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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 com- puter 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 func- tions (e.g. sin or normal). Every input expression must be terminated with either a semicolon (;) or a colon (:). If terminated with a semi- colon, ginsh will evaluate the expression and print the result to std- out. If terminated with a colon, ginsh will only evaluate the expres- sion but not print the result. It is possible to enter multiple expres- sions 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 ar- bitrary precision integers and rationals as well as floating point num- bers in standard or scientific notation (e.g. 1.2E6). The general rule is that if a number contains a decimal point (.), it is an (inex- act) floating point number; otherwise it is an (exact) integer or ra- tional. Integers can be specified in binary, octal, hexadecimal or ar- bitrary (2-36) base by prefixing them with #b, #o, #x, or #nR , respec- tively. SYMBOLS Symbols are made up of a string of alphanumeric characters and the un- derscore (_), 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 as- signed value) when they are used. To refer to the unevaluated symbol, put single quotes (') around the name, as demonstrated for the "unas- sign" 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 preci- sion 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 previ- ous 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 possi- ble. If the part you typed is not unique, hitting Tab again will dis- play 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 ob- ject^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 func- tion 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" other- wise (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 ratio- nal 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 poly- nomials 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 frac- tion 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 polyno- mial time(expression) - returns the time in seconds needed to evalu- ate 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 func- tions 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 ex- pression. 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 dec- imal, octal, and hexadecimal representations. Finally, the shell escape ! [command [arguments]] passes the given command and optionally arguments to the shell for exe- cution. 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 cer- tain 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 (C) 1999-2025 Johannes Gutenberg Universitat 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 MER- CHANTABILITY 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. GiNaC 1.8.9 January, 2000 ginsh(1)
NAME | SYNPOSIS | DESCRIPTION | USAGE | EXAMPLES | DIAGNOSTICS | AUTHOR | SEE ALSO | COPYRIGHT
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