Pari gp binary trading
Many of the conversion functions pari gp binary trading rounding or truncating operations. In this case, if the argument is a rational function, the result is the Euclidean quotient of the numerator by the denominator, and if the argument is a vector or a matrix, the operation is done componentwise.
This will not be restated for every function. The dimension of the resulting vector can be optionally specified via the extra parameter n. If n is omitted or 0, the dimension depends on the type of x; the vector has a single component, except when x is. In the case of a polynomial, the coefficients of the vector start with the leading coefficient of the polynomial, while for power series only the significant coefficients are taken into account, but this time by increasing order of degree.
In this last case, Vec is the reciprocal function of Pol and Ser respectively. In the last two cases matrix and character string pari gp binary trading, n is meaningless and must be omitted or an error is raised. The dimension of the resulting vector is n. In particular, Colrev is the reciprocal function of Polrev: Similarly for a list, but rather useless in this case.
For other types, creates a list with the single element x. Note that, except when x is omitted, this function creates a small memory leak; so, either initialize all pari gp binary trading to the empty list, or use them sparingly.
The variant GEN mklist void creates an empty list. If the argument x pari gp binary trading omitted, creates an empty map, which may be filled later via mapput. If x is already a matrix, a copy of x is created. If x is a row resp. Pari gp binary trading x is a binary quadratic form, creates the attached 2 x 2 matrix. Otherwise, this creates a 1 x 1 matrix containing x.
Mod a, b In its basic form, creates an intmod or a polmod a mod b ; b must be an integer or a polynomial. Note that such "modular" objects can be lifted via lift or centerlift. If t is a scalar, this gives a constant polynomial. If t is a power series with non-negative valuation or a rational function, the effect is similar to truncatei.
The main use of this function is when t is a vector: Polrev can be used if one wants x to be pari gp binary trading constant coefficient:. The reciprocal function of Pol resp. Polrev is Vec resp. This is not a substitution function. If t is a power series, the effect is identical to truncatei. Pol can be used if one wants t to be the leading coefficient:.
Negative definite forms are not implemented, use their positive definite counterpart instead. If s is a scalar, this gives a constant power series in v with precision d. If s is a polynomial, the polynomial is truncated to d terms if needed. If s is a vector, on the other hand, the coefficients of the vector are understood to be the coefficients of the power series starting from the constant term as in Polrev xand the precision d is ignored: Finally, if s is already a power series in v, we return it verbatim, ignoring d again.
All others are converted to a set with one element. To recover an ordinary GEN from a string, apply pari gp binary trading to it. The arguments of Str are evaluated in string context, see Section se: This function is mostly useless in library mode. The latter returns a malloced string, which should be freed after usage. Strchr x Converts x to a string, translating each integer into a character.
Then perform environment expansion, see Section se: This feature can be used to read environment variable values. Vec is the reciprocal function of Pol for a polynomial and of Pari gp binary trading for a power series.
In the last four cases matrix, character string, map, errorn is meaningless and must be omitted or an error is raised. In particular, Vecrev is pari gp binary trading reciprocal function of Polrev: This acts as Vec x,nbut only on a limited set of objects: If x is a character string, a vector of individual characters in ASCII encoding is returned Strchr yields back the character string. Negative numbers behave 2-adically, i. The result is an ordinary integer, possibly negative.
If n is missing, the function pari gp binary trading the floating point precision in bits of the PARI object x. If n is present and positive, the function creates a new object equal to x with the new bit-precision roughly n. In fact, the smallest multiple of 64 resp. For x a vector or a matrix, the operation is done componentwise; for series and polynomials, the operation is done coefficientwise. For real x, n is the number of desired significant bits. If n is smaller than the precision of x, x is truncated, otherwise x is extended with zeros.
For exact or non-floating point types, no change. The result is 0 or 1. Applied to a rational function, ceil x returns the Euclidean quotient of the numerator by the denominator. Use bestappr for this. For backward compatibility, centerlift x,'v is allowed as an alias for lift x,'v.
This is to be understood as follows: The components are counted, starting at 1, after these code words. In particular if x is a vector, this is indeed the n-th-component of x, if x is a matrix, the n-th column, if x is a polynomial, the n-th coefficient i.
For polynomials and power series, one should rather use polcoeffand for vectors and matrices, the  operator. Namely, if x is a vector, then x[n] represents the n-th component of x. If x is a matrix, x[m,n] represents the coefficient of row m and column n of the matrix, x[m,] represents the m-th row of x, and x[,n] represents the n-th column of x.
Using of this function requires detailed knowledge of the structure of the different PARI pari gp binary trading, and thus it should almost never be used directly. The meaning of this is clear, except that for real quadratic numbers, it means conjugation in the real quadratic pari gp binary trading. This function pari gp binary trading no effect on integers, reals, intmods, fractions or p-adics. The only forbidden type is polmod see conjvec for this.
If z is a polmod, equal to Mod a,Tthis gives a vector of length degree T containing:. If z is a row or column vector, the result is a matrix whose columns are the conjugate vectors of the individual elements of z.
The meaning of this is clear when x is a rational number or function. If x is an integer or a polynomial, it is treated as a rational number or function, respectively, and the result is equal to 1. For polynomials, you probably want to use. If x is a recursive structure, for instance a vector or matrix, the lcm of the denominators of its components a common denominator is computed.
See fromdigits for the reverse operation. Applied to a rational function, floor x returns the Euclidean quotient of the numerator pari gp binary trading the denominator. Identical to x-floor x. If x is real, the result is in [0,1[. This is the reverse of digits:.
This is mostly useful for. The routine is in fact defined for arbitrary GP types, but is awkward and useless in other cases: More generally, components for which such lifts are meaningless e. Lifts are performed recursively on an object components, but only by pari gp binary trading level: To recursively lift all components not only by one level, but as long as possible, use liftall.
If x is an pari gp binary trading or a polynomial, it is treated as pari gp binary trading rational number or function, respectively, and the result is x itself. The number k is taken modulo n!
The numbering used is the standard lexicographic ordering, starting at 0. The function raises an exception if it encounters an object pari gp binary trading with p-adic computations:.
If n is missing, the function returns the precision in decimal digits of the PARI object x. If n is present, pari gp binary trading function creates a new object equal to x with a new floating point precision n: In both, the accuracy is expressed in pari gp binary trading bit or bit depending on the architecture.
More precisely if the curve has a single point at infinity! Note that this is definitely not a uniform distribution over E kbut it should be good enough for applications. The coefficients are drawn by applying random to the leading coefficient of N.
Pari gp binary trading variants all depend on a single internal generator, and are independent from your operating system's random number generators. A random seed may be obtained via getrandand reset using setrand:
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