CoCalc -- final.ipynb

⁶⁷⁸ views
ubuntu1804

Kernel: SageMath 9.8

In [3]:

from lie_algebra_tools import calculatePartition, calculateMultiplicity, findAltSet, printPartitions
print(findAltSet("C2", [2,1],[1,0]))
#print(calculatePartition("A2", [2,1]))
#print(calculatePartition("C2", [2,1], q_analog=True))
print(calculatePartition("A3", [2,1,1]))
print(calculateMultiplicity("C2", [2,1], [1,0], True))
#printPartitions("A2", [4,0,-4], "simple.tex", simple=True, simple_weight=False)

Out[3]:

[1, s2]
4
q^2

In [4]:

print(findAltSet("A4", [1,1,1,1], [-1,-1,-1,-1]))
#print(calculatePartition("A2", [-1,0]))
print(calculateMultiplicity("A4", [1,1,1,1], [-1,-1,-1,-1], True))

Out[4]:

[1, s1, s2, s3, s4, s3*s1, s4*s1, s2*s3, s4*s2, s3*s2, s2*s3*s2]
q^8 + q^7 - q^4

In [50]:

print(calculateMultiplicity("A6", [1,1,1,1,1,1], [0,1,1,0,0,0], True))
print(findAltSet("A6", [1,1,1,1,1,1], [0,1,1,0,0,0]))

Out[50]:

q^4
[1, s4, s5]

In [6]:

A=print(len(findAltSet("A6", [1,1,1,1,1,1], [0,0,0,0,0,-1])))
#print(calculateMultiplicity("A4", [1,1,1,1], [-1,-1,-1,-1], True))

Out[6]:

13

In [7]:

print(calculateMultiplicity("D4", [1,1,1,1], [1,0,0,0], True))

Out[7]:

0

In [8]:

print(findAltSet("C4", [2,2,2,1],[1,0,0,0]))
print(calculateMultiplicity("C4", [2,2,2,1], [1,0,0,0], True))

Out[8]:

[1, s2, s3, s4, s2*s3, s4*s2, s3*s2, s2*s3*s2]
q^6

In [9]:

print(findAltSet("C5", [2,2,2,2,1],[1,0,0,0,0]))
print(calculateMultiplicity("C5", [2,2,2,2,1], [1,0,0,0,0], True))

Out[9]:

[1, s2, s3, s4, s5, s2*s3, s4*s2, s5*s2, s3*s2, s3*s4, s5*s3, s4*s3, s2*s3*s2, s5*s2*s3, s4*s2*s3, s5*s3*s2, s3*s4*s3, s5*s2*s3*s2]
q^8

In [10]:

    print(findAltSet("C6", [2,2,2,2,2,1],[0,0,0,1,1,1]))
print(calculateMultiplicity("C6", [2,2,2,2,2,1], [0,0,0,1,1,1], True))

Out[10]:

[1, s2, s3, s4, s5, s2*s3, s4*s2, s5*s2, s3*s2, s3*s4, s5*s3, s2*s3*s2, s5*s2*s3, s5*s3*s2, s5*s2*s3*s2]
q^8

In [0]:

print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[0,0,0,-1,-1,-1,-1,0,0]))

In [11]:

print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1]))
print(calculateMultiplicity("A9", [1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1], True))

Out[11]:

[1, s2, s4, s6, s4*s2, s6*s2, s6*s4, s6*s4*s2]
q^3 - 3*q^2 + 3*q - 1

In [12]:

print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[0,1,1,0,0,0,0,0,0]))
print(findAltSet("A9", [1,1,1,1,1,1,1,1,1],[0,0,0,0,0,1,1,0,0]))

print(calculateMultiplicity("A9", [1,1,1,1,1,1,1,1,1],[0,1,1,0,0,0,0,0,0], True))
print(calculateMultiplicity("A9", [1,1,1,1,1,1,1,1,1],[0,0,0,0,0,1,1,0,0], True))

Out[12]:

[1, s4, s5, s6, s7, s8, s6*s4, s7*s4, s8*s4, s7*s5, s8*s5, s8*s6, s8*s6*s4]
[1, s2, s3, s4, s5, s8, s4*s2, s5*s2, s8*s2, s5*s3, s8*s3, s8*s4, s8*s5, s8*s4*s2, s8*s5*s2, s8*s5*s3]
q^7
q^7

In [13]:

print(findAltSet("A10", [1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0]))
print(calculateMultiplicity("A10", [1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0], True))

Out[13]:

[1, s2, s4, s6, s4*s2, s6*s2, s6*s4, s6*s4*s2]
q^4 - 3*q^3 + 3*q^2 - q

In [14]:

print(findAltSet("A11", [1,1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0,0]))
print(calculateMultiplicity("A11", [1,1,1,1,1,1,1,1,1,1,1],[1,0,1,0,1,0,1,1,1,0,0], True))

Out[14]:

[1, s2, s4, s6, s10, s4*s2, s6*s2, s10*s2, s6*s4, s10*s4, s10*s6, s6*s4*s2, s10*s4*s2, s10*s6*s2, s10*s6*s4, s10*s6*s4*s2]
q^5 - 3*q^4 + 3*q^3 - q^2

In [15]:

print(findAltSet("A6", [1,1,1,1,1,1],[0,1,1,0,0,0]))
#print(calculatePartition("A2", [2,1]))
#print(calculatePartition("C2", [2,1], q_analog=True))
print(calculatePartition("A3", [2,1,1]))
print(calculateMultiplicity("A6", [1,1,1,1,1,1],[0,1,1,0,0,0], True))

Out[15]:

[1, s4, s5]
4
q^4

In [0]:

In [0]:

In [0]:

In [0]:

In [0]:

In [0]:

In [0]:

In [0]:

In [0]:

In [16]:

11-8

Out[16]:

3

In [0]:

In [0]:

In [0]:

In [17]:

print(calculateMultiplicity("A5",[4,6,8,9,10],[2,4,6,8,10], q_analog=True))

Out[17]:

q^7 + q^6 + 2*q^5 + q^4 + q^3

In [0]:

In [0]:

In [0]:

In [18]:

print(calculatePartition("A2", [2,1], q_analog=True))

Out[18]:

q^3 + q^2

In [0]:

In [19]:

calculateMultiplicity("A2", [-1, 0],[2,1], q_analog=True)

Out[19]:

0

In [20]:

calculateMultiplicity("A2", [5,5],[2,1], q_analog=True)

Out[20]:

q^7 + q^6 + q^5 + q^4

In [21]:

calculateMultiplicity("A2", [5,5],[-1,1], q_analog=True)

Out[21]:

q^10 + q^9 + q^8 + q^7 + q^6 - q^4

In [22]:

calculateMultiplicity("A2", [5,5],[-1,0], q_analog=True)

Out[22]:

q^11 + q^10 + q^9 + q^8 + q^7 + q^6 - q^5

In [23]:

calculateMultiplicity("A2", [5,5],[-3,-4], q_analog=True)

Out[23]:

q^17 + q^16 + q^15 + q^14 + q^13 + q^12 - q^11 - q^10 - q^9 - q^8

In [24]:

calculateMultiplicity("A2", [4,4],[-1,-1],q_analog=True)

Out[24]:

q^10 + q^9 + q^8 + q^7 + q^6 - q^5

In [25]:

calculateMultiplicity("A2", [4,2],[1,0],q_analog=True)

Out[25]:

q^5

In [26]:

calculateMultiplicity("A2", [2,4],[1,0],q_analog=True)

Out[26]:

q^5

In [0]:

In [27]:

calculateMultiplicity("A2", [2,0],[-1,-1], q_analog=True)

Out[27]:

-q^5

In [28]:

calculateMultiplicity("A2", [9,3],[1,0],q_analog=True)

Out[28]:

-q^13 - q^12

In [29]:

calculateMultiplicity("A2", [3,9],[1,0],q_analog=True)

Out[29]:

-q^13 - q^12

In [30]:

calculateMultiplicity("A2", [-1,-1],[0,0],q_analog=True)

Out[30]:

0

In [31]:

calculateMultiplicity("A2", [7,3],[2,1],q_analog=True)

Out[31]:

0

In [32]:

calculateMultiplicity("A2", [3,1],[-1,-1],q_analog=True)

Out[32]:

0

In [33]:

calculateMultiplicity("A2", [11,5],[1,0],q_analog=True)

Out[33]:

0

In [34]:

calculateMultiplicity("A2", [0,-1],[0,-1],q_analog=True)

Out[34]:

-q + 1

In [35]:

calculateMultiplicity("A2", [3,1],[-5,-5],q_analog=True)

Out[35]:

0

In [36]:

calculateMultiplicity("A2", [-1,0],[-1,-1],q_analog=True)

Out[36]:

-q^2

In [37]:

calculateMultiplicity("A2", [1,2],[1,0],q_analog=True)

Out[37]:

q^2

In [38]:

calculateMultiplicity("A2", [-1,0],[-1,0],q_analog=True)

Out[38]:

-q + 1

In [39]:

calculateMultiplicity("A2", [-1,0],[-1,-1],q_analog=True)

Out[39]:

-q^2

In [40]:

calculateMultiplicity("A2", [-1,0],[-1,-2],q_analog=True)

Out[40]:

-q^3 + q^2 + q - 1

In [41]:

calculateMultiplicity("A2", [1,1],[-1,-2],q_analog=True)

Out[41]:

q^5 + q^4 - q^3 - q^2

In [0]:

In [42]:

calculateMultiplicity("A2", [1,1],[-2,-1],q_analog=True)

Out[42]:

q^5 + q^4 - q^3 - q^2

In [43]:

calculateMultiplicity("A2", [1,2],[-2,-1],q_analog=True)

Out[43]:

q^6

In [44]:

calculateMultiplicity("A2", [4,3],[-2,-1],q_analog=True)

Out[44]:

q^10 + q^9 + q^8 - q^4

In [45]:

calculateMultiplicity("A2", [1,1],[1,1],q_analog=True)

Out[45]:

1

In [46]:

calculatePartition("G2", [1,1])

Out[46]:

2

In [47]:

findAltSet("A9", [1,1,1,1,1,1,1,1,1],[1,0,0,0,0,0,0,0,0])

Out[47]:

[1,
 s2,
 s3,
 s4,
 s5,
 s6,
 s7,
 s8,
 s4*s2,
 s5*s2,
 s6*s2,
 s7*s2,
 s8*s2,
 s5*s3,
 s6*s3,
 s7*s3,
 s8*s3,
 s6*s4,
 s7*s4,
 s8*s4,
 s7*s5,
 s8*s5,
 s8*s6,
 s6*s4*s2,
 s7*s4*s2,
 s8*s4*s2,
 s7*s5*s2,
 s8*s5*s2,
 s8*s6*s2,
 s7*s5*s3,
 s8*s5*s3,
 s8*s6*s3,
 s8*s6*s4,
 s8*s6*s4*s2]

In [0]:

In [48]:

print(findAltSet("A4",[1,1,1,1],[1,1,1,1]))

Out[48]:

[1]

In [49]:

print(calculateMultiplicity("A3",[1,1,1],[1,0,0], q_analog=True))

Out[49]:

q^2

In [0]:

Product

Resources

Company