ginsh(1)

NAME
ginsh - GiNaC Interactive Shell

SYNPOSIS
ginsh [file...]

DESCRIPTION
ginsh is an interactive frontend for the GiNaC symbolic computation framework. It is intended as a tool for testing and experimenting with GiNaC's features, not as a replacement for traditional interactive computer algebra systems. Although it can do many things these traditional systems can do, ginsh provides no programming constructs like loops or conditional expressions. If you need this functionality you are advised to write your program in C++, using the "native" GiNaC class framework.

USAGE

  INPUT FORMAT
After startup, ginsh displays a prompt ("> ") signifying that it is ready to accept your input. Acceptable input are numeric or symbolic expressions consisting of numbers (e.g. 42, 2/3 or 0.17), symbols (e.g. x or result), mathematical operators like + and *, and functions (e.g. sin or normal). Every input expression must be terminated with either a semicolon (;) or a colon (:). If terminated with a semicolon, ginsh will evaluate the expression and print the result to stdout. If terminated with a colon, ginsh will only evaluate the expression but not print the result. It is possible to enter multiple expressions on one line. Whitespace (spaces, tabs, newlines) can be applied freely between tokens. To quit ginsh, enter quit or exit, or type an EOF (Ctrl-D) at the prompt.

  COMMENTS
Anything following a double slash (//) up to the end of the line, and all lines starting with a hash mark (#) are treated as a comment and ignored.

  NUMBERS
ginsh accepts numbers in the usual decimal notations. This includes arbitrary precision integers and rationals as well as floating point numbers in standard or scientific notation (e.g. 1.2E6). The general rule is that if a number contains a decimal point (.), it is an (inexact) floating point number; otherwise it is an (exact) integer or rational. Integers can be specified in binary, octal, hexadecimal or arbitrary (2-36) base by prefixing them with #b, #o, #x, or #nR , respectively.

  SYMBOLS
Symbols are made up of a string of alphanumeric characters and the underscore (_), with the first character being non-numeric. E.g. a and mu_1 are acceptable symbol names, while 2pi is not. It is possible to use symbols with the same names as functions (e.g. sin); ginsh is able to distinguish between the two.

Symbols can be assigned values by entering
    symbol = expression;

To unassign the value of an assigned symbol, type
    unassign('symbol');

Assigned symbols are automatically evaluated (= replaced by their assigned value) when they are used. To refer to the unevaluated symbol, put single quotes (') around the name, as demonstrated for the "unassign" command above.

Symbols are considered to be in the complex domain by default, i.e. they are treated as if they stand in for complex numbers. This behavior can be changed by using the keywords real_symbols and complex_symbols and affects all newly created symbols.

The following symbols are pre-defined constants that cannot be assigned a value by the user:

    Pi  Archimedes' Constant

    Catalan
        Catalan's Constant

    Euler
        Euler-Mascheroni Constant

    I   sqrt(-1)

    FAIL
        an object of the GiNaC "fail" class

There is also the special
    Digits
symbol that controls the numeric precision of calculations with inexact numbers. Assigning an integer value to digits will change the precision to the given number of decimal places.

  WILDCARDS
The has(), find(), match() and subs() functions accept wildcards as placeholders for expressions. These have the syntax
    $number
for example $0, $1 etc.

  LAST PRINTED EXPRESSIONS
ginsh provides the three special symbols
    %, %% and %%%
that refer to the last, second last, and third last printed expression, respectively. These are handy if you want to use the results of previous computations in a new expression.

  OPERATORS
ginsh provides the following operators, listed in falling order of precedence:

        ! postfix factorial

    ^   powering

    +   unary plus

    -   unary minus

    *   multiplication

    /   division

    +   addition

    -   subtraction

    <   less than

    >   greater than

    <=  less or equal

    >=  greater or equal

    ==  equal

    !=  not equal

    =   symbol assignment

All binary operators are left-associative, with the exception of ^ and = which are right-associative. The result of the assignment operator (=) is its right-hand side, so it's possible to assign multiple symbols in one expression (e.g. a = b = c = 2;).

  LISTS
Lists are used by the subs and lsolve functions. A list consists of an opening curly brace ({), a (possibly empty) comma-separated sequence of expressions, and a closing curly brace (}).

  MATRICES
A matrix consists of an opening square bracket ([), a non-empty comma-separated sequence of matrix rows, and a closing square bracket (]). Each matrix row consists of an opening square bracket ([), a non-empty comma-separated sequence of expressions, and a closing square bracket (]). If the rows of a matrix are not of the same length, the width of the matrix becomes that of the longest row and shorter rows are filled up at the end with elements of value zero.

  FUNCTIONS
A function call in ginsh has the form
    name(arguments)
where arguments is a comma-separated sequence of expressions. ginsh provides a couple of built-in functions and also "imports" all symbolic functions defined by GiNaC and additional libraries. There is no way to define your own functions other than linking ginsh against a library that defines symbolic GiNaC functions.

ginsh provides Tab-completion on function names: if you type the first part of a function name, hitting Tab will complete the name if possible. If the part you typed is not unique, hitting Tab again will display a list of matching functions. Hitting Tab twice at the prompt will display the list of all available functions.

A list of the built-in functions follows. They nearly all work as the respective GiNaC methods of the same name, so I will not describe them in detail here. Please refer to the GiNaC documentation.

    charpoly(matrix, symbol) - characteristic polynomial of a matrix
    coeff(expression, object, number) - extracts coefficient of object^number from a polynomial
    collect(expression, object-or-list) - collects coefficients of like powers (result in recursive form)
    collect_distributed(expression, list) - collects coefficients of like powers (result in distributed form)
    collect_common_factors(expression) - collects common factors from the terms of sums
    conjugate(expression) - complex conjugation
    content(expression, symbol) - content part of a polynomial
    decomp_rational(expression, symbol) - decompose rational function into polynomial and proper rational function
    degree(expression, object) - degree of a polynomial
    denom(expression) - denominator of a rational function
    determinant(matrix) - determinant of a matrix
    diag(expression...) - constructs diagonal matrix
    diff(expression, symbol [, number]) - partial differentiation
    divide(expression, expression) - exact polynomial division
    eval(expression [, level]) - evaluates an expression, replacing symbols by their assigned value
    evalf(expression [, level]) - evaluates an expression to a floating point number
    evalm(expression) - evaluates sums, products and integer powers of matrices
    expand(expression) - expands an expression
    find(expression, pattern) - returns a list of all occurrences of a pattern in an expression
    fsolve(expression, symbol, number, number) - numerically find root of a real-valued function within an interval
    gcd(expression, expression) - greatest common divisor
    has(expression, pattern) - returns "1" if the first expression contains the pattern as a subexpression, "0" otherwise
    integer_content(expression) - integer content of a polynomial
    inverse(matrix) - inverse of a matrix
    is(relation) - returns "1" if the relation is true, "0" otherwise (false or undecided)
    lcm(expression, expression) - least common multiple
    lcoeff(expression, object) - leading coefficient of a polynomial
    ldegree(expression, object) - low degree of a polynomial
    lsolve(equation-list, symbol-list) - solve system of linear equations
    map(expression, pattern) - apply function to each operand; the function to be applied is specified as a pattern with the "$0" wildcard standing for the operands
    match(expression, pattern) - check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
    nops(expression) - number of operands in expression
    normal(expression [, level]) - rational function normalization
    numer(expression) - numerator of a rational function
    numer_denom(expression) - numerator and denumerator of a rational function as a list
    op(expression, number) - extract operand from expression
    power(expr1, expr2) - exponentiation (equivalent to writing expr1^expr2)
    prem(expression, expression, symbol) - pseudo-remainder of polynomials
    primpart(expression, symbol) - primitive part of a polynomial
    quo(expression, expression, symbol) - quotient of polynomials
    rank(matrix) - rank of a matrix
    rem(expression, expression, symbol) - remainder of polynomials
    resultant(expression, expression, symbol) - resultant of two polynomials with respect to symbol s
    series(expression, relation-or-symbol, order) - series expansion
    sprem(expression, expression, symbol) - sparse pseudo-remainder of polynomials
    sqrfree(expression [, symbol-list]) - square-free factorization of a polynomial
    sqrt(expression) - square root
    subs(expression, relation-or-list)
    subs(expression, look-for-list, replace-by-list) - substitute subexpressions (you may use wildcards)
    tcoeff(expression, object) - trailing coefficient of a polynomial
    time(expression) - returns the time in seconds needed to evaluate the given expression
    trace(matrix) - trace of a matrix
    transpose(matrix) - transpose of a matrix
    unassign(symbol) - unassign an assigned symbol
    unit(expression, symbol) - unit part of a polynomial

  SPECIAL COMMANDS
To exit ginsh, enter
    quit
or
    exit

ginsh can display a (short) help for a given topic (mostly about functions and operators) by entering
    ?topic
Typing
    ??
will display a list of available help topics.

The command
    print(expression);
will print a dump of GiNaC's internal representation for the given expression. This is useful for debugging and for learning about GiNaC internals.

The command
    print_latex(expression);
prints a LaTeX representation of the given expression.

The command
    print_csrc(expression);
prints the given expression in a way that can be used in a C or C++ program.

The command
    iprint(expression);
prints the given expression (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.

Finally, the shell escape
    ! [command [arguments]]
passes the given command and optionally arguments to the shell for execution. With this method, you can execute shell commands from within ginsh without having to quit.

EXAMPLES
> a = x^2-x-2;
-2-x+x^2
> b = (x+1)^2;
(x+1)^2
> s = a/b;
(x+1)^(-2)*(-2-x+x^2)
> diff(s, x);
(2*x-1)*(x+1)^(-2)-2*(x+1)^(-3)*(-x+x^2-2)
> normal(s);
(x-2)*(x+1)^(-1)
> x = 3^50;
717897987691852588770249
> s;
717897987691852588770247/717897987691852588770250
> Digits = 40;
40
> evalf(s);
0.999999999999999999999995821133292704384960990679
> unassign('x');
x
> s;
(x+1)^(-2)*(-x+x^2-2)
> series(sin(x),x==0,6);
1*x+(-1/6)*x^3+1/120*x^5+Order(x^6)
> lsolve({3*x+5*y == 7}, {x, y});
{x==-5/3*y+7/3,y==y}
> lsolve({3*x+5*y == 7, -2*x+10*y == -5}, {x, y});
{x==19/8,y==-1/40}
> M = [ [a, b], [c, d] ];
[[-x+x^2-2,(x+1)^2],[c,d]]
> determinant(M);
-2*d-2*x*c-x^2*c-x*d+x^2*d-c
> collect(%, x);
(-d-2*c)*x+(d-c)*x^2-2*d-c
> solve quantum field theory;
parse error at quantum
> quit

DIAGNOSTICS

parse error at foo
    You entered something which ginsh was unable to parse. Please check the syntax of your input and try again.

argument num to function must be a type
    The argument number num to the given function must be of a certain type (e.g. a symbol, or a list). The first argument has number 0, the second argument number 1, etc.

AUTHOR

The GiNaC Group:
    Christian Bauer <Christian.Bauer@uni-mainz.de>
    Alexander Frink <Alexander.Frink@uni-mainz.de>
    Richard Kreckel <Richard.Kreckel@uni-mainz.de>
    Jens Vollinga <vollinga@thep.physik.uni-mainz.de>

SEE ALSO
GiNaC Tutorial - An open framework for symbolic computation within the C++ programming language

CLN - A Class Library for Numbers, Bruno Haible

COPYRIGHT
Copyright © 1999-2006 Johannes Gutenberg Universität Mainz, Germany This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.