| 1 | cdef extern from 'symmetrica/def.h': |
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| 2 | INT dimension_symmetrization(OP n, OP part, OP a) |
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| 3 | INT bdg(OP part, OP perm, OP D) |
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| 4 | INT sdg(OP part, OP perm, OP D) |
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| 5 | INT odg(OP part, OP perm, OP D) |
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| 6 | INT ndg(OP part, OP perm, OP D) |
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| 7 | INT specht_dg(OP part, OP perm, OP D) |
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| 8 | INT glmndg(OP m, OP n, OP M, INT VAR) |
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| 9 | |
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| 10 | |
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| 11 | def dimension_symmetrization_symmetrica(n, part): |
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| 12 | """ |
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| 13 | computes the dimension of the degree of a irreducible |
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| 14 | representation of the GL_n, n is a INTEGER object, labeled |
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| 15 | by the PARTITION object a. |
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| 16 | """ |
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| 17 | cdef OP cn, cpart, cres |
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| 18 | |
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| 19 | |
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| 20 | cn = callocobject() |
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| 21 | cpart = callocobject() |
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| 22 | cres = callocobject() |
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| 23 | |
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| 24 | _op_partition(part, cpart) |
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| 25 | _op_integer(n, cn) |
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| 26 | |
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| 27 | dimension_symmetrization(cn, cpart, cres) |
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| 28 | res = _py_integer(cres) |
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| 29 | |
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| 30 | freeall(cn) |
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| 31 | freeall(cpart) |
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| 32 | freeall(cres) |
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| 33 | |
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| 34 | |
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| 35 | return res |
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| 36 | |
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| 37 | |
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| 38 | def bdg_symmetrica(part, perm): |
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| 39 | """ |
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| 40 | Calculates the irreduzible matrix representation |
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| 41 | D^part(perm), whose entries are of integral numbers. |
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| 42 | |
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| 43 | REFERENCE: H. Boerner: |
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| 44 | Darstellungen von Gruppen, Springer 1955. |
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| 45 | pp. 104-107. |
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| 46 | """ |
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| 47 | cdef OP cpart, cperm, cD |
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| 48 | |
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| 49 | |
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| 50 | cpart = callocobject() |
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| 51 | cperm = callocobject() |
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| 52 | cD = callocobject() |
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| 53 | |
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| 54 | _op_partition(part, cpart) |
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| 55 | _op_permutation(perm, cperm) |
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| 56 | |
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| 57 | bdg(cpart, cperm, cD) |
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| 58 | res = _py_matrix(cD) |
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| 59 | |
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| 60 | freeall(cpart) |
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| 61 | freeall(cperm) |
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| 62 | freeall(cD) |
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| 63 | |
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| 64 | |
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| 65 | |
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| 66 | def sdg_symmetrica(part, perm): |
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| 67 | """ |
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| 68 | |
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| 69 | Calculates the irreduzible matrix representation |
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| 70 | D^part(perm), which consists of rational numbers. |
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| 71 | |
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| 72 | REFERENCE: G. James/ A. Kerber: |
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| 73 | Representation Theory of the Symmetric Group. |
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| 74 | Addison/Wesley 1981. |
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| 75 | pp. 124-126. |
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| 76 | """ |
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| 77 | cdef OP cpart, cperm, cD |
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| 78 | |
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| 79 | |
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| 80 | cpart = callocobject() |
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| 81 | cperm = callocobject() |
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| 82 | cD = callocobject() |
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| 83 | |
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| 84 | _op_partition(part, cpart) |
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| 85 | _op_permutation(perm, cperm) |
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| 86 | |
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| 87 | sdg(cpart, cperm, cD) |
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| 88 | res = _py_matrix(cD) |
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| 89 | |
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| 90 | freeall(cpart) |
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| 91 | freeall(cperm) |
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| 92 | freeall(cD) |
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| 93 | |
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| 94 | |
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| 95 | |
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| 96 | return res |
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| 97 | |
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| 98 | def odg_symmetrica(part, perm): |
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| 99 | """ |
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| 100 | Calculates the irreduzible matrix representation |
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| 101 | D^part(perm), which consists of real numbers. |
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| 102 | |
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| 103 | REFERENCE: G. James/ A. Kerber: |
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| 104 | Representation Theory of the Symmetric Group. |
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| 105 | Addison/Wesley 1981. |
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| 106 | pp. 127-129. |
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| 107 | """ |
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| 108 | cdef OP cpart, cperm, cD |
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| 109 | |
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| 110 | |
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| 111 | cpart = callocobject() |
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| 112 | cperm = callocobject() |
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| 113 | cD = callocobject() |
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| 114 | |
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| 115 | _op_partition(part, cpart) |
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| 116 | _op_permutation(perm, cperm) |
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| 117 | |
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| 118 | odg(cpart, cperm, cD) |
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| 119 | res = _py_matrix(cD) |
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| 120 | |
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| 121 | freeall(cpart) |
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| 122 | freeall(cperm) |
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| 123 | freeall(cD) |
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| 124 | |
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| 125 | |
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| 126 | |
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| 127 | return res |
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| 128 | |
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| 129 | |
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| 130 | def ndg_symmetrica(part, perm): |
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| 131 | """ |
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| 132 | |
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| 133 | """ |
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| 134 | cdef OP cpart, cperm, cD |
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| 135 | |
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| 136 | |
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| 137 | cpart = callocobject() |
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| 138 | cperm = callocobject() |
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| 139 | cD = callocobject() |
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| 140 | |
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| 141 | _op_partition(part, cpart) |
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| 142 | _op_permutation(perm, cperm) |
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| 143 | |
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| 144 | ndg(cpart, cperm, cD) |
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| 145 | res = _py_matrix(cD) |
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| 146 | |
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| 147 | freeall(cpart) |
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| 148 | freeall(cperm) |
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| 149 | freeall(cD) |
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| 150 | |
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| 151 | |
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| 152 | |
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| 153 | return res |
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| 154 | |
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| 155 | def specht_dg_symmetrica(part, perm): |
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| 156 | """ |
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| 157 | |
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| 158 | """ |
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| 159 | cdef OP cpart, cperm, cD |
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| 160 | |
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| 161 | |
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| 162 | cpart = callocobject() |
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| 163 | cperm = callocobject() |
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| 164 | cD = callocobject() |
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| 165 | |
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| 166 | _op_partition(part, cpart) |
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| 167 | _op_permutation(perm, cperm) |
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| 168 | |
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| 169 | specht_dg(cpart, cperm, cD) |
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| 170 | res = _py_matrix(cD) |
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| 171 | |
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| 172 | freeall(cpart) |
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| 173 | freeall(cperm) |
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| 174 | freeall(cD) |
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| 175 | |
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| 176 | |
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| 177 | |
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| 178 | return res |
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| 179 | |
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| 180 | |
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| 181 | ## def glmndg_symmetrica(m, n, VAR=0): |
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| 182 | ## """ |
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| 183 | ## If VAR is equal to 0 the orthogonal representation |
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| 184 | ## is used for the decomposition, otherwise, if VAR |
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| 185 | ## equals 1, the natural representation is considered. |
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| 186 | |
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| 187 | ## The result is the VECTOR-Object M, consisting of |
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| 188 | ## components of type MATRIX, representing the several |
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| 189 | ## irreducible matrix representations of GLm(C) with |
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| 190 | ## part_1' <= m, where part is a partition of n. |
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| 191 | |
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| 192 | ## """ |
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| 193 | ## cdef OP cm, cn, cM |
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| 194 | |
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| 195 | ## |
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| 196 | |
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| 197 | ## cm = callocobject() |
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| 198 | ## _op_integer(m, cm) |
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| 199 | |
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| 200 | ## cn = callocobject() |
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| 201 | ## _op_integer(n, cn) |
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| 202 | |
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| 203 | ## cM = callocobject() |
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| 204 | |
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| 205 | |
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| 206 | |
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| 207 | ## glmndg(cm, cn, cM, VAR) |
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| 208 | ## res = _py(cM) |
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| 209 | |
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| 210 | |
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| 211 | ## freeall(cm) |
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| 212 | ## freeall(cn) |
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| 213 | ## freeall(cM) |
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| 214 | |
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| 215 | ## |
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| 216 | |
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| 217 | ## return res |
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