_fmpz_vec_init len

Returns an initialised vector of fmpz's of given length.

_fmpz_vec_clear vec len

Clears the entries of (vec, len) and frees the space allocated for vec.

_fmpz_vec_randtest f state len bits

Sets the entries of a vector of the given length to random integers with up to the given number of bits per entry.

_fmpz_vec_randtest_unsigned f state len bits

Sets the entries of a vector of the given length to random unsigned integers with up to the given number of bits per entry.

_fmpz_vec_max_bits vec len

If \(b\) is the maximum number of bits of the absolute value of any coefficient of vec, then if any coefficient of vec is negative, \(-b\) is returned, else \(b\) is returned.

_fmpz_vec_max_bits_ref vec len

If \(b\) is the maximum number of bits of the absolute value of any coefficient of vec, then if any coefficient of vec is negative, \(-b\) is returned, else \(b\) is returned. This is a slower reference implementation of _fmpz_vec_max_bits.

_fmpz_vec_sum_max_bits sumabs maxabs vec len

Sets sumabs to the bit count of the sum of the absolute values of the elements of vec. Sets maxabs to the bit count of the maximum of the absolute values of the elements of vec.

_fmpz_vec_max_limbs vec len

Returns the maximum number of limbs needed to store the absolute value of any entry in (vec, len). If all entries are zero, returns zero.

_fmpz_vec_height height vec len

Computes the height of (vec, len), defined as the largest of the absolute values the coefficients. Equivalently, this gives the infinity norm of the vector. If len is zero, the height is \(0\).

_fmpz_vec_height_index vec len

Returns the index of an entry of maximum absolute value in the vector. The the length must be at least 1.

_fmpz_vec_fread file vec len

Reads a vector from the stream file and stores it at *vec. The format is the same as the output format of _fmpz_vec_fprint(), followed by either any character or the end of the file.

The interpretation of the various input arguments depends on whether or not *vec is NULL:

If *vec == NULL, the value of *len on input is ignored. Once the length has been read from file, *len is set to that value and a vector of this length is allocated at *vec. Finally, *len coefficients are read from the input stream. In case of a file or parsing error, clears the vector and sets *vec and *len to NULL and 0, respectively.

Otherwise, if *vec != NULL, it is assumed that (*vec, *len) is a properly initialised vector. If the length on the input stream does not match *len, a parsing error is raised. Attempts to read the right number of coefficients from the input stream. In case of a file or parsing error, leaves the vector (*vec, *len) in its current state.

In case of success, returns a positive value. In case of failure, returns a non-positive value.

_fmpz_vec_read vec len

Reads a vector from stdin and stores it at *vec.

For further details, see _fmpz_vec_fread().

_fmpz_vec_fprint file vec len

Prints the vector of given length to the stream file. The format is the length followed by two spaces, then a space separated list of coefficients. If the length is zero, only \(0\) is printed.

In case of success, returns a positive value. In case of failure, returns a non-positive value.

_fmpz_vec_print vec len

Prints the vector of given length to stdout.

For further details, see _fmpz_vec_fprint().

_fmpz_vec_get_nmod_vec res poly len mod

Reduce the coefficients of (poly, len) modulo the given modulus and set (res, len) to the result.

_fmpz_vec_set_nmod_vec res poly len mod

Set the coefficients of (res, len) to the symmetric modulus of the coefficients of (poly, len), i.e. convert the given coefficients modulo the given modulus \(n\) to their signed integer representatives in the range \([-n/2, n/2)\).

_fmpz_vec_get_fft coeffs_f coeffs_m l length

Convert the vector of coeffs coeffs_m to an fft vector coeffs_f of the given length with l limbs per coefficient with an additional limb for overflow.

_fmpz_vec_set_fft coeffs_m length coeffs_f limbs sign

Convert an fft vector coeffs_f of fully reduced Fermat numbers of the given length to a vector of fmpz's. Each is assumed to be the given number of limbs in length with an additional limb for overflow. If the output coefficients are to be signed then set sign, otherwise clear it. The resulting fmpzs will be in the range \([-n,n]\) in the signed case and in the range \([0,2n]\) in the unsigned case where n = 2^(FLINT_BITS*limbs - 1).

_fmpz_vec_get_d_vec_2exp appv vec len

Export the array of len entries starting at the pointer vec to an array of doubles appv, each entry of which is notionally multiplied by a single returned exponent to give the original entry. The returned exponent is set to be the maximum exponent of all the original entries so that all the doubles in appv have a maximum absolute value of 1.0.

_fmpz_vec_set vec1 vec2 len2

Makes a copy of (vec2, len2) into vec1.

_fmpz_vec_swap vec1 vec2 len2

Swaps the integers in (vec1, len2) and (vec2, len2).

_fmpz_vec_zero vec len

Zeros the entries of (vec, len).

_fmpz_vec_neg vec1 vec2 len2

Negates (vec2, len2) and places it into vec1.

_fmpz_vec_scalar_abs vec1 vec2 len2

Takes the absolute value of entries in (vec2, len2) and places the result into vec1.

_fmpz_vec_equal vec1 vec2 len

Compares two vectors of the given length and returns \(1\) if they are equal, otherwise returns \(0\).

_fmpz_vec_is_zero vec len

Returns \(1\) if (vec, len) is zero, and \(0\) otherwise.

_fmpz_vec_max vec1 vec2 vec3 len

Sets vec1 to the pointwise maximum of vec2 and vec3.

_fmpz_vec_max_inplace vec1 vec2 len

Sets vec1 to the pointwise maximum of vec1 and vec2.

_fmpz_vec_sort vec len

Sorts the coefficients of vec in ascending order.

_fmpz_vec_add res vec1 vec2 len2

Sets (res, len2) to the sum of (vec1, len2) and (vec2, len2).

_fmpz_vec_sub res vec1 vec2 len2

Sets (res, len2) to (vec1, len2) minus (vec2, len2).

_fmpz_vec_scalar_mul_fmpz vec1 vec2 len2 x

Sets (vec1, len2) to (vec2, len2) multiplied by \(c\), where \(c\) is an fmpz_t.

_fmpz_vec_scalar_mul_si vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) multiplied by \(c\), where \(c\) is a slong.

_fmpz_vec_scalar_mul_ui vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) multiplied by \(c\), where \(c\) is an ulong.

_fmpz_vec_scalar_mul_2exp vec1 vec2 len2 exp

Sets (vec1, len2) to (vec2, len2) multiplied by 2^exp.

_fmpz_vec_scalar_divexact_fmpz vec1 vec2 len2 x

Sets (vec1, len2) to (vec2, len2) divided by \(x\), where the division is assumed to be exact for every entry in vec2.

_fmpz_vec_scalar_divexact_si vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(x\), where the division is assumed to be exact for every entry in vec2.

_fmpz_vec_scalar_divexact_ui vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(x\), where the division is assumed to be exact for every entry in vec2.

_fmpz_vec_scalar_fdiv_q_fmpz vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(c\), rounding down towards minus infinity whenever the division is not exact.

_fmpz_vec_scalar_fdiv_q_si vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(c\), rounding down towards minus infinity whenever the division is not exact.

_fmpz_vec_scalar_fdiv_q_ui vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(c\), rounding down towards minus infinity whenever the division is not exact.

_fmpz_vec_scalar_fdiv_q_2exp vec1 vec2 len2 exp

Sets (vec1, len2) to (vec2, len2) divided by 2^exp, rounding down towards minus infinity whenever the division is not exact.

_fmpz_vec_scalar_fdiv_r_2exp vec1 vec2 len2 exp

Sets (vec1, len2) to the remainder of (vec2, len2) divided by 2^exp, rounding down the quotient towards minus infinity whenever the division is not exact.

_fmpz_vec_scalar_tdiv_q_fmpz vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(c\), rounding towards zero whenever the division is not exact.

_fmpz_vec_scalar_tdiv_q_si vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(c\), rounding towards zero whenever the division is not exact.

_fmpz_vec_scalar_tdiv_q_ui vec1 vec2 len2 c

Sets (vec1, len2) to (vec2, len2) divided by \(c\), rounding towards zero whenever the division is not exact.

_fmpz_vec_scalar_tdiv_q_2exp vec1 vec2 len2 exp

Sets (vec1, len2) to (vec2, len2) divided by 2^exp, rounding down towards zero whenever the division is not exact.

_fmpz_vec_scalar_addmul_fmpz vec1 vec2 len2 c

Adds (vec2, len2) times \(c\) to (vec1, len2).

_fmpz_vec_scalar_addmul_si_2exp vec1 vec2 len2 c exp

Adds (vec2, len2) times c * 2^exp to (vec1, len2), where \(c\) is a slong.

_fmpz_vec_scalar_submul_fmpz vec1 vec2 len2 x

Subtracts (vec2, len2) times \(c\) from (vec1, len2), where \(c\) is a fmpz_t.

_fmpz_vec_scalar_submul_si vec1 vec2 len2 c

Subtracts (vec2, len2) times \(c\) from (vec1, len2), where \(c\) is a slong.

_fmpz_vec_scalar_submul_si_2exp vec1 vec2 len2 c e

Subtracts (vec2, len2) times \(c \times 2^e\) from (vec1, len2), where \(c\) is a slong.

_fmpz_vec_sum res vec len

Sets res to the sum of the entries in (vec, len). Aliasing of res with the entries in vec is not permitted.

_fmpz_vec_prod res vec len

Sets res to the product of the entries in (vec, len). Aliasing of res with the entries in vec is not permitted. Uses binary splitting.

_fmpz_vec_scalar_mod_fmpz res vec len p

Reduces all entries in (vec, len) modulo \(p > 0\).

_fmpz_vec_scalar_smod_fmpz res vec len p

Reduces all entries in (vec, len) modulo \(p > 0\), choosing the unique representative in \((-p/2, p/2]\).

_fmpz_vec_content res vec len

Sets res to the non-negative content of the entries in vec. The content of a zero vector, including the case when the length is zero, is defined to be zero.

_fmpz_vec_content_chained res vec len input

Sets res to the non-negative content of input and the entries in vec. This is useful for calculating the common content of several vectors.

_fmpz_vec_lcm res vec len

Sets res to the nonnegative least common multiple of the entries in vec. The least common multiple is zero if any entry in the vector is zero. The least common multiple of a length zero vector is defined to be one.

_fmpz_vec_dot res vec1 vec2 len2

Sets res to the dot product of (vec1, len2) and (vec2, len2).

_fmpz_vec_dot_ptr res vec1 vec2 offset len

Sets res to the dot product of len values at vec1 and the len values vec2[i] + offset for 0 \leq i < len.