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/dports/math/p5-Math-BigInt-FastCalc/Math-BigInt-FastCalc-0.5012/xt/author/
H A Dlib-arithmetic-binary-_nok.dat1 # binomial(0, k) for 0 <= k <= 0
5 # binomial(1, k) for 0 <= k <= 1
10 # binomial(2, k) for 0 <= k <= 2
16 # binomial(3, k) for 0 <= k <= 3
23 # binomial(4, k) for 0 <= k <= 4
31 # binomial(5, k) for 0 <= k <= 5
40 # binomial(6, k) for 0 <= k <= 6
50 # binomial(7, k) for 0 <= k <= 7
61 # binomial(8, k) for 0 <= k <= 8
73 # binomial(9, k) for 0 <= k <= 9
[all …]
/dports/math/p5-Math-BigInt-GMP/Math-BigInt-GMP-1.6009/xt/author/
H A Dlib-arithmetic-binary-_nok.dat1 # binomial(0, k) for 0 <= k <= 0
5 # binomial(1, k) for 0 <= k <= 1
10 # binomial(2, k) for 0 <= k <= 2
16 # binomial(3, k) for 0 <= k <= 3
23 # binomial(4, k) for 0 <= k <= 4
31 # binomial(5, k) for 0 <= k <= 5
40 # binomial(6, k) for 0 <= k <= 6
50 # binomial(7, k) for 0 <= k <= 7
61 # binomial(8, k) for 0 <= k <= 8
73 # binomial(9, k) for 0 <= k <= 9
[all …]
/dports/math/p5-Math-BigInt/Math-BigInt-1.999827/xt/author/
H A Dlib-arithmetic-binary-_nok.dat1 # binomial(0, k) for 0 <= k <= 0
5 # binomial(1, k) for 0 <= k <= 1
10 # binomial(2, k) for 0 <= k <= 2
16 # binomial(3, k) for 0 <= k <= 3
23 # binomial(4, k) for 0 <= k <= 4
31 # binomial(5, k) for 0 <= k <= 5
40 # binomial(6, k) for 0 <= k <= 6
50 # binomial(7, k) for 0 <= k <= 7
61 # binomial(8, k) for 0 <= k <= 8
73 # binomial(9, k) for 0 <= k <= 9
[all …]
H A Dbnok-mbi.t40 # binomial(0, k) for 0 <= k <= 0
44 # binomial(1, k) for 0 <= k <= 1
49 # binomial(2, k) for 0 <= k <= 2
55 # binomial(3, k) for 0 <= k <= 3
62 # binomial(4, k) for 0 <= k <= 4
70 # binomial(5, k) for 0 <= k <= 5
79 # binomial(6, k) for 0 <= k <= 6
89 # binomial(7, k) for 0 <= k <= 7
100 # binomial(8, k) for 0 <= k <= 8
112 # binomial(9, k) for 0 <= k <= 9
[all …]
/dports/math/p5-Math-BigInt-Pari/Math-BigInt-Pari-1.3008/xt/author/
H A Dlib-arithmetic-binary-_nok.dat1 # binomial(0, k) for 0 <= k <= 0
5 # binomial(1, k) for 0 <= k <= 1
10 # binomial(2, k) for 0 <= k <= 2
16 # binomial(3, k) for 0 <= k <= 3
23 # binomial(4, k) for 0 <= k <= 4
31 # binomial(5, k) for 0 <= k <= 5
40 # binomial(6, k) for 0 <= k <= 6
50 # binomial(7, k) for 0 <= k <= 7
61 # binomial(8, k) for 0 <= k <= 8
73 # binomial(9, k) for 0 <= k <= 9
[all …]
H A Dbnok-mbi.t40 # binomial(0, k) for 0 <= k <= 0
44 # binomial(1, k) for 0 <= k <= 1
49 # binomial(2, k) for 0 <= k <= 2
55 # binomial(3, k) for 0 <= k <= 3
62 # binomial(4, k) for 0 <= k <= 4
70 # binomial(5, k) for 0 <= k <= 5
79 # binomial(6, k) for 0 <= k <= 6
89 # binomial(7, k) for 0 <= k <= 7
100 # binomial(8, k) for 0 <= k <= 8
112 # binomial(9, k) for 0 <= k <= 9
[all …]
/dports/math/mppp/mppp-0.26/test/
H A Drational_binomial.cpp35 REQUIRE(binomial(rational{}, integer{}) == 1); in operator ()()
40 REQUIRE(binomial(rational{}, 0) == 1); in operator ()()
41 REQUIRE(binomial(rational{5}, 2u) == 10); in operator ()()
43 REQUIRE(binomial(rational{-5}, -2ll) == 0); in operator ()()
44 REQUIRE(binomial(rational{-5}, 2ul) == 15); in operator ()()
51 REQUIRE(binomial(rational{-5, 2}, -2l) == 0); in operator ()()
58 REQUIRE(binomial(rational{-5, 2}, 0l) == 1); in operator ()()
69 REQUIRE(binomial(rational{3, 4}, 0) == 1); in operator ()()
70 REQUIRE(binomial(rational{3, 4}, -1) == 0); in operator ()()
71 REQUIRE(binomial(rational{3, 4}, -2) == 0); in operator ()()
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H A Dinteger_bin.cpp110 REQUIRE(binomial(n, 0) == 1); in operator ()()
111 REQUIRE(binomial(n, 1) == 0); in operator ()()
112 REQUIRE(binomial(n, false) == 1); in operator ()()
113 REQUIRE(binomial(n, true) == 0); in operator ()()
115 REQUIRE(binomial(n, 1) == 1); in operator ()()
117 REQUIRE(binomial(n, 3) == 10); in operator ()()
119 REQUIRE(binomial(n, int_type(4)) == 70); in operator ()()
132 CHECK_NOTHROW(binomial(n, tmp2)); in operator ()()
146 REQUIRE(binomial(int_type{-3}, -1) == 0); in operator ()()
147 REQUIRE(binomial(int_type{3}, -1) == 0); in operator ()()
[all …]
/dports/math/singular/Singular-Release-4-2-1/IntegerProgramming/
H A Dbinomial.h47 class binomial
97 binomial(const binomial&);
101 ~binomial();
119 binomial& operator=(const binomial&);
179 friend binomial& S_binomial(const binomial& a, const binomial& b,
189 friend BOOLEAN relatively_prime(const binomial& a, const binomial& b);
192 friend BOOLEAN M(const binomial& a,const binomial& b,const binomial& c);
195 friend BOOLEAN F(const binomial& a, const binomial& b, const binomial& c);
198 friend BOOLEAN B(const binomial& a, const binomial& b, const binomial& c);
202 friend BOOLEAN second_crit(const binomial& a, const binomial& b,
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H A Dbinomial.cc18 binomial::binomial(const short& number_of_variables) in binomial() function in binomial
80 binomial::binomial(const binomial& b) in binomial() function in binomial
101 binomial::binomial(const short& number_of_variables) in binomial() function in binomial
228 binomial::binomial(const binomial& b) in binomial() function in binomial
245 binomial::~binomial() in ~binomial()
281 binomial& binomial::operator=(const binomial& b) in operator =()
333 BOOLEAN binomial::operator==(const binomial& b) const in operator ==()
975 binomial& S_binomial(const binomial& a, const binomial& b, in S_binomial()
1138 BOOLEAN M(const binomial& a, const binomial& b, const binomial& c) in M()
1185 BOOLEAN F(const binomial& a, const binomial& b, const binomial& c) in F()
[all …]
/dports/math/py-sympy/sympy-1.9/sympy/functions/combinatorial/tests/
H A Dtest_comb_factorials.py427 assert binomial(n, 3).func == binomial
434 assert binomial(n, u).func == binomial
435 assert binomial(kp, u).func == binomial
436 assert binomial(n, p).func == binomial
437 assert binomial(n, k).func == binomial
438 assert binomial(n, n + p).func == binomial
439 assert binomial(kp, kp + p).func == binomial
467 assert isinstance(binomial(u, u), binomial)
469 assert isinstance(binomial(x, x), binomial)
489 assert binomial(nt, kt).func == binomial
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/dports/science/dalton/dalton-66052b3af5ea7225e31178bf9a8b031913c72190/external/gen1int/src/basic/
H A Dhgto_to_sgto.F90114 binomial(1) = 1
126 binomial(2:jang+1) = binomial(2:jang+1)+binomial(1:jang)
143 binomial(2:imag+1:2) = binomial(2:imag+1:2)+binomixy(1:imag:2)
144 binomial(3:imag+1:2) = binomial(3:imag+1:2)-binomixy(2:imag:2)
165 binomial(3:iang+1) = binomial(3:iang+1)+binomial(1:iang-1)
177 deallocate(binomial)
284 binomial(1) = 1
296 binomial(2:jang+1) = binomial(2:jang+1)+binomial(1:jang)
313 binomial(2:imag+1:2) = binomial(2:imag+1:2)+binomixy(1:imag:2)
314 binomial(3:imag+1:2) = binomial(3:imag+1:2)-binomixy(2:imag:2)
[all …]
/dports/math/py-Diofant/Diofant-0.13.0/diofant/tests/functions/
H A Dtest_comb_factorials.py258 assert binomial(0, 0) == 1
269 assert binomial(n, -1).func == binomial
276 assert binomial(n, 3).func == binomial
281 assert isinstance(expand_func(binomial(n, -1, evaluate=False)), binomial)
282 assert isinstance(expand_func(binomial(n, k)), binomial)
284 assert binomial(n, n + 1).func == binomial # e.g. (-1, 0) == 1
286 assert binomial(n, u).func == binomial
288 assert binomial(n, p).func == binomial
289 assert binomial(n, k).func == binomial
290 assert binomial(n, n + p).func == binomial
[all …]
/dports/math/maxima/maxima-5.43.2/share/solve_rec/
H A Dsimplify_sum_test.mac25 sum(r/k*binomial(n,r)*binomial(m,k-r)/binomial(n+m,k),r,0,k),
39 sum((-1)^k * binomial(a+b, a+k) * binomial(b+c, b+k) * binomial(c+a, c+k), k, -a, a),
60 sum((binomial(3*k+1,k)*binomial(3*(n-k),n-k))/(3*k+1), k, 0, n),
67 sum(binomial(n, k) * binomial(m, r - k), k, 0, r),
81 sum((-1)^k*binomial(x-2*k,n-k)*binomial(x-k+1,k),k,0,n),
102 sum(binomial(n,k)^2*binomial(3*n+k,2*n), k, -inf, inf),
116 sum(binomial(x,k)*binomial(y,k), k, 0, y),
123 sum((-1)^(n-k)*binomial(n,k)*binomial(k+b,k), k, 0, n),
158 sum(((-1)^k*binomial(2*k,k)*binomial(n,k))/4^k,k,0,n),
165 sum((-1)^k*binomial(2*k,k)*binomial(2*n,k)*binomial(4*n-2*k,2*n-k),k,0,2*n),
[all …]
H A Drtest_simplify_sum.mac24 sum(r/k*binomial(n,r)*binomial(m,k-r)/binomial(n+m,k),r,0,k),
40 sum((-1)^k * binomial(a+b, a+k) * binomial(b+c, b+k) * binomial(c+a, c+k), k, -a, a),
64 sum((binomial(3*k+1,k)*binomial(3*(n-k),n-k))/(3*k+1), k, 0, n),
72 sum(binomial(n, k) * binomial(m, r - k), k, 0, r),
88 sum((-1)^k*binomial(x-2*k,n-k)*binomial(x-k+1,k),k,0,n),
112 sum(binomial(n,k)^2*binomial(3*n+k,2*n), k, -inf, inf),
128 sum(binomial(x,k)*binomial(y,k), k, 0, y),
136 sum((-1)^(n-k)*binomial(n,k)*binomial(k+b,k), k, 0, n),
176 sum(((-1)^k*binomial(2*k,k)*binomial(n,k))/4^k,k,0,n),
184 sum((-1)^k*binomial(2*k,k)*binomial(2*n,k)*binomial(4*n-2*k,2*n-k),k,0,2*n),
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/dports/math/maxima/maxima-5.43.2/share/contrib/Zeilberger/
H A Drtest_zeilberger.mac54 binomial(n,k)$
59 binomial(n,k)^2$
64 binomial(n,k)^3$
80 h2: binomial(a, k)* binomial(b, n-k);
81 binomial(a, k)* binomial(b, n-k);
98 h10: binomial(n, k)^2 * binomial( 2*k, k);
99 binomial(n, k)^2 * binomial( 2*k, k)$
122 h3: binomial(n+b, n+k)* binomial(n+c, c+k)*binomial(b+c, b+k)*(-1)^k;
123 binomial(n+b, n+k)* binomial(n+c, c+k)*binomial(b+c, b+k)*(-1)^k$
148 h11: binomial(n, k)^2 * binomial( 2*k, k+a);
[all …]
H A DtestZeilberger.mac25 f1 : binomial(n,k);
27 f2 : binomial(n,k)^2;
29 f3 : binomial(n,k)^3;
31 f4 : binomial(n,k)^4;
33 f5 : binomial(n,k)^5;
41 f9: binomial(n,k)^9;
49 h2: binomial(a, k)* binomial(b, n-k);
52 h3: binomial(n+b, n+k)* binomial(n+c, c+k)*binomial(b+c, b+k)*(-1)^k;
79 h10: binomial(n, k)^2 * binomial( 2*k, k);
83 h11: binomial(n, k)^2 * binomial( 2*k, k+a);
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/sum/
H A Dzeilberg.tst96 summand:=binomial(n,k)^2/binomial(2*n,n)$
117 % summand:=(-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*binomial(b+c,b+k)*
225 % (-1)^k*binomial(2*n,k)*binomial(2*k,k)*binomial(4*n-2*k,2*n-k),k,n);
227 sumrecursion(binomial(n,k)^2/binomial(2*n,n),k,n);
256 (-1)^(k-n)*binomial(2*n,k)^3/(binomial(3*n,n)*binomial(2*n,n)),k,n);
279 sumrecursion(binomial(n,k)*binomial(a,k),k,n);
282 sumrecursion(binomial(n,k)*binomial(n+k,k),k,n);
301 sumrecursion(binomial(r,m)*binomial(s,t-m),m,r);
302 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,s);
303 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,t);
[all …]
H A Dzeilberg.rlg387 (n + 1 - k)*(binomial(n + 1,k) - 2*binomial(n,k))
394 summand:=binomial(n,k)^2/binomial(2*n,n)$
401 ((binomial(n + 1,k) *binomial(2*n,n) - binomial(2*(n + 1),n + 1)*binomial(n,k) )
409 *binomial(2*(n + 1),n + 1)*binomial(2*n,n))
430 % summand:=(-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*binomial(b+c,b+k)*
632 % (-1)^k*binomial(2*n,k)*binomial(2*k,k)*binomial(4*n-2*k,2*n-k),k,n);
702 (-1)^(k-n)*binomial(2*n,k)^3/(binomial(3*n,n)*binomial(2*n,n)),k,n);
750 sumrecursion(binomial(n,k)*binomial(a,k),k,n);
765 sumrecursion(binomial(n,k)*binomial(n+k,k),k,n);
820 sumrecursion(binomial(r,m)*binomial(s,t-m),m,r);
[all …]
/dports/math/reduce/Reduce-svn5758-src/xmpl/
H A Dzeilberg.tst96 summand:=binomial(n,k)^2/binomial(2*n,n)$
117 % summand:=(-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*binomial(b+c,b+k)*
225 % (-1)^k*binomial(2*n,k)*binomial(2*k,k)*binomial(4*n-2*k,2*n-k),k,n);
227 sumrecursion(binomial(n,k)^2/binomial(2*n,n),k,n);
256 (-1)^(k-n)*binomial(2*n,k)^3/(binomial(3*n,n)*binomial(2*n,n)),k,n);
279 sumrecursion(binomial(n,k)*binomial(a,k),k,n);
282 sumrecursion(binomial(n,k)*binomial(n+k,k),k,n);
301 sumrecursion(binomial(r,m)*binomial(s,t-m),m,r);
302 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,s);
303 % sumrecursion(binomial(r,m)*binomial(s,t-m),m,t);
[all …]
H A Dzeilberg.rlg387 (n + 1 - k)*(binomial(n + 1,k) - 2*binomial(n,k))
394 summand:=binomial(n,k)^2/binomial(2*n,n)$
401 ((binomial(n + 1,k) *binomial(2*n,n) - binomial(2*(n + 1),n + 1)*binomial(n,k) )
409 *binomial(2*(n + 1),n + 1)*binomial(2*n,n))
430 % summand:=(-1)^k*binomial(n+b,n+k)*binomial(n+c,c+k)*binomial(b+c,b+k)*
632 % (-1)^k*binomial(2*n,k)*binomial(2*k,k)*binomial(4*n-2*k,2*n-k),k,n);
702 (-1)^(k-n)*binomial(2*n,k)^3/(binomial(3*n,n)*binomial(2*n,n)),k,n);
750 sumrecursion(binomial(n,k)*binomial(a,k),k,n);
765 sumrecursion(binomial(n,k)*binomial(n+k,k),k,n);
820 sumrecursion(binomial(r,m)*binomial(s,t-m),m,r);
[all …]
/dports/audio/praat/praat-6.2.03/melder/
H A DNUMspecfunc.cpp78 struct binomial *binomial = (struct binomial *) binomial_void; in binomialP() local
79 return NUMbinomialP (p, binomial -> k, binomial -> n) - binomial -> p; in binomialP()
83 struct binomial *binomial = (struct binomial *) binomial_void; in binomialQ() local
84 return NUMbinomialQ (p, binomial -> k, binomial -> n) - binomial -> p; in binomialQ()
88 static struct binomial binomial; in NUMinvBinomialP() local
91 binomial. p = p; in NUMinvBinomialP()
92 binomial. k = k; in NUMinvBinomialP()
93 binomial. n = n; in NUMinvBinomialP()
98 static struct binomial binomial; in NUMinvBinomialQ() local
101 binomial. p = p; in NUMinvBinomialQ()
[all …]
/dports/math/py-sympy/sympy-1.9/sympy/simplify/tests/
H A Dtest_combsimp.py2 combsimp, factorial, gamma, binomial, FallingFactorial, RisingFactorial,
11 assert combsimp(binomial(n, k)) == binomial(n, k)
14 assert combsimp(binomial(n + 1, k + 1)/binomial(n, k)) == (1 + n)/(1 + k)
16 assert combsimp(binomial(3*n + 4, n + 1)/binomial(3*n + 1, n)) == \
21 assert combsimp(factorial(n)*binomial(n + 1, k + 1)/binomial(n, k)) == \
33 assert combsimp(binomial(n, n - k)) == binomial(n, k)
37 binomial(n, k)
39 1/binomial(n, k)
40 assert combsimp(factorial(2*n)/factorial(n)**2) == binomial(2*n, n)
42 factorial(n)**3) == binomial(2*n, n)/binomial(n, k)
[all …]
/dports/comms/wsjtz/wsjtx/lib/ftrsd/ftrsd_paper/
H A Dbinomial.c45 printf("%lu\n", binomial(5, 3)); // 10 in main()
46 printf("%lu\n", binomial(40, 19)); // 131282408400 in main()
51 a=(double)binomial(40, 35); in main()
52 b=(double)binomial(23, 5); in main()
53 c=(double)binomial(63, 40); in main()
57 a=(double)binomial(40, 36); in main()
58 b=(double)binomial(23, 4); in main()
59 c=(double)binomial(63, 40); in main()
63 a=(double)binomial(40, 37); in main()
64 b=(double)binomial(23, 8); in main()
[all …]
/dports/math/pari/pari-2.13.3/src/test/32/
H A Dbinomial5 *** at top-level: binomial(1,2.)
7 *** binomial: incorrect type in binomial (t_REAL).
8 *** at top-level: binomial(-1)
10 *** binomial: incorrect type in binomial (t_INT).
11 *** at top-level: binomial(1.)
13 *** binomial: incorrect type in binomial (t_REAL).

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