Nothing
test_that("Sum of the e_i is zero.", {
omega1 <- 1.4 - 1i
omega2 <- 1.6 + 0.5i
omega <- c(omega1, omega2)
e1 <- wp(omega1, omega = omega)
e2 <- wp(omega2, omega = omega)
e3 <- wp(-omega1-omega2, omega = omega)
expect_equal(e1 + e2 + e3, 0i)
})
test_that("Relations involving the e_i.", {
omega1 <- 1.4 - 1i
omega2 <- 1.6 + 0.5i
omega <- c(omega1, omega2)
e1 <- wp(omega1, omega = omega)
e2 <- wp(omega2, omega = omega)
e3 <- wp(-omega1-omega2, omega = omega)
g2g3 <- ellipticInvariants(c(omega1, omega2))
g2 <- g2g3[1L]
g3 <- g2g3[2L]
expect_equal(
g2^3 - 27*g3^2,
16*(e1-e2)^2*(e2-e3)^2*(e3-e1)^2
)
expect_equal(
3*g2/2,
(e1-e2)^2 + (e2-e3)^2 + (e3-e1)^2
)
})
test_that("Differential equation.", {
z <- 1 + 1i
g2 <- 5 + 3i
g3 <- 2 + 7i
g <- c(g2, g3)
pw <- wp(z, g)
pwprimesquared <- wp(z, g, derivative = 1)^2
expect_equal(
pwprimesquared,
4*pw**3 - g2*pw - g3
)
})
test_that("Differential equation second derivative.", {
z <- 1 + 1i
g2 <- 5 + 3i
g3 <- 2 + 7i
g <- c(g2, g3)
pw <- wp(z, g)
pwprimeprime <- wp(z, g, derivative = 2)
expect_equal(
pwprimeprime,
6*pw**2 - g2/2
)
})
test_that("wpprime value.", {
z <- 0.1 + 0.1i
g2 <- 2 + 1i
g3 <- 2 - 1i
g <- c(g2, g3)
wpprime <- wp(z, g, derivative = 1)
expect_equal(
wpprime,
500.009714501399 + 500.03085572727i,
tolerance = 1e-4
)
})
test_that("Equianharmonic case.", {
omega2 <- gamma(1/3)^3 / 4 / pi
z0 <- omega2 * (1 + 1i/sqrt(3))
expect_equal(
wp(z0, g = c(0, 1)), 0i
)
expect_equal(
wp(Conj(z0), g = c(0, 1)), 0i
)
})
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