Coverage for local/lib/python2.7/site-packages/sage/libs/symmetrica/sb.pxi : 74%

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(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(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 or i <= 0: 

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