# Regina - A Normal Surface Theory Calculator
# Python Test Suite Component
#
# Copyright (c) 2007-2025, Ben Burton
# For further details contact Ben Burton (bab@debian.org).
#
# Provides some simple tests for arrow polynomials.
#
# This file is a single component of Regina's python test suite.  To run
# the python test suite, move to the main python directory in the source
# tree and run "make check".
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License as
# published by the Free Software Foundation; either version 2 of the
# License, or (at your option) any later version.
#
# As an exception, when this program is distributed through (i) the
# App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or
# (iii) Google Play by Google Inc., then that store may impose any
# digital rights management, device limits and/or redistribution
# restrictions that are required by its terms of service.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program.  If not, see <https://www.gnu.org/licenses/>.

a = Arrow()
print(a, a.isZero())

print('--------')

a.initDiagram(3, 0, 1, 2)
print(a, a.isZero())

try:
    a.initDiagram(3, 0, 'a')
except InvalidArgument:
    print('Exception caught')

try:
    a.initDiagram(1, 1, 0)
except InvalidArgument:
    print('Exception caught')

print(a, a.isZero())
b = Arrow(a)
a += a
print(a, a.isZero(), b, b.isZero())
a -= a
print(a, a.isZero(), b, b.isZero())

print('--------')

a.set(Laurent(-1, [2, 0, 0, -1]))
a.set(1, Laurent(-2, [3, -1]))

try:
    a.set(3, 0)
except InvalidArgument:
    print('Exception caught')

try:
    a.set(2, 0, Laurent(-2, [3, -1]))
except InvalidArgument:
    print('Exception caught')

print(a, a.isZero())

print('--------')

b = Arrow()
b.set(1, Laurent(-2, [3, -1]))
print(b)
print(a + b)
print(a - b)
print(b + a)
print(b - a)
print(- a)

print('--------')

a += b
print(a)
a -= b
print(a)
a -= b
print(a)

print('--------')

a += b
print(a, 'vs', b)
a.swap(b)
print(a, 'vs', b)
swap(b, a)
print(a, 'vs', b)

print('--------')

print(a * -3)
print(-3 * a)
print(a * Laurent(2, [1]))
print(Laurent(2, [1]) * a)

print('--------')

print(a[[]])
print(a[[1]])
print(a[[2]])
print(a[[0, 1]])
a[[0, 1]] = Laurent(3, [2, 0, -5])
print(a)
print(a[[0, 1]])

try:
    print(a[[0, 1, 0]])
except InvalidArgument:
    print('Exception caught')

a[[0, 1]] = Laurent()
print(a)

print('--------')

a *= -3
print(a)
a *= Laurent(2, [1])
print(a)

print('--------')

a.shift(-2)
print(a)
a.negate()
print(a)
a.invertA()
print(a)
a.scaleUp(2)
print(a)
a.scaleDown(-2)
print(a)

print('--------')

print(a.tightEncoding())
print(Arrow.tightDecoding(a.tightEncoding()))
a.init()
print(a, a.isZero())
print(a.tightEncoding())
print(Arrow.tightDecoding(a.tightEncoding()))

print('--------')

print(Arrow([([], Laurent(-4, [1])), ([1], Laurent(-10, [-1,0,0,0,1]))]))
print(Arrow([([], (-4, [1])), ([1], (-10, [-1,0,0,0,1]))]))
print(Arrow([([], (-4, [1])), ([], (-4, [2])), ([1], (-10, [-1,0,0,0,1]))]))
print(Arrow([([], (-4, [1])), ([], (-4, [-1])), ([1], (-10, [-1,0,0,0,1]))]))

try:
    print(Arrow([([], (-4, [1])), ([1, 'a'], (-10, [-1,0,0,0,1]))]))
except InvalidArgument:
    print('Exception caught')

try:
    print(Arrow([([], (-4, [1])), ([1, -2], (-10, [-1,0,0,0,1]))]))
except InvalidArgument:
    print('Exception caught')

laurent = Laurent(-2, [4,0,0,-1])
print(Arrow([([], laurent)]) == laurent)
print(Arrow([([1], laurent)]) == laurent)
print(Arrow([([], laurent), ([1], laurent)]) == laurent)
print(Arrow([([], laurent), ([1], laurent)])[[1]] == laurent)

print('--------')

# Compute some actual arrow polynomials.
# The following examples are all taken from Dye & Kauffman, JKTR 18 (2009).
# These are also in the C++ test suite; see there for further discussion
# (including the reasons why some of our answers differ from Dye-Kauffman).

# Section 3.1: Virtual Hopf link
l = Link.fromData([-1], [[1], [-1]])
print(l); print(l.arrow())

# Section 3.2: Virtualised trefoil (not the virtual trefoil!)
l = Link.fromData([+1, +1, -1], [1, -2, 3, -1, 2, -3])
print(l); print(l.arrow())

# Section 3.3: Kishino's knot
l = Link.fromData([+1, -1, +1, -1], [1, -2, 4, -3, -4, 3, -1, 2])
print(l); print(l.arrow())

# Section 3.4: Slavik's knot
l = Link.fromData([+1, +1, -1, -1, -1], [1, -3, 4, -1, 2, -5, 3, -4, 5, -2])
print(l); print(l.arrow())

# Section 3.5: Miyazawa's knot
# Note: our answer differs by sign (+/-) for the coefficient of K_1^2 A^-4.
# However: our answer is consistent with the Jones polynomial for that same
# knot, and so it seems likely that the sign error is in the Dye-Kauffman paper.
l = Link.fromData([+1, -1, +1, +1], [1, -2, -3, -1, 3, 4, 2, -4])
print(l); print(l.arrow())

# Section 3.6: Two knots differentiated only by K_1 and K_3
l1 = Link.fromSignedGauss('O1-O2-O3-O4+U1-U3-U2-U4+') # knot 4.93
l2 = Link.fromSignedGauss('O1-O2-U3-O4+U2-U1-O3-U4+') # knot 4.103
print(l1); print(l1.arrow());
print(l2); print(l2.arrow());

# Section 3.8: Two virtual torus links
# Note: In the Dye-Kauffman paper, the polynomials for these links do not
# appear to be normalised using the writhe (though this is perhaps explicitly
# noted in the paper since they use the subscript <..>_A instead of <..>_NA.
l1 = Link.fromData([+1, +1, +1], [[1, -2, 3], [-1, 2, -3]])
l2 = Link.fromData([-1, -1, -1], [[3, -2, 1], [-1, 2, -3]])
print(l1); print(l1.arrow());
print(l2); print(l2.arrow());