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ginsh - GiNaC Interactive Shell

ginsh[file...]

ginshis 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.

INPUTFORMATAfter 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.42,2/3or0.17), symbols (e.g.xorresult), mathematical operators like+and*, and functions (e.g.sinornormal). 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, enterquitorexit, or type an EOF (Ctrl-D) at the prompt.COMMENTSAnything 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.NUMBERSginsh 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.SYMBOLSSymbols are made up of a string of alphanumeric characters and the underscore (_), with the first character being non-numeric. E.g.aandmu_1are acceptable symbol names, while2piis 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 enteringsymbol=expression;To unassign the value of an assigned symbol, typeunassign(’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 keywordsreal_symbolsandcomplex_symbolsand affects all newly created symbols. The following symbols are pre-defined constants that cannot be assigned a value by the user:PiArchimedes’ ConstantCatalanCatalan’s ConstantEulerEuler-Mascheroni ConstantIsqrt(-1)FAILan object of the GiNaC "fail" class There is also the specialDigitssymbol 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.WILDCARDSThe has(), find(), match() and subs() functions accept wildcards as placeholders for expressions. These have the syntax$numberfor example $0, $1 etc.LASTPRINTEDEXPRESSIONSginsh 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.OPERATORSginsh 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;).LISTSLists are used by thesubsandlsolvefunctions. A list consists of an opening curly brace ({), a (possibly empty) comma-separated sequence of expressions, and a closing curly brace (}).MATRICESA 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.FUNCTIONSA function call in ginsh has the formname(arguments)whereargumentsis 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 matrixcoeff(expression,object,number)- extracts coefficient of object^number from a polynomialcollect(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 sumsconjugate(expression)- complex conjugationcontent(expression,symbol)- content part of a polynomialdecomp_rational(expression,symbol)- decompose rational function into polynomial and proper rational functiondegree(expression,object)- degree of a polynomialdenom(expression)- denominator of a rational functiondeterminant(matrix)- determinant of a matrixdiag(expression...)- constructs diagonal matrixdiff(expression,symbol[,number])- partial differentiationdivide(expression,expression)- exact polynomial divisioneval(expression[,level])- evaluates an expression, replacing symbols by their assigned valueevalf(expression[,level])- evaluates an expression to a floating point numberevalm(expression)- evaluates sums, products and integer powers of matricesexpand(expression)- expands an expressionfactor(expression)- factorizes an expression (univariate)find(expression,pattern)- returns a list of all occurrences of a pattern in an expressionfsolve(expression,symbol,number,number)- numerically find root of a real-valued function within an intervalgcd(expression,expression)- greatest common divisorhas(expression,pattern)- returns "1" if the first expression contains the pattern as a subexpression, "0" otherwiseinteger_content(expression)- integer content of a polynomialinverse(matrix)- inverse of a matrixis(relation)- returns "1" if the relation is true, "0" otherwise (false or undecided)lcm(expression,expression)- least common multiplelcoeff(expression,object)- leading coefficient of a polynomialldegree(expression,object)- low degree of a polynomiallsolve(equation-list,symbol-list)- solve system of linear equationsmap(expression,pattern)- apply function to each operand; the function to be applied is specified as a pattern with the "$0" wildcard standing for the operandsmatch(expression,pattern)- check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no matchnops(expression)- number of operands in expressionnormal(expression[,level])- rational function normalizationnumer(expression)- numerator of a rational functionnumer_denom(expression)- numerator and denumerator of a rational function as a listop(expression,number)- extract operand from expressionpower(expr1,expr2)- exponentiation (equivalent to writing expr1^expr2)prem(expression,expression,symbol)- pseudo-remainder of polynomialsprimpart(expression,symbol)- primitive part of a polynomialquo(expression,expression,symbol)- quotient of polynomialsrank(matrix)- rank of a matrixrem(expression,expression,symbol)- remainder of polynomialsresultant(expression,expression,symbol)- resultant of two polynomials with respect to symbol sseries(expression,relation-or-symbol,order)- series expansionsprem(expression,expression,symbol)- sparse pseudo-remainder of polynomialssqrfree(expression[,symbol-list])- square-free factorization of a polynomialsqrt(expression)- square rootsubs(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 polynomialtime(expression)- returns the time in seconds needed to evaluate the given expressiontrace(matrix)- trace of a matrixtranspose(matrix)- transpose of a matrixunassign(symbol)- unassign an assigned symbol (mind the quotes, please!)unit(expression,symbol)- unit part of a polynomialSPECIALCOMMANDSTo exit ginsh, enterquitorexitginsh can display a (short) help for a given topic (mostly about functions and operators) by entering?topicTyping??will display a list of available help topics. The commandprint(expression);will print a dump of GiNaC’s internal representation for the givenexpression. This is useful for debugging and for learning about GiNaC internals. The commandprint_latex(expression);prints a LaTeX representation of the givenexpression. The commandprint_csrc(expression);prints the givenexpressionin a way that can be used in a C or C++ program. The commandiprint(expression);prints the givenexpression(which must evaluate to an integer) in decimal, octal, and hexadecimal representations. Finally, the shell escape![command[arguments]] passes the givencommandand optionallyargumentsto the shell for execution. With this method, you can execute shell commands from within ginsh without having to quit.

> 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

parse error atfooYou entered something which ginsh was unable to parse. Please check the syntax of your input and try again. argumentnumtofunctionmust be atypeThe argument numbernumto the givenfunctionmust be of a certain type (e.g. a symbol, or a list). The first argument has number 0, the second argument number 1, etc.

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>

GiNaC Tutorial - An open framework for symbolic computation within the C++ programming language CLN - A Class Library for Numbers, Bruno Haible

Copyright © 1999-2010 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.