.. _ratmat.at_ref: ratmat.at Function References ======================================================= | .. _gcd_mat_m->int1: gcd ------------------------------------------------- | ``gcd:mat M->int`` Defined in line number 13. | | .. _simplify_ratmat(m,,d)->ratmat1: simplify ------------------------------------------------- | ``simplify:ratmat(M,,d)->ratmat`` Defined in line number 16. | | .. _\/_mat_M,int_d->ratmat1: \/ ------------------------------------------------- | ``/:mat M,int d->ratmat`` Defined in line number 19. | | .. _\*_rat_f,mat_M->ratmat1: \* ------------------------------------------------- | ``*:rat f,mat M->ratmat`` Defined in line number 23. | | .. _\/_mat_M,rat_f->ratmat1: \/ ------------------------------------------------- | ``/:mat M,rat f->ratmat`` Defined in line number 24. | | .. _entry_ratmat(m,,d),int_i,int_j->rat1: entry ------------------------------------------------- | ``entry:ratmat(M,,d),int i,int j->rat`` Defined in line number 26. | | .. _matrix_(int,int)(r,c),(int,int->rat)_f->ratmat1: matrix ------------------------------------------------- | ``matrix:(int,int)(r,c),(int,int->rat) f->ratmat`` Defined in line number 29. | | .. _n_rows_ratmat(m,,)->int1: n_rows ------------------------------------------------- | ``n_rows:ratmat(M,,)->int`` Defined in line number 34. | | .. _n_columns_ratmat(m,,)->int1: n_columns ------------------------------------------------- | ``n_columns:ratmat(M,,)->int`` Defined in line number 35. | | .. _columns_ratmat(m,,d)->[ratvec]1: columns ------------------------------------------------- | ``columns:ratmat(M,,d)->[ratvec]`` Defined in line number 37. | | .. _rows_ratmat(m,,d)->[ratvec]1: rows ------------------------------------------------- | ``rows:ratmat(M,,d)->[ratvec]`` Defined in line number 38. | | .. _column_ratmat(m,,d),int_j->ratvec1: column ------------------------------------------------- | ``column:ratmat(M,,d),int j->ratvec`` Defined in line number 39. | | .. _row_ratmat(m,,d),int_i->ratvec1: row ------------------------------------------------- | ``row:ratmat(M,,d),int i->ratvec`` Defined in line number 40. | | .. _columns_with_(int,ratvec->bool)_p,ratmat(m,,d)->ratmat1: columns_with ------------------------------------------------- | ``columns_with:(int,ratvec->bool) p,ratmat(M,,d)->ratmat`` Defined in line number 42. | | .. _columns_with_(ratvec->bool)_p,ratmat_t->ratmat1: columns_with ------------------------------------------------- | ``columns_with:(ratvec->bool) p,ratmat T->ratmat`` Defined in line number 45. | | .. _columns_with_(int->bool)_p,ratmat(m,,d)->ratmat1: columns_with ------------------------------------------------- | ``columns_with:(int->bool) p,ratmat(M,,d)->ratmat`` Defined in line number 47. | | .. _rows_with_(int,ratvec->bool)_p,ratmat(m,,d)->ratmat1: rows_with ------------------------------------------------- | ``rows_with:(int,ratvec->bool) p,ratmat(M,,d)->ratmat`` Defined in line number 50. | | .. _rows_with_(ratvec->bool)_p,ratmat_t->ratmat1: rows_with ------------------------------------------------- | ``rows_with:(ratvec->bool) p,ratmat T->ratmat`` Defined in line number 53. | | .. _rows_with_(int->bool)_p,ratmat(m,,d)->ratmat1: rows_with ------------------------------------------------- | ``rows_with:(int->bool) p,ratmat(M,,d)->ratmat`` Defined in line number 55. | | .. _det_ratmat(m,,d)->rat1: det ------------------------------------------------- | ``det:ratmat(M,,d)->rat`` Defined in line number 58. | | .. _\^_ratmat(M,,d)->ratmat1: \^ ------------------------------------------------- | ``^:ratmat(M,,d)->ratmat`` Defined in line number 60. | | .. _\+_ratmat(M,,d),ratmat(MM,,dd)->ratmat1: \+ ------------------------------------------------- | ``+:ratmat(M,,d),ratmat(MM,,dd)->ratmat`` Defined in line number 62. | | .. _\-_ratmat(M,,d),ratmat(MM,,dd)->ratmat1: \- ------------------------------------------------- | ``-:ratmat(M,,d),ratmat(MM,,dd)->ratmat`` Defined in line number 63. | | .. _\*_ratvec_v,ratmat(M,,d)->ratvec1: \* ------------------------------------------------- | ``*:ratvec v,ratmat(M,,d)->ratvec`` Defined in line number 66. | | .. _\*_ratmat(M,,d),ratvec_v->ratvec1: \* ------------------------------------------------- | ``*:ratmat(M,,d),ratvec v->ratvec`` Defined in line number 67. | | .. _\*_ratmat(M,,d),mat_MM->ratmat1: \* ------------------------------------------------- | ``*:ratmat(M,,d),mat MM->ratmat`` Defined in line number 69. | | .. _\*_mat_M,ratmat(MM,,d)->ratmat1: \* ------------------------------------------------- | ``*:mat M,ratmat(MM,,d)->ratmat`` Defined in line number 70. | | .. _\*_ratmat(M,,d),ratmat(MM,,dd)->ratmat1: \* ------------------------------------------------- | ``*:ratmat(M,,d),ratmat(MM,,dd)->ratmat`` Defined in line number 71. | | .. _\/_ratmat(M,,d)->ratmat1: \/ ------------------------------------------------- | ``/:ratmat(M,,d)->ratmat`` Defined in line number 73. | | .. _\^_ratmat(M,,d):Md,int_e->ratmat1: \^ ------------------------------------------------- | ``^:ratmat(M,,d):Md,int e->ratmat`` Defined in line number 77. | | .. _ratmat_as_mat_ratmat(m,,d)->mat1: ratmat_as_mat ------------------------------------------------- | ``ratmat_as_mat:ratmat(M,,d)->mat`` Defined in line number 80. | | .. _mat_as_ratmat_mat_m->ratmat1: mat_as_ratmat ------------------------------------------------- | ``mat_as_ratmat:mat M->ratmat`` Defined in line number 82. | | .. _diagonal_ratvec_v->ratmat1: diagonal ------------------------------------------------- | ``diagonal:ratvec v->ratmat`` Defined in line number 83. | | .. _ratvecs_as_ratmat_[ratvec]_a->ratmat1: ratvecs_as_ratmat ------------------------------------------------- | ``ratvecs_as_ratmat:[ratvec] A->ratmat`` Defined in line number 86. | | .. _det_[ratvec]_m->rat1: det ------------------------------------------------- | ``det:[ratvec] M->rat`` Defined in line number 89. | | .. _\^_[ratvec]_M->ratmat1: \^ ------------------------------------------------- | ``^:[ratvec] M->ratmat`` Defined in line number 90. | | .. _\*_[ratvec]_M,ratmat_MM->ratmat1: \* ------------------------------------------------- | ``*:[ratvec] M,ratmat MM->ratmat`` Defined in line number 91. | | .. _\*_ratmat_M,[ratvec]_MM->ratmat1: \* ------------------------------------------------- | ``*:ratmat M,[ratvec] MM->ratmat`` Defined in line number 92. | | .. _\+_[ratvec]_M,ratmat_MM->ratmat1: \+ ------------------------------------------------- | ``+:[ratvec] M,ratmat MM->ratmat`` Defined in line number 93. | | .. _\+_ratmat_M,[ratvec]_MM->ratmat1: \+ ------------------------------------------------- | ``+:ratmat M,[ratvec] MM->ratmat`` Defined in line number 94. | | .. _\-_[ratvec]_M,ratmat_MM->ratmat1: \- ------------------------------------------------- | ``-:[ratvec] M,ratmat MM->ratmat`` Defined in line number 95. | | .. _\-_ratmat_M,[ratvec]_MM->ratmat1: \- ------------------------------------------------- | ``-:ratmat M,[ratvec] MM->ratmat`` Defined in line number 96. | | .. _inverse_ratmat(m,,d)->ratmat1: inverse ------------------------------------------------- | ``inverse:ratmat(M,,d)->ratmat`` Defined in line number 98. | | .. _solve_ratmat(m,,d),_ratvec_v->[ratvec]1: solve ------------------------------------------------- | ``solve:ratmat(M,,d), ratvec v->[ratvec]`` Defined in line number 99. | | .. _\*_[ratvec]_M,mat_MM->ratmat1: \* ------------------------------------------------- | ``*:[ratvec] M,mat MM->ratmat`` Defined in line number 102. | | .. _\*_mat_M,[ratvec]_MM->ratmat1: \* ------------------------------------------------- | ``*:mat M,[ratvec] MM->ratmat`` Defined in line number 103. | | .. _\+_[ratvec]_M,mat_MM->ratmat1: \+ ------------------------------------------------- | ``+:[ratvec] M,mat MM->ratmat`` Defined in line number 104. | | .. _\+_mat_M,[ratvec]_MM->ratmat1: \+ ------------------------------------------------- | ``+:mat M,[ratvec] MM->ratmat`` Defined in line number 105. | | .. _\-_[ratvec]_M,mat_MM->ratmat1: \- ------------------------------------------------- | ``-:[ratvec] M,mat MM->ratmat`` Defined in line number 106. | | .. _\-_mat_M,[ratvec]_MM->ratmat1: \- ------------------------------------------------- | ``-:mat M,[ratvec] MM->ratmat`` Defined in line number 107. | | .. _rational_inverse_mat_m->ratmat1: rational_inverse ------------------------------------------------- | ``rational_inverse:mat M->ratmat`` Defined in line number 110. | | .. _right_inverse_ratmat_m->ratmat1: right_inverse ------------------------------------------------- | ``right_inverse:ratmat M->ratmat`` Defined in line number 113. | | Right inverse of a rational matrix | .. _left_inverse_ratmat_m->ratmat1: left_inverse ------------------------------------------------- | ``left_inverse:ratmat M->ratmat`` Defined in line number 117. | | Left inverse of rational matrix | .. _ratvec_to_string_ratvec_v->string1: ratvec_to_string ------------------------------------------------- | ``ratvec_to_string:ratvec v->string`` Defined in line number 119. | | .. _show_ratmat(m,,d)->void1: show ------------------------------------------------- | ``show:ratmat(M,,d)->void`` Defined in line number 126. | | .. _ratmat1: ratmat ----------------------------------------- | ``(mat,string,int)`` Defined in line number 10. | |