44
44
char *fake = N_("Given two factorizations, give the factorization of the product, see Factorize");
45
45
char *fake = N_("Convert a vector of values indicating powers of b to a number");
46
46
char *fake = N_("Convert a number to a vector of powers for elements in base b");
47
char *fake = N_("Find discrete log of n base b in F_q where q is a prime using the Silver-Pohlig-Hellman algoritm");
47
char *fake = N_("Find discrete log of n base b in F_q where q is a prime using the Silver-Pohlig-Hellman algorithm");
48
48
char *fake = N_("Compute phi(n), the Euler phi function, that is the number of integers between 1 and n relatively prime to n");
49
49
char *fake = N_("Return all factors of a number");
50
char *fake = N_("Attempt fermat factorization of n into (t-s)*(t+s), returns t and s as a vector if possible, null otherwise");
50
char *fake = N_("Attempt Fermat factorization of n into (t-s)*(t+s), returns t and s as a vector if possible, null otherwise");
51
51
char *fake = N_("Find the first primitive element in F_q (q must be a prime)");
52
52
char *fake = N_("Find a random primitive element in F_q (q must be a prime)");
53
53
char *fake = N_("Compute discrete log base b of n in F_q (q a prime) using the factor base S. S should be a column of primes possibly with second column precalculated by IndexCalculusPrecalculation.");
66
66
char *fake = N_("Returns the p-adic valuation (number of trailing zeros in base p).");
67
67
char *fake = N_("Compute a^b mod m");
68
68
char *fake = N_("Return all prime factors of a number");
69
char *fake = N_("Pseudoprime test, true iff b^(n-1) == 1 (mod n)");
69
char *fake = N_("Pseudoprime test, true if and only if b^(n-1) == 1 (mod n)");
70
70
char *fake = N_("Removes all instances of the factor m from the number n");
71
char *fake = N_("Find discrete log of n base b in F_q where q is a prime using the Silver-Pohlig-Hellman algoritm, given f being the factorization of q-1");
71
char *fake = N_("Find discrete log of n base b in F_q where q is a prime using the Silver-Pohlig-Hellman algorithm, given f being the factorization of q-1");
72
72
char *fake = N_("Find square root of n mod p (a prime). Null is returned if not a quadratic residue.");
73
73
char *fake = N_("Apply a function over all entries of a matrix and return a matrix of the results");
74
74
char *fake = N_("Apply a function over all entries of 2 matrices (or 1 value and 1 matrix) and return a matrix of the results");
119
119
char *fake = N_("Inverse Hilbert matrix of order n");
120
120
char *fake = N_("Is a matrix Hermitian");
121
121
char *fake = N_("Test if a vector is in a subspace");
122
char *fake = N_("Is a matrix (or number) invertible (Integer matrix is invertible iff it's invertible over the integers)");
122
char *fake = N_("Is a matrix (or number) invertible (Integer matrix is invertible if and only if it is invertible over the integers)");
123
123
char *fake = N_("Is a matrix (or number) invertible over a field");
124
124
char *fake = N_("Is a matrix normal");
125
125
char *fake = N_("Is a matrix positive definite");
126
126
char *fake = N_("Is a matrix positive semidefinite");
127
127
char *fake = N_("Is a matrix skew-Hermitian");
128
128
char *fake = N_("Is a matrix unitary");
129
char *fake = N_("Get the jordan block corresponding to lambda and n");
129
char *fake = N_("Get the Jordan block corresponding to lambda and n");
130
130
char *fake = N_("Get the kernel (nullspace) of a linear transform");
131
131
char *fake = N_("Get the LU decomposition of A and store the result in the L and U which should be references. If not possible returns false.");
132
132
char *fake = N_("Get the i-j minor of a matrix");
159
159
char *fake = N_("The sum of the vector spaces M and N, that is {w | w=m+n, m in M, n in N}");
160
160
char *fake = N_("Get the classical adjoint (adjugate) of a matrix");
161
161
char *fake = N_("Compute the Column Reduced Echelon Form");
162
char *fake = N_("Get n'th catalan number");
162
char *fake = N_("Get nth Catalan number");
163
163
char *fake = N_("Double factorial: n(n-2)(n-4)...");
164
164
char *fake = N_("Factorial: n(n-1)(n-2)...");
165
165
char *fake = N_("Falling factorial: (n)_k = n(n-1)...(n-(k-1))");
166
char *fake = N_("Calculate n'th Fibonacci number");
166
char *fake = N_("Calculate nth Fibonacci number");
167
167
char *fake = N_("Calculate the Frobenius number for a coin problem");
168
168
char *fake = N_("Galois matrix given a linear combining rule (a_1*x_+...+a_n*x_n=x_(n+1))");
169
169
char *fake = N_("Use greedy algorithm to find c, for c . v = n. (v must be sorted)");
170
170
char *fake = N_("Harmonic Number, the nth harmonic number of order r");
171
171
char *fake = N_("Hofstadter's function q(n) defined by q(1)=1, q(2)=1, q(n)=q(n-q(n-1))+q(n-q(n-2))");
172
char *fake = N_("Compute linear recursive sequence using galois stepping");
172
char *fake = N_("Compute linear recursive sequence using Galois stepping");
173
173
char *fake = N_("Calculate multinomial coefficients");
174
char *fake = N_("Get the pascal's triangle as a matrix");
174
char *fake = N_("Get the Pascal's triangle as a matrix");
175
175
char *fake = N_("(Pochhammer) Rising factorial: (n)_k = n(n+1)...(n+(k-1))");
176
176
char *fake = N_("Stirling number of the first kind");
177
177
char *fake = N_("Stirling number of the second kind");
211
211
char *fake = N_("Compute two-sided derivative using three-point formula");
212
212
char *fake = N_("argument (angle) of complex number");
213
213
char *fake = N_("Dirichlet kernel of order n");
214
char *fake = N_("Returns 1 iff all elements are zero");
214
char *fake = N_("Returns 1 if and only if all elements are zero");
215
215
char *fake = N_("The error function, 2/sqrt(pi) * int_0^x e^(-t^2) dt");
216
216
char *fake = N_("Fejer kernel of order n");
217
char *fake = N_("Returns 1 iff all elements are equal");
217
char *fake = N_("Returns 1 if and only if all elements are equal");
218
218
char *fake = N_("Find the first value where f(x)=0");
219
219
char *fake = N_("Moebius mapping of the disk to itself mapping a to 0");
220
220
char *fake = N_("Moebius mapping using the cross ratio taking z2,z3,z4 to 1,0, and infinity respectively");
256
256
char *fake = N_("Return the dth Macaulay representation of a positive integer c");
257
257
char *fake = N_("Attempt to symbolically differentiate a function n times");
258
258
char *fake = N_("Attempt to symbolically differentiate a function n times quietly and return null on failure");
259
char *fake = N_("Attempt to construct the taylor approximation function around x0 to the nth degree.");
259
char *fake = N_("Attempt to construct the Taylor approximation function around x0 to the nth degree.");