schubmult.sage_integration

29def FastSchubertPolynomialRing(
30    R,
31    num_vars,
32    varname,
33    *,
34    code_index=False,
35    q_varname="q",
36    quantum=False,
37    indices=tuple([1]),
38):
39    if quantum:
40        QR = PolynomialRing(R, num_vars, q_varname)
41    else:
42        QR = R
43    return FastSchubertPolynomialRing_xbasis(
44        R, num_vars, varname, q_varname, code_index, indices, quantum, QR
45    )

32def FastDoubleSchubertPolynomialRing(
33    R,
34    num_vars,
35    base_variable_name,
36    coeff_variable_names,
37    *,
38    indices=tuple([1]),
39    code_index=False,
40    q_varname="q",
41    quantum=False,
42):
43    """Wrapper function to return a double Schubert polynomial Ring
44
45    Calls the _xbasis class to return a double or quantum double Schubert
46    polynomial ring with the indicated base ring, number of variables,
47    variable names (base variable, and then one or more sets of coefficient)
48    variables, coproduct indices, code_index representation option, q-ring
49    variable name, and whether the ring is quantum.
50
51    Example call:
52
53```python
54X = FastDoubleSchubertPolynomialRing(ZZ, 100, "x", ("y", "z"))
55X([2, 4, 3, 1])
56```
57
58    Args:
59        R (sage ring): The base ring
60        num_vars (int): Cardinality of the sets of variables
61        base_variable_name (str): Base variable name
62        coeff_variable_names (str | tuple[str]): Coefficient variable name(s)
63        indices (tuple[int], optional): Indicies of the variables to split on for the coproduct.
64        code_index (bool, optional): Whether to display the indices as the Lehmer code. Defaults to False.
65        q_varname (str, optional): Variable name of the q-ring. Defaults to "q".
66        quantum (bool, optional): Whether or not the ring is quantum. Default the FAlse.
67
68    Returns:
69        FastDoubleSchubertPolynomialRing_xbasis: Basis element generator of the ring
70    """
71    QR = None
72    if quantum:
73        QR = PolynomialRing(R, num_vars, q_varname)
74    return FastDoubleSchubertPolynomialRing_xbasis(
75        R,
76        num_vars,
77        base_variable_name,
78        coeff_variable_names,
79        q_varname,
80        code_index,
81        indices,
82        quantum,
83        QR,
84    )

48def FastQuantumSchubertPolynomialRing(
49    R, num_vars, varname, *, code_index=False, q_varname="q"
50):
51    return FastSchubertPolynomialRing(
52        R, num_vars, varname, q_varname=q_varname, code_index=code_index, quantum=True
53    )

 87def FastQuantumDoubleSchubertPolynomialRing(
 88    R,
 89    num_vars,
 90    base_variable_name,
 91    coeff_variable_names,
 92    *,
 93    code_index=False,
 94    q_varname="q",
 95):
 96    """Quantum double Schubert ring generator
 97
 98    Wraps FastDoubleSchubertPolynomialRing(), omitting indices and setting
 99    quantum to True.
100    
101    Args:
102        R (sage ring): The base ring
103        num_vars (int): Cardinality of the sets of variables
104        base_variable_name (str): Base variable name
105        coeff_variable_names (str | tuple[str]): Coefficient variable name(s)
106        code_index (bool, optional): Whether to display the indices as the Lehmer code. Defaults to False.
107        q_varname (str, optional): Variable name of the q-ring. Defaults to "q".
108
109    Returns:
110        FastDoubleSchubertPolynomialRing_xbasis: Basis element generator of the quantum ring
111    """
112    return FastDoubleSchubertPolynomialRing(
113        R,
114        num_vars,
115        base_variable_name,
116        coeff_variable_names,
117        code_index=code_index,
118        indices=tuple([1]),
119        quantum=True,
120        q_varname=q_varname,
121    )