def test_lcs_d():
lcs2 = get_poly_conversion(2)
assert lcs2[0, 0] == -1 / S(2) # xx
assert lcs2[0, 1] == 0 # xy
assert lcs2[0, 2] == 0 # xz
assert lcs2[0, 3] == -1 / S(2) # yy
assert lcs2[0, 4] == 0 # yz
assert lcs2[0, 5] == 1 # zz
def test_lcs_d():
lcs2 = get_poly_conversion(2)
assert lcs2[0,0] == -1/S(2) # xx
assert lcs2[0,1] == 0 # xy
assert lcs2[0,2] == 0 # xz
assert lcs2[0,3] == -1/S(2) # yy
assert lcs2[0,4] == 0 # yz
assert lcs2[0,5] == 1 # zz
def test_lcs_f():
lcs3 = get_poly_conversion(3)
assert lcs3[0, 0] == 0 # xxx
assert lcs3[0, 1] == 0 # xxy
assert lcs3[0, 2] == -3 / S(2) / sqrt(5) # xxz
assert lcs3[0, 3] == 0 # xyy
assert lcs3[0, 4] == 0 # xyz
assert lcs3[0, 5] == 0 # xzz
assert lcs3[0, 6] == 0 # yyy
assert lcs3[0, 7] == -3 / S(2) / sqrt(5) # yyz
assert lcs3[0, 8] == 0 # yzz
assert lcs3[0, 9] == 1 # zzz
def test_lcs_f():
lcs3 = get_poly_conversion(3)
assert lcs3[0,0] == 0 # xxx
assert lcs3[0,1] == 0 # xxy
assert lcs3[0,2] == -3/S(2)/sqrt(5) # xxz
assert lcs3[0,3] == 0 # xyy
assert lcs3[0,4] == 0 # xyz
assert lcs3[0,5] == 0 # xzz
assert lcs3[0,6] == 0 # yyy
assert lcs3[0,7] == -3/S(2)/sqrt(5) # yyz
assert lcs3[0,8] == 0 # yzz
assert lcs3[0,9] == 1 # zzz
def test_lcs_g():
lcs4 = get_poly_conversion(4)
assert lcs4[0, 0] == 3 / S(8) # xxxx
assert lcs4[0, 1] == 0 # xxxy
assert lcs4[0, 2] == 0 # xxxz
assert lcs4[0, 3] == 3 * sqrt(3) / sqrt(35) / S(4) # xxyy
assert lcs4[0, 4] == 0 # xxyz
assert lcs4[0, 5] == -3 * sqrt(3) / sqrt(35) # xxzz
assert lcs4[0, 6] == 0 # xyyy
assert lcs4[0, 7] == 0 # xyyz
assert lcs4[0, 8] == 0 # xyzz
assert lcs4[0, 9] == 0 # xzzz
assert lcs4[0, 10] == 3 / S(8) # yyyy
assert lcs4[0, 11] == 0 # yyyz
assert lcs4[0, 12] == -3 * sqrt(3) / sqrt(35) # yyzz
assert lcs4[0, 13] == 0 # yzzz
assert lcs4[0, 14] == 1 # zzzz
def test_lcs_g():
lcs4 = get_poly_conversion(4)
assert lcs4[0,0] == 3/S(8) # xxxx
assert lcs4[0,1] == 0 # xxxy
assert lcs4[0,2] == 0 # xxxz
assert lcs4[0,3] == 3*sqrt(3)/sqrt(35)/S(4) # xxyy
assert lcs4[0,4] == 0 # xxyz
assert lcs4[0,5] == -3*sqrt(3)/sqrt(35) # xxzz
assert lcs4[0,6] == 0 # xyyy
assert lcs4[0,7] == 0 # xyyz
assert lcs4[0,8] == 0 # xyzz
assert lcs4[0,9] == 0 # xzzz
assert lcs4[0,10] == 3/S(8) # yyyy
assert lcs4[0,11] == 0 # yyyz
assert lcs4[0,12] == -3*sqrt(3)/sqrt(35) # yyzz
assert lcs4[0,13] == 0 # yzzz
assert lcs4[0,14] == 1 # zzzz
def test_lcs_h():
lcs4 = get_poly_conversion(5)
assert lcs4[0, 0] == 0 # xxxxx
assert lcs4[0, 1] == 0 # xxxxy
assert lcs4[0, 2] == 5 / S(8) # xxxxz
assert lcs4[0, 3] == 0 # xxxyy
assert lcs4[0, 4] == 0 # xxxyz
assert lcs4[0, 5] == 0 # xxxzz
assert lcs4[0, 6] == 0 # xxyyy
assert lcs4[0, 7] == sqrt(15) / S(4) / sqrt(7) # xxyyz
assert lcs4[0, 8] == 0 # xxyzz
assert lcs4[0, 9] == -5 / sqrt(21) # xxzzz
assert lcs4[0, 10] == 0 # xyyyy
assert lcs4[0, 11] == 0 # xyyyz
assert lcs4[0, 12] == 0 # xyyzz
assert lcs4[0, 13] == 0 # xyzzz
assert lcs4[0, 14] == 0 # xzzzz
assert lcs4[0, 15] == 0 # yyyyy
assert lcs4[0, 16] == 5 / S(8) # yyyyz
assert lcs4[0, 17] == 0 # yyyzz
assert lcs4[0, 18] == -5 / sqrt(21) # yyzzz
assert lcs4[0, 19] == 0 # yzzzz
assert lcs4[0, 20] == 1 # zzzzz
def test_lcs_h():
lcs4 = get_poly_conversion(5)
assert lcs4[0,0] == 0 # xxxxx
assert lcs4[0,1] == 0 # xxxxy
assert lcs4[0,2] == 5/S(8) # xxxxz
assert lcs4[0,3] == 0 # xxxyy
assert lcs4[0,4] == 0 # xxxyz
assert lcs4[0,5] == 0 # xxxzz
assert lcs4[0,6] == 0 # xxyyy
assert lcs4[0,7] == sqrt(15)/S(4)/sqrt(7) # xxyyz
assert lcs4[0,8] == 0 # xxyzz
assert lcs4[0,9] == -5/sqrt(21) # xxzzz
assert lcs4[0,10] == 0 # xyyyy
assert lcs4[0,11] == 0 # xyyyz
assert lcs4[0,12] == 0 # xyyzz
assert lcs4[0,13] == 0 # xyzzz
assert lcs4[0,14] == 0 # xzzzz
assert lcs4[0,15] == 0 # yyyyy
assert lcs4[0,16] == 5/S(8) # yyyyz
assert lcs4[0,17] == 0 # yyyzz
assert lcs4[0,18] == -5/sqrt(21) # yyzzz
assert lcs4[0,19] == 0 # yzzzz
assert lcs4[0,20] == 1 # zzzzz
