SUBSET
Combinatorial Routines

SUBSET is a library of MATLAB routines for performing various combinatorial operations.

These include the enumeration, generation, random selection, ranking and unranking of

• compositions of an integer;
• partitions of a set of N objects;
• I4_PARTITION's, partitions of an integer;
• PERM's, permutations of the first N integers;
• polynomials in factorial, Newton, power sum, or Taylor form;
• subsets of a set of N objects;
• KSUB's, subsets of size K, from a set of N objects;
• vectors whose entries range from 1 to N;
• YTB's, Young tableaus;

Other objects considered include

• the Bell numbers,
• BVEC's, binary numbers represented as a vector of 0's and 1's;
• Catalan numbers,
• congruence equations.
• continued fractions,
• DEC's, decimal numbers represented as a mantissa and a power of 10;
• DERANGE's, derangements (permutations that leave no element in place),
• DVEC's, decimal numbers represented as a vector of digits;
• falling factorials (20*19*18...),
• Gray codes,
• matrix permanents (similar to determinants, but harder to compute, if you can believe that),
• Morse-Thue numbers,
• pentagonal numbers,
• Pythagorean triples,
• RAT's, rational numbers represented as a pair of integers;
• rising factorials (7*8*9...).

Related Data and Programs:

COMBO is a FORTRAN90 library of combinatorial routines.

GRAFPACK is a FORTRAN90 library of routines for abstract graphs.

SELECT is a FORTRAN90 library of routines for the generation of various combinatorial objects.

SUBSET is also available in a C++ version and a FORTRAN90 version.

Fortran77 source code for some of the algorithms is available in the Stony Brook Algorithm Archive.

Reference:

1. Milton Abramowitz, Irene Stegun,
   Handbook of Mathematical Functions,
   National Bureau of Standards, 1964,
   ISBN: 0-486-61272-4,
   LC: QA47.A34.
2. Walter Ball,
   Mathematical Recreations and Essays,
   Macmillan, 1962,
   ISBN: 1417921269.
3. Bill Buckles, Matthew Lybanon,
   Algorithm 515: Generation of a Vector from the Lexicographical Index,
   ACM Transactions on Mathematical Software,
   Volume 3, Number 2, June 1977, pages 180-182.
4. John Conway, Richard Guy,
   The Book of Numbers,
   Springer, 1998,
   ISBN: 038797993X.
5. Laurent Habsieger, Maxim Kazarian, Sergei Lando,
   On the Second Number of Plutarch,
   American Mathematical Monthly,
   Volume 105, Number 5, May 1998, page 446.
6. John Halton,
   On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals,
   Numerische Mathematik,
   Volume 2, Number 1, December 1960, pages 84-90.
7. John Hart, Ward Cheney, Charles Lawson, Hans Maehly, Charles Mesztenyi, John Rice, Henry Thatcher, Christoph Witzgall,
   Computer Approximations,
   Wiley, 1968.
8. Mark Herkommer,
   Number Theory, A Programmer's Guide,
   McGraw Hill, 1999,
   ISBN: 0-07-913074-7.
9. Donald Knuth,
   The Art of Computer Programming,
   Volume 3, Sorting and Searching,
   Second Edition,
   Addison Wesley, 1998,
   ISBN: 0201896850.
10. Hang Tong Lau,
    Algorithms on Graphs,
    Tab Books, 1989,
    ISBN: 0830634290
11. Charles Mifsud,
    Algorithm 154, Combination in Lexicographic Order,
    Communications of the ACM,
    Volume 6, Number 3, March 1963, page 103.
12. Albert Nijenhuis, Herbert Wilf,
    Combinatorial Algorithms for Computers and Calculators,
    Second Edition,
    Academic Press, 1978,
    ISBN: 0-12-519260-6,
    LC: QA164.N54.
13. Norman Richert,
    Strang's Strange Figures,
    American Mathematical Monthly,
    Volume 99, Number 2, February 1992, pages 101-107.
14. James Sandeson,
    Testing Ecological Patterns,
    American Scientist,
    Volume 88, July-August 2000, pages 332-339.
15. Ian Saunders,
    Algorithm AS 205,
    Enumeration of R x C Tables with Repeated Row Totals,
    Applied Statistics,
    Volume 33, Number 3, 1984, pages 340-352.
16. Robert Sedgewick,
    Algorithms in C,
    Addison-Wesley, 1990,
    ISBN: 0-201-51425-7,
    LC: QA76.73.C15S43.
17. Raymond Seroul,
    Programming for Mathematicians,
    Springer, 2000,
    ISBN: 3-540-66422-X.
18. Mok-Kong Shen,
    Algorithm 202: Generation of Permutations in Lexicographical Order,
    Communications of the ACM,
    Volume 6, Number 9, September 1963, page 517.
19. Dennis Stanton, Dennis White,
    Constructive Combinatorics,
    Springer, 1986,
    ISBN: 0387963472.
20. Jack vanLint, Richard Wilson,
    A Course in Combinatorics,
    Cambridge, 1992,
    ISBN: 0-521-42260-4.
21. Eric Weisstein,
    CRC Concise Encyclopedia of Mathematics,
    CRC Press, 2002,
    Second edition,
    ISBN: 1584883472,
    LC: QA5.W45
22. ML Wolfson, HV Wright,
    ACM Algorithm 160: Combinatorial of M Things Taken N at a Time,
    Communications of the ACM,
    Volume 6, Number 4, April 1963, page 161.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• subset_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• subset_m_src.tar.gz the GZIP'ed TAR file.

Source Code:

• asm_enum.m, returns the number of alternating sign matrices of a given order.
• asm_triangle.m, returns a row of the alternating sign matrix triangle.
• bell.m, computes the Bell numbers.
• bell_values.m, returns some values of the Bell numbers.
• bvec_add.m, adds two binary vectors.
• bvec_and.m, computes the logical AND of two binary vectors.
• bvec_check.m, checks a binary vector.
• bvec_complement2.m, returns the complement of a binary vector.
• bvec_mul.m, multiplies two binary vectors.
• bvec_not.m, negates a binary vector.
• bvec_or.m, returns the logical OR of two binary vectors.
• bvec_print.m, prints a binary vector.
• bvec_reverse.m, reverses a binary vector.
• bvec_sub.m, subtracts two binary vectors.
• bvec_to_i4.m, converts a (signed) binary vector to an integer.
• bvec_xor.m, returns the exclusive OR of two binary vectors.
• catalan.m, computes the Catalan numbers.
• catalan_row_next.m, returns the next row of the Catalan matrix.
• catalan_values.m, returns some values of the Catalan numbers.
• cfrac_to_rat.m, converts a continued fraction to a rational.
• cfrac_to_rfrac.m, converts a continued polynomial fraction to a rational polynomial fraction.
• ch_cap.m, capitalizes a single character.
• change_greedy.m, makes change using a greedy algorithm.
• change_next.m, computes the next set of change for a given total.
• chinese_check.m, checks a set of Chinese remainder moduluses.
• chinese_to_i4.m, converts a set of Chinese remainders to an equivalent integer.
• comb_next.m, returns the next combination of K things out of N.
• comb_row.m, computes row N of Pascal's triangle.
• comb_unrank.m, returns the RANK-th combination of N things out of M things.
• combin.m, computes the binomial coefficient C(N,K).
• combin2.m, computes the binomial coefficient C(N,K).
• comp_next.m, returns the next composition of an integer into K parts.
• comp_random.m, returns a random composition of an integer into K parts.
• compnz_next.m, returns the next composition of an integer into K nonzero parts.
• compnz_random.m, returns a random composition of an integer into K nonzero parts.
• congruence.m, solves a congruence of the form A * X = C (mod B).
• count_pose_random.m, poses a random problem for the game "The Count is Good".
• debruijn.m, constructs a de Bruijn string.
• dec_add.m, adds two decimal values.
• dec_div.m, divides two decimal values.
• dec_mul.m, multiplies two decimal values.
• dec_round.m, rounds a decimal value to a given number of digits.
• dec_to_r8.m, converts a decimal to a real value.
• dec_to_rat.m, converts a decimal to a rational value.
• dec_to_s.m, returns a string representation of a decimal.
• dec_width.m, returns the "width" of a decimal.
• decmat_det.m, computes the determinant of a decimal matrix.
• decmat_print.m, prints a decimal matrix.
• derange_back_candidate.m, finds possible values for the K-th entry of a derangement.
• derange_back_next.m, returns the next derangement of N items.
• derange_check.m, checks whether a permutation is a derangement.
• derange_enum.m, returns the number of derangements of N objects.
• derange_enum2.m, returns the number of derangements of 0 through N objects.
• derange_enum3.m, returns the number of derangements of N objects.
• derange_weed_next.m, returns next derangements of N objects.
• digit_to_ch.m, returns the character representation of a decimal digit.
• digraph_arc_euler.m, returns an Euler circuit in a directed graph.
• digraph_arc_print.m, prints out a digraph from an edge list.
• diophantine.m, solves a Diophantine equation A * X + B * Y = C.
• diophantine_solution_minimize.m, seeks a minimal solution of a Diophantine equation.
• dvec_add.m, adds two decimal vectors.
• dvec_complementx.m, returns the complement of a decimal vector.
• bvec_mul.m, multiplies two decimal vectors.
• dvec_print.m, prints a decimal vector.
• dvec_sub.m, subtracts two decimal vectors.
• dvec_to_i4.m, converts a (signed) decimal vector to an integer.
• equiv_next.m, returns the next partition of a set.
• equiv_next2.m, returns the next partition of a set.
• equiv_print.m, prints a partition of a set.
• equiv_random.m, returns a random partition of a set.
• euler.m, returns the N-th row of Euler's triangle.
• fall.m, computes the falling factorial.
• gamma_log.m, returns the logarithm of the Gamma function.
• gamma_log_values.m, returns some values of the logarithm of the Gamma function.
• get_seed.m, returns a random seed for the random number generator.
• gray_next.m, returns the next Gray code by switching one item at a time.
• gray_rank2.m, returns the rank of a given Gray code.
• gray_unrank2.m, returns the Gray code of a given rank.
• i4_btest.m, returns TRUE if bit POS of I is a 1.
• i4_factor.m, factors an integer into a product of primes.
• i4_factorial.m, computes N! for small values of N.
• i4_gcd.m, finds the greatest common divisor of I and J.
• i4_huge.m, returns a "huge" integer.
• i4_log_10.m, returns the integer part of the logarithm of a number.
• i4_modp.m, returns the nonnegative remainder of integer division.
• i4_moebius.m, evaluates the Moebius function.
• i4_partition_conj.m, computes the conjugate of a partition of an integer.
• i4_partition_count.m, returns the number of partitions of an integer.
• i4_partition_count2.m, returns the number of partitions of an integer.
• i4_partition_count_values.m, returns some values of the partition count function.
• i4_partition_next.m, computes the next partition of an integer.
• i4_partition_next2.m, computes the next partition of an integer.
• i4_partition_print.m, prints a partition of an integer.
• i4_partition_random.m, returns a random partition of an integer.
• i4_sign.m, returns the sign of an integer.
• i4_sqrt.m, finds the integer square root of an integer.
• i4_sqrt_cf.m, finds the continued fraction square root of an integer.
• i4_swap.m, interchanges two integer values.
• i4_to_bvec.m, converts an integer to a (signed) binary vector.
• i4_to_chinese.m, converts an integer to its Chinese remainder form.
• i4_to_dvec.m, converts an integer to a (signed) decimal vector.
• i4_to_halton.m, computes an element of a Halton sequence.
• i4_to_s_left.m, converts an integer to a left-justified string.
• i4_uniform.m, returns a random integer in a given range.
• i4mat_01_rowcolsum.m, creates a 0/1 matrix with given row and column sums.
• i4mat_perm.m, applies a permutation to the rows and columns of a square integer matrix.
• i4mat_perm2.m, applies permutations to the rows and columns of a rectangular integer matrix.
• i4mat_print.m, prints an integer matrix.
• i4mat_print_some.m, prints some of an integer matrix.
• i4mat_u1_inverse.m, computes the inverse of a unit upper triangular integer matrix.
• i4poly.m, performs operations on an integer polynomial.
• i4poly_cyclo.m, computes a cyclotomic polynomial.
• i4poly_degree.m, returns the degree of an integer polynomial.
• i4poly_div.m, divides one integer polynomial by another.
• i4poly_mul.m, multiplies two integer polynomials.
• i4poly_print.m, prints an integer polynomial.
• i4vec_ascends.m, is TRUE if an integer vector is increasing.
• i4vec_backtrack.m, supervises a backtrack search for an integer vector.
• i4vec_descends.m, is TRUE if an integer vector is decreasing.
• i4vec_frac.m, searches for the K-th smallest entry in an N vector.
• i4vec_index.m, returns the location of the first occurrence of a given value.
• i4vec_indicator.m, sets an integer vector to the indicator vector.
• i4vec_maxloc_last.m, returns the index of the last maximal element of an integer vector.
• i4vec_pairwise_prime.m, returns TRUE if the elements of an integer vector are pairwise prime.
• i4vec_print.m, prints an integer vector.
• i4vec_print_some.m, prints some of an integer vector.
• i4vec_reverse.m, reverses the elements of an integer vector.
• i4vec_sort_bubble_a.m, ascending sorts an integer vector using bubble sort.
• i4vec_sort_heap_index_d.m, produces an index vector that descending sorts an integer array, using heapsort.
• i4vec_transpose_print.m, prints the "transpose" of an integer vector.
• i4vec_uniform.m, returns a random integer vector.
• index_box_next_2d.m, produces index vectors on the surface of a box in 2D.
• index_box_next_3d.m, produces index vectors on the surface of a box in 3D.
• index_box2_next_2d.m, produces index vectors on the surface of a box in 2D.
• index_box2_next_3d.m, produces index vectors on the surface of a box in 3D.
• index_next0.m, generates all index vectors with given upper limits.
• index_next1.m, generates all index vectors with given upper limits.
• index_next2.m, generates all index vectors with given lower and upper limits.
• index_rank0.m, ranks an index vector with given upper limits.
• index_rank1.m, ranks an index vector with given upper limits.
• index_rank2.m, ranks an index vector with given lower and upper limits.
• index_unrank0.m, unranks an index vector with given upper limits.
• index_unrank1.m, unranks an index vector with given upper limits.
• index_unrank2.m, unranks an index vector with given upper and lower limits.
• ins_perm.m, computes a permutation from its inversion sequence.
• involute_enum.m, returns the number of involutions of N objects.
• jfrac_to_rfrac.m, converts a J-fraction to a rational polynomial fraction.
• josephus.m, returns the position of the K-th man to be executed.
• ksub_next.m, selects the next subset of size K from a set of size N.
• ksub_next2.m, selects the next subset of size K from a set of size N.
• ksub_next3.m, selects the next subset of size K from a set of size N.
• ksub_next4.m, selects the next subset of size K from a set of size N.
• ksub_random.m, selects a random subset of size K from a set of size N.
• ksub_random2.m, selects a random subset of size K from a set of size N.
• ksub_random3.m, selects a random subset of size K from a set of size N.
• ksub_random4.m, selects a random subset of size K from a set of size N.
• ksub_rank.m, returns the rank of a subset of size K from a set of size N.
• ksub_unrank.m, returns a subset of size K from a set of size N, of given rank.
• matrix_product_opt.m, determines the optimal cost of a matrix product.
• moebius_matrix.m, finds the Moebius matrix from a covering relation.
• morse_thue.m, generates a Morse-Thue number.
• multinomial_coef1.m, computes a multinomial coefficient.
• multinomial_coef2.m, computes a multinomial coefficient.
• nim_sum.m, computes the Nim sum of two integers.
• padovan.m, computes the Padovan numbers.
• pell_basic.m, returns the basic solution of Pell's equation.
• pell_next.m, returns the next solution of Pell's equation.
• pent_enum.m, computes the N-th pentagonal number.
• perm_ascend.m, returns the longest ascending subsequence of a permutation.
• perm_canon_to_cycle.m, converts a permutation from canonical to cycle form.
• perm_check.m, checks that a permutation is legal.
• perm_cycle.m, analyzes a permutation.
• perm_cycle_to_canon.m, converts a permutation from cycle to canonical format.
• perm_cycle_to_index.m, converts a permutation from cycle to standard index format.
• perm_distance.m, computes the Ulam metric distance of two permutations.
• perm_fixed_enum.m, enumerates the permutations of N objects with M of them unchanged.
• perm_free.m, reports the unused items in a partial permutation.
• perm_index_to_cycle.m, converts a permutation from standard index to cycle form.
• perm_ins.m, returns the inversion sequence of a permutation.
• perm_inv.m, inverts a permutation.
• perm_inv2.m, inverts a permutation.
• perm_lex_next.m, generates the next permutation, in lexical order.
• perm_mul.m, multiplies two permutations.
• perm_next.m, computes the next permutation of N objects.
• perm_next2.m, computes the next permutation of N objects.
• perm_next3.m, computes the next permutation of N objects.
• perm_mul.m, prints a permutation.
• perm_random.m, returns a random permutation.
• perm_random2.m, returns a random permutation.
• perm_random3.m, returns a random permutation.
• perm_rank.m, returns the rank of a permutation.
• perm_sign.m, returns the sign of a permutation.
• perm_to_equiv.m, converts a permutation to an equivalence relation.
• perm_to_ytb.m, converts a permutation to a Young tableau.
• perm_unrank.m, produces the permutation of given rank.
• perrin.m, computes the Perrin numbers.
• pord_check.m, checks a matrix representing a partial ordering.
• power_mod.m, computes mod ( A^N, M ).
• power_series1.m, computes the power series for (1+F(Z))^ALPHA.
• power_series2.m, computes the power series for exp(F(Z))-1.
• power_series3.m, computes the power series for G(F(Z)).
• power_series4.m, computes the power series for G(1/F(Z)).
• prime.m, returns any of the first MAXPRIME prime numbers.
• pythag_triple_next.m, computes the next Pythagorean triple.
• r4_uniform_01.m, is a uniform random number generator.
• r8_agm.m, finds the arithmetic-geometric mean of two real numbers.
• r8_epsilon.m, returns the arithmetic precision for real arithmetic.
• r8_is_int.m, determines if a real number represent an integer value.
• r8_swap.m, interchanges two real values.
• r8_to_cfrac.m, converts a double precision value to a continued fraction.
• r8_to_dec.m, converts a double precision value to a decimal value;
• r8_to_rat.m, converts a real value to a rational value.
• r8_to_s_left.m, converts a real value to a left-justified string.
• r8_uniform.m, returns a random real in a given range.
• r8_uniform_01.m, is a uniform random number generator.
• r8mat_det.m, computes the determinant of a real array.
• r8mat_perm.m, applies a permutation to the rows and columns of a square matrix.
• r8mat_perm2.m, applies a permutation to the rows and columns of a rectangular matrix.
• r8mat_permanent.m, computes the permanent of a square matrix.
• r8mat_print.m, prints a real matrix.
• r8mat_print_some.m, prints some of a real matrix.
• r8poly.m, performs operations on a real polynomial.
• r8poly_degree.m, returns the degree of a real polynomial.
• r8poly_div.m, computes the quotient and remainder of two real polynomials.
• r8poly_f2p.m, converts a real polynomial from factorial to standard form.
• r8poly_fval.m, evaluates a real polynomial in factorial form.
• r8poly_mul.m, computes the product of two real polynomials.
• r8poly_n2p.m, converts a polynomial from Newton to standard form.
• r8poly_nval.m, evaluates a polynomial in Newton form.
• r8poly_nx.m, replaces one of the base points in the Newton form of a polynomial.
• r8poly_p2f.m, converts a real polynomial from standard to factorial form.
• r8poly_p2n.m, converts a real polynomial from standard to Newton form.
• r8poly_p2t.m, converts a real polynomial from standard to Taylor form.
• r8poly_power.m, computes a power of a real polynomial.
• r8poly_print.m, prints a real polynomial.
• r8poly_pval.m, evaluates a real polynomial.
• r8poly_t2p.m, converts a real polynomial from Taylor to standard form.
• r8vec_backtrack.m, supervises a backtrack search for a real vector.
• r8vec_frac.m, searches for the K-th smallest entry in an N vector.
• r8vec_indicator.m, sets a real vector to the indicator vector.
• r8vec_mirror_next.m, steps through all sign variations of a real vector.
• r8vec_print.m, prints a real vector.
• r8vec_uniform.m, returns a random real vector.
• random_initialize.m, initializes the random number generator.
• rat_add.m, adds two rational values.
• rat_div.m, carries out division of rational values.
• rat_farey.m, returns a row of the Farey fraction table.
• rat_farey2.m, returns the next row of the Farey fraction table.
• rat_mul.m, multiplies two rational values.
• rat_normalize.m, normalizes a rational value.
• rat_sum_formula.m, computes the formulas for sums of powers of integers.
• rat_to_cfrac.m, converts a rational to a continued fraction.
• rat_to_dec.m, converts a rational to a decimal value.
• rat_to_r8.m, converts a rational to a real value.
• rat_to_s_left.m, converts a rational to a left-justified string.
• rat_width.m, returns the "width" of a rational number.
• ratmat_det.m, computes the determinant of a rational matrix.
• ratmat_print.m, prints a rational matrix.
• regro_next.m, computes the next restricted growth function.
• rfrac_to_cfrac.m, converts a rational polynomial fraction to continued fraction form.
• rfrac_to_jfrac.m, converts a rational polynomial fraction to a J fraction.
• rise.m, computes the rising factorial.
• s_blank_delete.m, deletes every blank from a string.
• s_blanks_delete.m, replaces consecutive blanks by one blank in a string.
• s_eqi.m, compares two strings for equality, ignoring case.
• s_len_trim.m, returns the length of a string to the last nonblank.
• schroeder.m, generates the Schroeder numbers.
• sort_heap_external.m, externally sorts a list of items into ascending order.
• sub_by_size_next.m, returns all the subsets of an N set, in decreasing order of size.
• sub_gray_next.m, generates the next subset of an N set.
• sub_gray_rank.m, ranks a subset of an N set using the Gray ordering.
• sub_gray_unrank.m, returns a subset of an N set with the given Gray ranking.
• sub_lex_next.m, returns the next subset of an N set, in lexicographic order.
• sub_random.m, selects a random subset of an N set.
• subcomp_next.m, computes the next subcomposition of N into K parts;
• subcompnz_next.m, computes the next subcomposition of N into K nonzero parts;
• subcompnz2_next.m, computes the next composition of N into K nonzero parts for N between N_LO and N_HI;
• thue_binary_next.m, returns the next element in a binary Thue sequence.
• thue_ternary_next.m, returns the next element in a ternary Thue sequence.
• timestamp.m, returns the current YMDHMS date as a timestamp.
• triang.m, renumbers items in accordance with a partial ordering.
• tuple_next.m, computes the next element of a tuple space.
• tuple2_next.m, computes the next element of a tuple space.
• tuple_next_fast.m, computes the next element of a tuple space, "fast".
• tuple_next_ge.m, computes the next "nondecreasing" element of a tuple space.
• ubvec_add.m, adds two unsigned binary vectors.
• ubvec_to_ui4.m, converts an unsigned binary vector to an unsigned integer.
• ui4_to_ubvec.m, converts an integer to an unsigned binary vector.
• vec_next.m, generates all N-vectors of integers modulo a given base.
• vec_next2.m, generates the elements of a product space.
• vec_random.m, selects a random N-vectors of integers modulo a given base.
• vec_rank.m, returns the rank of an N-vectors of integers modulo a given base.
• vec_unrank.m, computes the product space element of a given rank.
• vector_constrained_next.m, computes the "next" vector that lies in a given range and satisfies a particular constraint.
• vector_constrained_next2.m, computes the "next" vector that lies in a given range and satisfies a particular constraint.
• vector_constrained_next3.m, computes the "next" vector that lies in a given range and satisfies a particular constraint.
• vector_constrained_next4.m, computes the "next" vector that lies in a given range and satisfies a particular constraint.
• vector_constrained_next5.m, computes the "next" vector that lies in a given range and satisfies a particular constraint.
• ytb_enum.m, enumerates the Young tableaus of size N.
• ytb_next.m, returns the next Young tableau of size N.
• ytb_print.m, prints a Young tableau.
• ytb_random.m, returns a random Young tableau.

Examples and Tests:

• subset_test.m, runs all the tests;
• subset_test.out, the output from the tests;
• subset_test000.m, tests RANDOM_INITIALIZE;
• subset_test001.m, tests ASM_ENUM;
• subset_test002.m, tests ASM_TRIANGLE;
• subset_test003.m, tests BELL and BELL_VALUES;
• subset_test9001.m, tests BVEC_ADD and BVEC_SUB;
• subset_test9002.m, tests BVEC_COMPLEMENT2;
• subset_test9003.m, tests BVEC_MUL;
• subset_test005.m, tests CATALAN and CATALAN_VALUES;
• subset_test006.m, tests CATALAN_ROW_NEXT;
• subset_test007.m, tests CFRAC_TO_RAT and RAT_TO_CFRAC;
• subset_test008.m, tests CFRAC_TO_RFRAC and RFRAC_TO_CFRAC;
• subset_test009.m, tests CHANGE_GREEDY;
• subset_test010.m, tests CHANGE_NEXT;
• subset_test011.m, tests COMB_NEXT;
• subset_test012.m, tests COMB_ROW;
• subset_test013.m, tests COMB_UNRANK;
• subset_test014.m, tests COMBIN;
• subset_test015.m, tests COMBIN2;
• subset_test016.m, tests COMP_NEXT;
• subset_test017.m, tests COMP_RANDOM;
• subset_test0174.m, tests COMPNZ_NEXT;
• subset_test0175.m, tests COMPNZ_RANDOM;
• subset_test018.m, tests CONGRUENCE;
• subset_test019.m, tests COUNT_POSE_RANDOM;
• subset_test020.m, tests R8_TO_CFRAC;
• subset_test021.m, tests DEBRUIJN;
• subset_test022.m, tests DEC_ADD;
• subset_test023.m, tests DEC_DIV;
• subset_test024.m, tests DEC_MUL;
• subset_test025.m, tests DEC_ROUND;
• subset_test026.m, tests DEC_TO_RAT and RAT_TO_DEC;
• subset_test027.m, tests DEC_TO_S;
• subset_test028.m, tests DEC_WIDTH;
• subset_test029.m, tests DECMAT_DET;
• subset_test021a.m, tests DERANGE_ENUM and DERANGE_ENUM2;
• subset_test022a.m, tests DERANGE_BACK_NEXT;
• subset_test023a.m, tests DERANGE_WEED_NEXT;
• subset_test024a.m, tests DIGRAPH_ARC_EULER;
• subset_test025a.m, tests DIOPHANTINE;
• subset_test026a.m, tests DIOPHANTINE_MINIMIZE;
• subset_test026b.m, tests DVEC_ADD and DVEC_SUB;
• subset_test026c.m, tests DVEC_COMPLEMENTX;
• subset_test026d.m, tests DVEC_MUL;
• subset_test027a.m, tests EQUIV_NEXT;
• subset_test028a.m, tests EQUIV_NEXT2;
• subset_test029a.m, tests EQUIV_RANDOM;
• subset_test0295.m, tests EULER;
• subset_test030.m, tests FALL;
• subset_test0305.m, tests GAMMA_LOG and GAMMA_LOG_VALUES;
• subset_test031.m, tests GRAY_NEXT;
• subset_test0321.m, tests GRAY_RANK2 and GRAY_UNRANK2;
• subset_test0323.m, tests I4_BTEST;
• subset_test0325.m, tests I4_GCD;
• subset_test0327.m, tests I4_LOG10;
• subset_test058.m, tests I4_PARTITION_CONJ;
• subset_test059.m, tests I4_PARTITION_NEXT;
• subset_test060.m, tests I4_PARTITION_NEXT;
• subset_test061.m, tests I4_PARTITION_COUNT and I4_PARTITION_COUNT_VALUES;
• subset_test0615.m, tests I4_PARTITION_COUNT2 and I4_PARTITION_COUNT_VALUES;
• subset_test062.m, tests I4_PARTITION_RANDOM;
• subset_test033.m, tests I4_SQRT;
• subset_test034.m, tests I4_SQRT_CF;
• subset_test0625.m, tests I4_TO_BVEC and BVEC_TO_I4;
• subset_test035.m, tests I4_TO_CHINESE and CHINESE_TO_I4;
• subset_test0364.m, tests I4_TO_IPOLY and I4_TO_VAN_DER_CORPUT;
• subset_test0627.m, tests I4_TO_IPOLY and IPOLY_TO_I4;
• subset_test036.m, tests I4_TO_VAN_DER_CORPUT;
• subset_test0365.m, tests I4_BTEST;
• subset_test037.m, tests I4MAT_01_ROWCOLSUM;
• subset_test039.m, tests I4MAT_01_ROWCOLSUM;
• subset_test040.m, tests I4MAT_U1_INVERSE;
• subset_test041.m, tests I4MAT_PERM;
• subset_test042.m, tests I4MAT_PERM2;
• subset_test047.m, tests I4MAT_PERM2 and TRIANG;
• subset_test043.m, tests INDEX_BOX_NEXT_2D;
• subset_test044.m, tests INDEX_BOX_NEXT_3D;
• subset_test045.m, tests INDEX_BOX2_NEXT_2D;
• subset_test046.m, tests INDEX_BOX2_NEXT_3D;
• subset_test048.m, tests INDEX_NEXT0;
• subset_test049.m, tests INDEX_NEXT1;
• subset_test050.m, tests INDEX_NEXT2;
• subset_test051.m, tests INDEX_RANK0;
• subset_test052.m, tests INDEX_RANK1;
• subset_test053.m, tests INDEX_RANK2;
• subset_test054.m, tests INDEX_UNRANK0;
• subset_test055.m, tests INDEX_UNRANK1;
• subset_test056.m, tests INDEX_UNRANK2;
• subset_test057.m, tests INS_PERM and PERM_INS;
• subset_test063.m, tests INVOLUTE_ENUM;
• subset_test064.m, tests I4POLY;
• subset_test065.m, tests I4POLY_CYCLO;
• subset_test066.m, tests I4POLY_DIV;
• subset_test067.m, tests I4POLY_MUL;
• subset_test0675.m, tests I4VEC_DESCENDS;
• subset_test068.m, tests I4VEC_FRAC;
• subset_test0683.m, tests I4VEC_INDEX;
• subset_test0685.m, tests I4VEC_MAXLOC_LAST;
• subset_test0686.m, tests I4VEC_PAIRWISE_PRIME;
• subset_test0687.m, tests I4VEC_REVERSE;
• subset_test0688.m, tests I4VEC_SORT_BUBBLE_A;
• subset_test0689.m, tests I4VEC_SORT_HEAP_INDEX_D;
• subset_test069.m, tests JFRAC_TO_RFRAC and RFRAC_TO_JFRAC;
• subset_test070.m, tests JOSEPHUS;
• subset_test071.m, tests KSUB_NEXT;
• subset_test072.m, tests KSUB_NEXT2;
• subset_test073.m, tests KSUB_NEXT3;
• subset_test074.m, tests KSUB_NEXT4;
• subset_test075.m, tests KSUB_RANDOM;
• subset_test076.m, tests KSUB_RANDOM2;
• subset_test077.m, tests KSUB_RANDOM3;
• subset_test0771.m, tests KSUB_RANDOM4;
• subset_test0772.m, tests KSUB_RANK;
• subset_test0773.m, tests KSUB_UNRANK;
• subset_test078.m, tests MATRIX_PRODUCT_OPT;
• subset_test079.m, tests MOEBIUS_MATRIX;
• subset_test080.m, tests MORSE_THUE;
• subset_test081.m, tests MULTINOMIAL_COEF1 and MULTINOMIAL_COEF2;
• subset_test083.m, tests NIM_SUM;
• subset_test084.m, tests PELL_BASIC and PELL_NEXT;
• subset_test085.m, tests PENT_ENUM;
• subset_test093.m, tests PERM_ASCEND;
• subset_test086.m, tests PERM_BREAK_COUNT;
• subset_test087.m, tests PERM_CANON_TO_CYCLE;
• subset_test088.m, tests PERM_CYCLE;
• subset_test089.m, tests PERM_CYCLE_TO_CANON;
• subset_test090.m, tests PERM_CYCLE_TO_INDEX and PERM_INDEX_TO_CYCLE;
• subset_test091.m, tests PERM_DISTANCE;
• subset_test092.m, tests PERM_FIXED_ENUM;
• subset_test094.m, tests PERM_INV;
• subset_test095.m, tests PERM_IN2;
• subset_test096.m, tests PERM_LEX_NEXT;
• subset_test097.m, tests PERM_LEX_NEXT and PERM_SIGN;
• subset_test098.m, tests PERM_MUL;
• subset_test099.m, tests PERM_NEXT;
• subset_test100.m, tests PERM_NEXT2;
• subset_test101.m, tests PERM_NEXT3;
• subset_test102.m, tests PERM_RANDOM;
• subset_test103.m, tests PERM_RANDOM2;
• subset_test104.m, tests PERM_RANDOM3;
• subset_test105.m, tests PERM_RANK;
• subset_test106.m, tests PERM_TO_EQUIV;
• subset_test107.m, tests PERM_TO_YTB;
• subset_test108.m, tests PERM_UNRANK;
• subset_test109.m, tests POWER_MOD;
• subset_test110.m, tests POWER_SERIES1;
• subset_test111.m, tests POWER_SERIES2;
• subset_test112.m, tests POWER_SERIES3;
• subset_test113.m, tests POWER_SERIES4;
• subset_test114.m, tests PYTHAG_TRIPLE_NEXT;
• subset_test115.m, tests R8_AGM;
• subset_test116.m, tests R8_TO_CFRAC;
• subset_test1163.m, tests R8_TO_DEC and DEC_TO_R8;
• subset_test1165.m, tests R8_TO_RAT and RAT_TO_R8;
• subset_test117.m, tests RAT_ADD;
• subset_test118.m, tests RAT_DIV;
• subset_test119.m, tests RAT_FAREY;
• subset_test120.m, tests RAT_FAREY2;
• subset_test121.m, tests RAT_MUL;
• subset_test1215.m, tests RAT_WIDTH;
• subset_test122.m, tests RAT_SUM_FORMULA;
• subset_test123.m, tests RATMAT_DET;
• subset_test124.m, tests REGRO_NEXT;
• subset_test1245.m, tests RISE;
• subset_test125.m, tests R8MAT_DET;
• subset_test126.m, tests R8MAT_PERM;
• subset_test127.m, tests R8MAT_PERM2;
• subset_test128.m, tests R8MAT_PERMANENT;
• subset_test129.m, tests R8POLY;
• subset_test130.m, tests R8POLY_DIV;
• subset_test131.m, tests R8POLY_F2P and R8POLY_P2F;
• subset_test132.m, tests R8POLY_FVAL;
• subset_test133.m, tests R8POLY_MUL;
• subset_test134.m, tests R8POLY_N2P and R8POLY_P2N;
• subset_test135.m, tests R8POLY_NVAL;
• subset_test136.m, tests R8POLY_P2T and R8POLY_T2P;
• subset_test137.m, tests R8POLY_POWER;
• subset_test138.m, tests R8POLY_PVAL;
• subset_test139.m, tests R8VEC_FRAC;
• subset_test1395.m, tests R8VEC_MIRROR_NEXT;
• subset_test140.m, tests SCHROEDER;
• subset_test141.m, tests SORT_HEAP_EXTERNAL;
• subset_test142.m, tests SUB_BY_SIZE_NEXT;
• subset_test143.m, tests SUB_LEX_NEXT;
• subset_test1435.m, tests SUB_LEX_NEXT;
• subset_test144.m, tests SUB_GRAY_NEXT;
• subset_test145.m, tests SUB_RANDOM;
• subset_test146.m, tests SUB_GRAY_RANK;
• subset_test147.m, tests SUB_GRAY_UNRANK;
• subset_test1475.m, tests SUBCOMP_NEXT;
• subset_test1476.m, tests SUBCOMPNZ_NEXT;
• subset_test1477.m, tests SUBCOMPNZ2_NEXT;
• subset_test148.m, tests THUE_BINARY_NEXT;
• subset_test149.m, tests THUE_TERNARY_NEXT;
• subset_test150.m, tests TUPLE_NEXT;
• subset_test151.m, tests TUPLE_NEXT_FAST;
• subset_test152.m, tests TUPLE_NEXT_GE;
• subset_test153.m, tests TUPLE_NEXT2;
• subset_test1531.m, tests UBVEC_ADD;
• subset_test0626.m, tests UI4_TO_UBVEC and UBVEC_TO_UI4;
• subset_test154.m, tests VEC_NEXT;
• subset_test155.m, tests VEC_NEXT_GRAY, VEC_RANK and VEC_UNRANK;
• subset_test156.m, tests VEC_RANDOM;
• subset_test1565.m, tests VECTOR_CONSTRAINED_NEXT;
• subset_test1566.m, tests VECTOR_CONSTRAINED_NEXT2;
• subset_test1567.m, tests VECTOR_CONSTRAINED_NEXT3;
• subset_test1568.m, tests VECTOR_CONSTRAINED_NEXT4;
• subset_test1569.m, tests VECTOR_CONSTRAINED_NEXT4;
• subset_test157.m, tests YTB_ENUM;
• subset_test158.m, tests YTB_NEXT;
• subset_test159.m, tests YTB_RANDOM;

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