Provided by: ginac-tools_1.7.8-2build1_amd64 
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
evalf(expression) - 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) - 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 © 1999-2019 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, 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.