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ginsh(1) The GiNaC Group 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
 
factor(expression) - factorizes an expression (univariate)
 
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 (mind the quotes, please!)
 
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 © 1999-2011 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.
January, 2000 GiNaC 1.6.2