ginsh
Section: The GiNaC Group (1)
Updated: January, 2000
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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
series_to_poly(series)
- convert a series into a polynomial by dropping the Order() term
sprem(expression, expression, symbol)
- sparse pseudo-remainder of polynomials
sqrfree(expression [, symbol-list])
- square-free factorization of a polynomial
sqrfree_parfrac(expression, symbol)
- square-free partial fraction decomposition of rational function
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 maintainers <https://www.ginac.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 © 1999-2023 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.
Index
- NAME
-
- SYNPOSIS
-
- DESCRIPTION
-
- USAGE
-
- INPUT FORMAT
-
- COMMENTS
-
- NUMBERS
-
- SYMBOLS
-
- WILDCARDS
-
- LAST PRINTED EXPRESSIONS
-
- OPERATORS
-
- LISTS
-
- MATRICES
-
- FUNCTIONS
-
- SPECIAL COMMANDS
-
- EXAMPLES
-
- DIAGNOSTICS
-
- AUTHOR
-
- SEE ALSO
-
- COPYRIGHT
-
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