# HG changeset patch # User Mike Hansen # Date 1200867641 28800 # Node ID bbd5815336fbb9a7d8e2f5b18a90c59bcaf0871b # Parent 0f5c616f13f2b9423b071a47023905d5d27b1707 Fixed #1873 diff -r 0f5c616f13f2 -r bbd5815336fb sage/libs/symmetrica/schur.pxi --- a/sage/libs/symmetrica/schur.pxi Sat Jan 19 16:38:26 2008 -0800 +++ b/sage/libs/symmetrica/schur.pxi Sun Jan 20 14:20:41 2008 -0800 @@ -24,7 +24,7 @@ cdef extern from 'symmetrica/def.h': INT t_ELMSYM_MONOMIAL(OP a, OP b) INT t_ELMSYM_HOMSYM(OP a, OP b) - INT t_HOMSYM_SCHUR(OP a, OP b) + INT t_HOMSYM_SCHUR(OP a, OP b) INT t_HOMSYM_MONOMIAL(OP a, OP b) INT t_HOMSYM_ELMSYM(OP a, OP b) @@ -62,6 +62,10 @@ def outerproduct_schur_symmetrica(parta, Of course this can also be interpreted as the decomposition of the outer tensor product of two irreducibe representations of the symmetric group. + + EXAMPLES: + sage: symmetrica.outerproduct_schur([2],[2]) + s[2, 2] + s[3, 1] + s[4] """ cdef OP cparta, cpartb, cresult @@ -108,36 +112,6 @@ def dimension_schur_symmetrica(s): return res -def part_part_skewschur_symmetrica(big, small): - """ - you enter two PARTITION objects big and small, where big is - a partition which contains small, and result becomes a SCHUR - object, which represents the decomposition of the corresponding - skew partition. - - """ - - cdef OP cbig, csmall, cresult - - cbig = callocobject() - csmall = callocobject() - cresult = callocobject() - - _op_partition(big, cbig) - _op_partition(small, csmall) - _sig_on - part_part_skewschur(cbig, csmall, cresult) - _sig_off - res = _py(cresult) - - freeall(cbig) - freeall(csmall) - freeall(cresult) - - return res - - - def newtrans_symmetrica(perm): """ computes the decomposition of a schubertpolynomial labeled by @@ -162,21 +136,40 @@ def newtrans_symmetrica(perm): def compute_schur_with_alphabet_symmetrica(part, length, alphabet='x'): """ - computes the expansion of a schurfunction labeled by a + Computes the expansion of a schurfunction labeled by a partition PART as a POLYNOM erg. The INTEGER length specifies the length of the alphabet. + + EXAMPLES: + sage: symmetrica.compute_schur_with_alphabet(2,2) + x0^2 + x0*x1 + x1^2 + sage: symmetrica.compute_schur_with_alphabet([2],2) + x0^2 + x0*x1 + x1^2 + sage: symmetrica.compute_schur_with_alphabet(Partition([2]),2) + x0^2 + x0*x1 + x1^2 + sage: symmetrica.compute_schur_with_alphabet(Partition([2]),2,'y') + y0^2 + y0*y1 + y1^2 + sage: symmetrica.compute_schur_with_alphabet(Partition([2]),2,'a,b') + a^2 + a*b + b^2 + sage: symmetrica.compute_schur_with_alphabet([2,1],1,'x') + 0 """ late_import() cdef OP cpart = callocobject(), cresult = callocobject(), clength = callocobject() - _op_partition(part, cpart) + if isinstance(part, (int, Integer)): + _op_partition([part], cpart) + elif isinstance(part, (builtinlist, Partition_class)): + _op_partition(part, cpart) + else: + raise NotImplementedError, "n must be an integer or partition" _op_integer(length, clength) _sig_on compute_schur_with_alphabet(cpart, clength, cresult) _sig_off - res = _py_polynom_alphabet(cresult, alphabet) + res = _py_polynom_alphabet(cresult, alphabet, length) freeall(cresult) freeall(cpart) @@ -191,6 +184,19 @@ def compute_homsym_with_alphabet_symmetr The object number may also be a PARTITION or a HOM_SYM object. The INTEGER laenge specifies the length of the alphabet. Both routines are the same. + + EXAMPLES: + sage: symmetrica.compute_homsym_with_alphabet(3,1,'x') + x^3 + sage: symmetrica.compute_homsym_with_alphabet([2,1],1,'x') + x^3 + sage: symmetrica.compute_homsym_with_alphabet([2,1],2,'x') + x0^3 + 2*x0^2*x1 + 2*x0*x1^2 + x1^3 + sage: symmetrica.compute_homsym_with_alphabet([2,1],2,'a,b') + a^3 + 2*a^2*b + 2*a*b^2 + b^3 + sage: symmetrica.compute_homsym_with_alphabet([2,1],2,'x').parent() + Multivariate Polynomial Ring in x0, x1 over Integer Ring + """ late_import() cdef OP cn = callocobject(), clength = callocobject(), cresult = callocobject() @@ -200,7 +206,7 @@ def compute_homsym_with_alphabet_symmetr elif isinstance(n, (builtinlist, Partition_class)): _op_partition(n, cn) else: - raise NotImplementedError, "need to write code for HOM_SYM" + raise NotImplementedError, "n must be an integer or a partition" _op_integer(length, clength) @@ -208,7 +214,7 @@ def compute_homsym_with_alphabet_symmetr compute_homsym_with_alphabet(cn, clength, cresult) _sig_off - res = _py_polynom_alphabet(cresult, alphabet) + res = _py_polynom_alphabet(cresult, alphabet, length) freeall(cresult) freeall(cn) @@ -222,18 +228,35 @@ def compute_elmsym_with_alphabet_symmetr computes the expansion of a elementary symmetric function labeled by a INTEGER number as a POLYNOM erg. The object number may also be a PARTITION or a ELM_SYM object. - The INTEGER laenge specifies the length of the alphabet. + The INTEGER length specifies the length of the alphabet. Both routines are the same. + + EXAMPLES: + sage: a = symmetrica.compute_elmsym_with_alphabet(2,2); a + x0*x1 + sage: a.parent() + Multivariate Polynomial Ring in x0, x1 over Integer Ring + sage: a = symmetrica.compute_elmsym_with_alphabet([2],2); a + x0*x1 + sage: symmetrica.compute_elmsym_with_alphabet(3,2) + 0 + sage: symmetrica.compute_elmsym_with_alphabet([3,2,1],2) + 0 + """ late_import() cdef OP cn = callocobject(), clength = callocobject(), cresult = callocobject() if isinstance(n, (int, Integer)): + if n > length: + return 0 _op_integer(n, cn) elif isinstance(n, (builtinlist, Partition_class)): + if max(n) > length: + return 0 _op_partition(n, cn) else: - raise NotImplementedError, "need to write code for ELM_SYM" + raise NotImplementedError, "n must be an integer or a partition" _op_integer(length, clength) @@ -241,7 +264,7 @@ def compute_elmsym_with_alphabet_symmetr compute_elmsym_with_alphabet(cn, clength, cresult) _sig_off - res = _py_polynom_alphabet(cresult, alphabet) + res = _py_polynom_alphabet(cresult, alphabet, length) freeall(cresult) freeall(cn) @@ -256,18 +279,37 @@ def compute_monomial_with_alphabet_symme function labeled by a PARTITION number as a POLYNOM erg. The INTEGER laenge specifies the length of the alphabet. + EXAMPLES: + sage: symmetrica.compute_monomial_with_alphabet([2,1],2,'x') + x0^2*x1 + x0*x1^2 + sage: symmetrica.compute_monomial_with_alphabet([1,1,1],2,'x') + 0 + sage: symmetrica.compute_monomial_with_alphabet(2,2,'x') + x0^2 + x1^2 + sage: symmetrica.compute_monomial_with_alphabet(2,2,'a,b') + a^2 + b^2 + sage: symmetrica.compute_monomial_with_alphabet(2,2,'x').parent() + Multivariate Polynomial Ring in x0, x1 over Integer Ring + """ late_import() cdef OP cn = callocobject(), clength = callocobject(), cresult = callocobject() - - _op_partition(n, cn) + if isinstance(n, (int, Integer)): + _op_integer(n, cn) + elif isinstance(n, (builtinlist, Partition_class)): + if len(n) > length: + return 0 + _op_partition(n, cn) + else: + raise NotImplementedError, "n must be an integer or a partition" + _op_integer(length, clength) _sig_on compute_monomial_with_alphabet(cn, clength, cresult) _sig_off - res = _py_polynom_alphabet(cresult, alphabet) + res = _py_polynom_alphabet(cresult, alphabet, length) freeall(cresult) freeall(cn) @@ -282,6 +324,19 @@ def compute_powsym_with_alphabet_symmetr function labeled by a INTEGER label or by a PARTITION label or a POW_SYM label as a POLYNOM erg. The INTEGER laenge specifies the length of the alphabet. + + EXAMPLES: + sage: symmetrica.compute_powsym_with_alphabet(2,2,'x') + x0^2 + x1^2 + sage: symmetrica.compute_powsym_with_alphabet(2,2,'x').parent() + Multivariate Polynomial Ring in x0, x1 over Integer Ring + sage: symmetrica.compute_powsym_with_alphabet([2],2,'x') + x0^2 + x1^2 + sage: symmetrica.compute_powsym_with_alphabet([2],2,'a,b') + a^2 + b^2 + sage: symmetrica.compute_powsym_with_alphabet([2,1],2,'a,b') + a^3 + a^2*b + a*b^2 + b^3 + """ late_import() cdef OP cn = callocobject(), clength = callocobject(), cresult = callocobject() @@ -299,7 +354,7 @@ def compute_powsym_with_alphabet_symmetr compute_powsym_with_alphabet(cn, clength, cresult) _sig_off - res = _py_polynom_alphabet(cresult, alphabet) + res = _py_polynom_alphabet(cresult, alphabet, length) freeall(cresult) freeall(cn) @@ -310,22 +365,34 @@ def compute_powsym_with_alphabet_symmetr def compute_schur_with_alphabet_det_symmetrica(part, length, alphabet='x'): """ - computes the expansion of a skewschurfunction labeled by the - SKEWPARTITION skewpart, using the Jacobi Trudi Identity, - the result is the - POLYNOM erg, the length of the alphabet is given by INTEGER length. - + EXAMPLES: + sage: symmetrica.compute_schur_with_alphabet_det(2,2) + x0^2 + x0*x1 + x1^2 + sage: symmetrica.compute_schur_with_alphabet_det([2],2) + x0^2 + x0*x1 + x1^2 + sage: symmetrica.compute_schur_with_alphabet_det(Partition([2]),2) + x0^2 + x0*x1 + x1^2 + sage: symmetrica.compute_schur_with_alphabet_det(Partition([2]),2,'y') + y0^2 + y0*y1 + y1^2 + sage: symmetrica.compute_schur_with_alphabet_det(Partition([2]),2,'a,b') + a^2 + a*b + b^2 """ cdef OP cpart = callocobject(), cresult = callocobject(), clength = callocobject() - _op_partition(part, cpart) + if isinstance(part, (int, Integer)): + _op_partition([part], cpart) + elif isinstance(part, (builtinlist, Partition_class)): + _op_partition(part, cpart) + else: + raise NotImplementedError, "n must be an integer or partition" + _op_integer(length, clength) _sig_on compute_schur_with_alphabet_det(cpart, clength, cresult) _sig_off - res = _py_polynom_alphabet(cresult, alphabet) + res = _py_polynom_alphabet(cresult, alphabet, length) freeall(cresult) freeall(cpart) @@ -333,7 +400,7 @@ def compute_schur_with_alphabet_det_symm return res -def part_part_skewschur_symmetric(outer, inner): +def part_part_skewschur_symmetrica(outer, inner): """ Returns the skew schur function s_{outer/inner} diff -r 0f5c616f13f2 -r bbd5815336fb sage/libs/symmetrica/symmetrica.pxi --- a/sage/libs/symmetrica/symmetrica.pxi Sat Jan 19 16:38:26 2008 -0800 +++ b/sage/libs/symmetrica/symmetrica.pxi Sun Jan 20 14:20:41 2008 -0800 @@ -697,7 +697,16 @@ cdef object _py_polynom(OP a): return P(d) -cdef object _py_polynom_alphabet(OP a, object alphabet): +cdef object _py_polynom_alphabet(OP a, object alphabet, object length): + """ + Converts a symmetrica multivariate polynomial a to a Sage multivariate + polynomials. Alphabet specifies the names of the variables which are + fed into PolynomialRing. length specifies the number of variables; if + it is set to 0, then the number of variables is autodetected based on + the number of variables in alphabet or the result obtained from + symmetrica. + + """ late_import() cdef OP pointer = a @@ -705,10 +714,15 @@ cdef object _py_polynom_alphabet(OP a, o return 0 parent_ring = _py(s_po_k(pointer)).parent() - if isinstance(alphabet, (builtinlist, tuple)): - l = len(alphabet) + if length == 0: + if isinstance(alphabet, (builtinlist, tuple)): + l = len(alphabet) + elif isinstance(alphabet, str) and ',' in alphabet: + l = len(alphabet.split(',')) + else: + l = _py(s_po_sl(a)) else: - l = _py(s_po_sl(a)) + l = length P = PolynomialRing(parent_ring, l, alphabet) x = P.gens()