cdef extern from 'symmetrica/def.h':
INT mult_schubert_schubert(OP a, OP b, OP result)
INT m_perm_sch(OP a, OP b)
INT t_SCHUBERT_POLYNOM(OP a, OP b)
INT t_POLYNOM_SCHUBERT(OP a, OP b)
INT mult_schubert_variable(OP a, OP i, OP r)
INT divdiff_perm_schubert(OP perm, OP sb, OP res)
INT scalarproduct_schubert(OP a, OP b, OP c)
INT divdiff_schubert(OP a, OP schub, OP res)
INT t_2SCHUBERT_POLYNOM(OP a,OP b)
INT mult_schubert_polynom(OP a,OP b,OP c)
cdef object _check_schubert(object a, OP ca):
if a in Permutations():
if isinstance(a, builtinlist):
a = Permutation_class(a)
_op_schubert_perm(a, ca)
return max(a.reduced_word()+[0])
elif isinstance(a, SchubertPolynomial_class):
br = a.parent().base_ring()
if (br == QQ or br == ZZ):
_op_schubert_sp(a, ca)
return min([max(i.reduced_word()+[0]) for i in a.support()])
else:
raise ValueError, "a must be a Schubert polynomial over ZZ or QQ"
else:
raise TypeError, "a must be a permutation or a Schubert polynomial"
def mult_schubert_schubert_symmetrica(a, b):
"""
Multiplies the Schubert polynomials a and b.
EXAMPLES:
sage: symmetrica.mult_schubert_schubert([3,2,1], [3,2,1])
X[5, 3, 1, 2, 4]
"""
late_import()
cdef OP ca = callocobject(), cb = callocobject(), cres = callocobject()
try:
max_a = _check_schubert(a, ca)
max_b = _check_schubert(b, cb)
except (ValueError, TypeError), err:
freeall(ca); freeall(cb); freeall(cres)
raise err
sig_on()
mult_schubert_schubert(ca, cb, cres)
sig_off()
res = _py(cres)
freeall(ca)
freeall(cb)
freeall(cres)
return res
def t_SCHUBERT_POLYNOM_symmetrica(a):
"""
Converts a Schubert polynomial to a 'regular' multivariate
polynomial.
EXAMPLES:
sage: symmetrica.t_SCHUBERT_POLYNOM([3,2,1])
x0^2*x1
"""
late_import()
cdef OP ca = callocobject(), cres = callocobject()
try:
max_a = _check_schubert(a, ca)
except (ValueError, TypeError), err:
freeall(ca); freeall(cres)
raise err
sig_on()
t_SCHUBERT_POLYNOM(ca, cres)
sig_off()
res = _py(cres)
freeall(ca)
freeall(cres)
return res
def t_POLYNOM_SCHUBERT_symmetrica(a):
"""
Converts a multivariate polynomial a to a Schubert polynomial.
EXAMPLES:
sage: R.<x1,x2,x3> = QQ[]
sage: w0 = x1^2*x2
sage: symmetrica.t_POLYNOM_SCHUBERT(w0)
X[3, 2, 1]
"""
late_import()
cdef OP ca = callocobject(), cres = callocobject()
if not is_MPolynomial(a):
freeall(ca); freeall(cres)
raise TypeError, "a (= %s) must be a multivariate polynomial"
else:
br = a.parent().base_ring()
if br != QQ and br != ZZ:
freeall(ca); freeall(cres)
raise ValueError, "a's base ring must be either ZZ or QQ"
else:
_op_polynom(a, ca)
sig_on()
t_POLYNOM_SCHUBERT(ca, cres)
sig_off()
res = _py(cres)
freeall(ca)
freeall(cres)
return res
def mult_schubert_variable_symmetrica(a, i):
"""
Returns the product of a and x_i. Note that indexing with i
starts at 1.
EXAMPLES:
sage: symmetrica.mult_schubert_variable([3,2,1], 2)
X[3, 2, 4, 1]
sage: symmetrica.mult_schubert_variable([3,2,1], 4)
X[3, 2, 1, 4, 6, 5] - X[3, 2, 1, 5, 4]
"""
late_import()
cdef OP ca = callocobject(), ci = callocobject(), cres = callocobject()
try:
max_a = _check_schubert(a, ca)
except (ValueError, TypeError), err:
freeall(ca); freeall(ci); freeall(cres)
raise err
_op_integer(i, ci)
sig_on()
mult_schubert_variable(ca, ci, cres)
sig_off()
res = _py(cres)
freeall(ca); freeall(ci); freeall(cres)
return res
def divdiff_perm_schubert_symmetrica(perm, a):
r"""
Returns the result of applying the divided difference operator
$\delta_i$ to $a$ where $a$ is either a permutation or a
Schubert polynomial over QQ.
EXAMPLES:
sage: symmetrica.divdiff_perm_schubert([2,3,1], [3,2,1])
X[2, 1]
sage: symmetrica.divdiff_perm_schubert([3,1,2], [3,2,1])
X[1, 3, 2]
sage: symmetrica.divdiff_perm_schubert([3,2,4,1], [3,2,1])
Traceback (most recent call last):
...
ValueError: cannot apply \delta_{[3, 2, 4, 1]} to a (= [3, 2, 1])
"""
late_import()
cdef OP ca = callocobject(), cperm = callocobject(), cres = callocobject()
try:
max_a = _check_schubert(a, ca)
except (ValueError, TypeError), err:
freeall(ca); freeall(cperm); freeall(cres)
raise err
if perm not in Permutations():
freeall(ca); freeall(cperm); freeall(cres)
raise TypeError, "perm must be a permutation"
else:
perm = Permutation_class(perm)
rw = perm.reduced_word()
max_perm = max(rw)
_op_permutation(perm, cperm)
if max_perm > max_a:
freeall(ca); freeall(cperm); freeall(cres)
raise ValueError, r"cannot apply \delta_{%s} to a (= %s)"%(perm, a)
sig_on()
divdiff_perm_schubert(cperm, ca, cres)
sig_off()
res = _py(cres)
freeall(ca); freeall(cperm); freeall(cres)
return res
def scalarproduct_schubert_symmetrica(a, b):
"""
EXAMPLES:
sage: symmetrica.scalarproduct_schubert([3,2,1], [3,2,1])
X[1, 3, 5, 2, 4]
sage: symmetrica.scalarproduct_schubert([3,2,1], [2,1,3])
X[1, 2, 4, 3]
"""
late_import()
cdef OP ca = callocobject(), cb = callocobject(), cres = callocobject()
try:
max_a = _check_schubert(a, ca)
max_b = _check_schubert(b, cb)
except (ValueError, TypeError), err:
freeall(ca); freeall(cb); freeall(cres)
raise err
sig_on()
scalarproduct_schubert(ca, cb, cres)
sig_off()
if empty_listp(cres):
res = Integer(0)
else:
res = _py(cres)
freeall(ca); freeall(cb); freeall(cres)
return res
def divdiff_schubert_symmetrica(i, a):
r"""
Returns the result of applying the divided difference operator
$\delta_i$ to $a$ where $a$ is either a permutation or a
Schubert polynomial over QQ.
EXAMPLES:
sage: symmetrica.divdiff_schubert(1, [3,2,1])
X[2, 3, 1]
sage: symmetrica.divdiff_schubert(2, [3,2,1])
X[3, 1, 2]
sage: symmetrica.divdiff_schubert(3, [3,2,1])
Traceback (most recent call last):
...
ValueError: cannot apply \delta_{3} to a (= [3, 2, 1])
"""
late_import()
cdef OP ca = callocobject(), ci = callocobject(), cres = callocobject()
try:
max_a = _check_schubert(a, ca)
except (ValueError, TypeError), err:
freeall(ca); freeall(ci); freeall(cres)
raise err
if not isinstance(i, (int, Integer)):
freeall(ca); freeall(ci); freeall(cres)
raise TypeError, "i must be an integer"
else:
_op_integer(i, ci)
if i > max_a:
freeall(ca); freeall(ci); freeall(cres)
raise ValueError, r"cannot apply \delta_{%s} to a (= %s)"%(i, a)
sig_on()
divdiff_schubert(ci, ca, cres)
sig_off()
res = _py(cres)
freeall(ca); freeall(ci); freeall(cres)
return res
