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def lyness_jespersen_06():
a0, a1 = [(3 + i * sqrt(3)) / 6 for i in [+1, -1]]
weights, points = concat(
s3(+frac(9, 20)), s2([-frac(1, 60), 0]), s1([+frac(1, 10), a0, a1])
)
return T2Scheme("Lyness-Jespersen 6", weights, points, 4, source)
def taylor_wingate_bos_1():
weights, points = s2([frac(2, 3), frac(1, 6)])
weights /= 2
return T2Scheme("Taylor-Wingate-Bos 1", weights, points, 2, source)
def laursen_gellert_02b():
weights, points = s2([frac(1, 3), frac(1, 2)])
return T2Scheme("Laursen-Gellert 2b", weights, points, 2, source)
def laursen_gellert_15a():
weights, points = concat(
s3(0.079894504741240),
s2(
[0.071123802232377, 0.425086210602091],
[0.008223818690464, 0.023308867510000],
),
s1(
[0.045430592296170, 0.147925626209534, 0.223766973576973],
[0.037359856234305, 0.029946031954171, 0.358740141864431],
[0.030886656884564, 0.035632559587504, 0.143295370426867],
),
)
return T2Scheme("Laursen-Gellert 15a", weights, points, 10, source)
def liu_vinokur_03():
weights, points = alpha([frac(1, 3), -frac(1, 2)])
return T2Scheme("Liu-Vinokur 3", weights, points, 2, source)
def strang_fix_cowper_06():
weights, points = concat(
s3(3.0 / 8.0), s1([5.0 / 48.0, 0.736712498968435, 0.237932366472434])
)
return T2Scheme("Strang-Fix-Cowper 6", weights, points, 4, source)
def hammer_marlowe_stroud_5():
w1, w2 = [(155 - i * sqrt(15)) / 1200 for i in [+1, -1]]
x1, x2 = [(1 + i * sqrt(15)) / 7 for i in [+1, -1]]
weights, points = concat(s3(frac(9, 40)), r([w1, x1], [w2, x2]))
return T2Scheme("Hammer-Marlowe-Stroud 5", weights, points, 5, source, 2.776e-16)
def witherden_vincent_13():
return T2Scheme("Witherden-Vincent 13", *_read("wv13.json"))
def papanicolopulos_sym_4():
return T2Scheme("Papanicolopulos 4 (full symmetry)", *_read("full04.json"))
def witherden_vincent_14():
return T2Scheme("Witherden-Vincent 14", *_read("wv14.json"))