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This code uses a separate function to do a first-order forward difference, which is then called several times for calculating n-th order forward difference. No error checking is implemented. J is array oriented, so you can even ask for more than one forward difference at a time i.

N can be a list, parigp bin re alternatives of a single number:. Here we use signature matching to bind both an entire array and a version missing the head. The Z- operator is a zip metaoperator with a minus to subtract the two lists pairwise. It's almost a shame to define difn, since parigp bin re alternatives series and subscript are hardly longer than the call itself would be, and arguably more self-documenting than the name of the function would be.

It's possible to implement differences using row indices. For instance, first forward differences of a variable x can be defined by:. However, it's much more natural to use time-series varlists. In order to use them, it's necessary to first set a time variable, which may be simply an index variable. This function doesn't need to be defined because it's in a library already, but it could be defined like this:.

Create account Log in. Page Discussion Edit History. Forward difference From Rosetta Code. Fortran version 90 and later. Rakudo Star version Retrieved from " https: This page was last modified on 30 Januaryat parigp bin re alternatives Privacy policy About Rosetta Code Disclaimers.

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A number of control statements are available in GP. They are simpler and have a syntax slightly different from their C counterparts, but are quite powerful enough to write any kind of program.

Some of them are specific to GP, since they are made for number theorists. As usual, X will denote any simple variable name, and seq will always denote a sequence of expressions, including the empty sequence.

If the sequence seq modifies the loop index, then the loop is modified accordingly:. If n is greater than the number of enclosing loops, all enclosing loops are exited.

It is assumed that factor can handle n, without negative exponents. Instead of n, it is possible to input a factorization matrix, i.

This routine uses divisors as a subroutine, then loops over the divisors. In particular, if n is an integer, divisors are sorted by increasing size. To avoid storing all divisors, possibly using a lot of memory, the following much slower routine loops over the divisors using essentially constant space:.

Th elldata database must be installed and contain data for the specified conductors. More precisely, the value of X is incremented to the smallest prime strictly larger than X at the end of each iteration. Note that a and b must be in R. In the latter case, the successive steps are used in the order they appear in s.

The subgroups are not ordered in any obvious way, unless G is a p-group in which case Birkhoff's algorithm produces them by decreasing index. A subgroup is given as a matrix whose columns give its generators on the implicit generators of G. This routine is intended to treat huge groups, when subgrouplist is not an option due to the sheer size of the output. For maximal speed the subgroups have been left as produced by the algorithm. To print them in canonical form as left divisors of G in HNF form , one can for instance use.

Note that in this last representation, the index [G: H] is given by the determinant. See galoissubcyclo and galoisfixedfield for nfsubfields applications to Galois theory. This routine evaluates seq , where the formal variables X[1], The formal variable with the highest index moves the fastest. Of course, seq1 or seq2 may be empty:. You could get the same result using the! Recall that functions such as break and next operate on loops such as forxxx , while , until.

The if statement is not a loop obviously! If n is specified, resume at the n-th enclosing loop. If n is bigger than the number of enclosing loops, all enclosing loops are exited. If x is omitted, return the void value return no result, like print.

If a is initially not equal to 0, seq is evaluated once more generally, the condition on a is tested after execution of the seq , not before as in while. The test is made before evaluating the seq, hence in particular if a is initially equal to zero the seq will not be evaluated at all.

In addition to the general PARI functions, it is necessary to have some functions which will be of use specifically for gp , though a few of these can be accessed under library mode. Before we start describing these, we recall the difference between strings and keywords see Section [ Label: The former are dynamic objects, where everything outside quotes gets immediately expanded. The string str is expanded on the spot and stored as the online help for S.

If S is a function you have defined, its definition will still be printed before the message str. It is recommended that you document global variables and user functions in this way. Of course gp will not protest if you skip this. Nothing prevents you from modifying the help of built-in PARI functions. But if you do, we would like to hear why you needed to do it! This is different from the general user macros in that alias expansion takes place immediately upon execution, without having to look up any function code, and is thus much faster.

Alias commands are meant to be read upon startup from the. Although it is a function, allocatemem cannot be used in loop-like constructs, or as part of a larger expression, e. Such an attempt will raise an error. The technical reason is that this routine usually moves the stack, so objects from the current expression may not be correct anymore, e.

The library syntax is allocatemoremem x , where x is an unsigned long, and the return type is void. If val is present, sets the default to val first which is subject to string expansion first. See Section [ Label: Note that the shortcut are meant for interactive use and usually display more information than default. This command is immediately run and its input fed into gp , just as if read from a file.

Useful mainly for debugging purposes. Should be equal to 0 in between commands. From now on, you will be forbidden to use them as formal parameters for function definitions or as loop indexes. This is especially useful when patching together various scripts, possibly written with different naming conventions. For instance the following situation is dangerous:. Calling global without arguments prints the list of global variables in use.

In particular, eval global will output the values of all global variables. If a sequence of expressions is given, the result is the result of the last expression of the sequence. When using this instruction, it is useful to prompt for the string by using the print1 function. Note that in the present version 2. Assigns to it the name gpname in this gp session, with argument code code see the Libpari Manual for an explanation of those.

If lib is omitted, uses libpari. If gpname is omitted, uses name. This function is useful for adding custom functions to the gp interpreter, or picking useful functions from unrelated libraries. For instance, it makes the function system obsolete:. But it also gives you access to all non static functions defined in the PARI library.

Re-installing a function will print a Warning, and update the prototype code if needed, but will reload a symbol from the library, even it the latter has been recompiled. This function may not work on all systems, especially when gp has been compiled statically. In that case, the first use of an installed function will provoke a Segmentation Fault, i. Hence, if you intend to use this function, please check first on some harmless example such as the ones above that it works properly on your machine.

The corresponding identifier can now be used to name any GP object variable or function. This is the only way to replace a variable by a function having the same name or the other way round , as in the following example:.

When you kill a variable, all objects that used it become invalid. You can still display them, even though the killed variable will be printed in a funny way. If you simply want to restore a variable to its "undefined" value monomial of degree one , use the quote operator: Predefined symbols x and GP function names cannot be killed. This output can then be used in a TeX manuscript.

The printing is done on the standard output. If you want to print it to a file you should use writetex see there. Another possibility is to enable the log default seeSection [ Label: You could for instance do:. If filename is omitted, re-reads the last file that was fed into gp.

The return value is the result of the last expression evaluated. If a GP binary file is read using this command see Section [ Label: The return value is a vector whose components are the evaluation of all sequences of instructions contained in the file. For instance, if file contains. If x is the empty vector, this gives the vector whose components are the existing variables in increasing order i. Killed variables see kill will be shown as 0. If x is non-empty, it must be a permutation of variable names, and this permutation gives a new order of importance of the variables, for output only.

For example, if the existing order is [x,y,z] , then after reorder [z,x] the order of importance of the variables, with respect to output, will be [z,y,x]. The internal representation is unaffected. The library syntax is setrand n , where n is a long.

This command is executed, its output written to the standard output this won't get into your logfile , and control returns to the PARI system. This simply calls the C system command. If e is omitted, all exceptions are trapped. If seq is omitted, defines rec as a default action when catching exception e, provided no other trap as above intercepts it first.