expect_true(hodge(dx,3) == dy^dz)

        expect_true(hodge(dy,2) == -dx)
        expect_true(hodge(dy,3) == -dx^dz)
        expect_error(hodge(dy,1))

        expect_true(hodge(dz,3) == dx^dy)

        expect_true(coeffs(scalar(5)) == 5)


        expect_true(identical(`0form`(5),scalar(5)))
        expect_true(identical(`0tensor`(5),scalar(5,kform=FALSE)))

})

test_that("Miscellaneous tensor functionality", {
        expect_true(is.empty(as.ktensor(1+diag(5),0)))
        expect_false(is.empty(as.ktensor(1+diag(5))))

        a  <- as.ktensor(matrix(1,1,2))
        a0 <- as.ktensor(matrix(1,1,2))

        expect_true(arity(a )==2)
        expect_true(arity(a0)==2)
        expect_true(arity(a  %X% a   )==4)
        expect_true(arity(a  %X% a0  )==4)
        expect_true(arity(a0 %X% a   )==4)
        expect_true(arity(a0 %X% a0  )==4)
        
})

test_that("as.symbolic() functionality", {
        expect_true(is.character(as.symbolic(rtensor())))
        expect_true(is.character(as.symbolic(rform())))
})