1 .TH ginsh 1 "January, 2000" "GiNaC @VERSION@" "The GiNaC Group"
3 ginsh \- GiNaC Interactive Shell
9 is an interactive frontend for the GiNaC symbolic computation framework.
10 It is intended as a tool for testing and experimenting with GiNaC's
11 features, not as a replacement for traditional interactive computer
12 algebra systems. Although it can do many things these traditional systems
13 can do, ginsh provides no programming constructs like loops or conditional
14 expressions. If you need this functionality you are advised to write
15 your program in C++, using the "native" GiNaC class framework.
18 After startup, ginsh displays a prompt ("> ") signifying that it is ready
19 to accept your input. Acceptable input are numeric or symbolic expressions
20 consisting of numbers (e.g.
21 .BR 42 ", " 2/3 " or " 0.17 ),
23 .BR x " or " result ),
24 mathematical operators like
27 .BR sin " or " normal ).
28 Every input expression must be terminated with either a semicolon
32 If terminated with a semicolon, ginsh will evaluate the expression and print
33 the result to stdout. If terminated with a colon, ginsh will only evaluate the
34 expression but not print the result. It is possible to enter multiple
35 expressions on one line. Whitespace (spaces, tabs, newlines) can be applied
36 freely between tokens. To quit ginsh, enter
37 .BR quit " or " exit ,
38 or type an EOF (Ctrl-D) at the prompt.
40 Anything following a double slash
42 up to the end of the line, and all lines starting with a hash mark
44 are treated as a comment and ignored.
46 ginsh accepts numbers in the usual decimal notations. This includes arbitrary
47 precision integers and rationals as well as floating point numbers in standard
48 or scientific notation (e.g.
50 The general rule is that if a number contains a decimal point
52 it is an (inexact) floating point number; otherwise it is an (exact) integer or
54 Integers can be specified in binary, octal, hexadecimal or arbitrary (2-36) base
55 by prefixing them with
56 .BR #b ", " #o ", " #x ", or "
60 Symbols are made up of a string of alphanumeric characters and the underscore
62 with the first character being non-numeric. E.g.
64 are acceptable symbol names, while
66 is not. It is possible to use symbols with the same names as functions (e.g.
68 ginsh is able to distinguish between the two.
70 Symbols can be assigned values by entering
72 .IB symbol " = " expression ;
75 To unassign the value of an assigned symbol, type
77 .BI unassign(' symbol ');
80 Assigned symbols are automatically evaluated (= replaced by their assigned value)
81 when they are used. To refer to the unevaluated symbol, put single quotes
83 around the name, as demonstrated for the "unassign" command above.
85 The following symbols are pre-defined constants that cannot be assigned
96 Euler-Mascheroni Constant
102 an object of the GiNaC "fail" class
105 There is also the special
109 symbol that controls the numeric precision of calculations with inexact numbers.
110 Assigning an integer value to digits will change the precision to the given
111 number of decimal places.
113 The has(), find(), match() and subs() functions accept wildcards as placeholders
114 for expressions. These have the syntax
118 for example $0, $1 etc.
119 .SS LAST PRINTED EXPRESSIONS
120 ginsh provides the three special symbols
124 that refer to the last, second last, and third last printed expression, respectively.
125 These are handy if you want to use the results of previous computations in a new
128 ginsh provides the following operators, listed in falling order of precedence:
131 \" GINSH_OP_HELP_START
179 All binary operators are left-associative, with the exception of
181 which are right-associative. The result of the assignment operator
183 is its right-hand side, so it's possible to assign multiple symbols in one
185 .BR "a = b = c = 2;" ).
187 Lists are used by the
191 functions. A list consists of an opening curly brace
193 a (possibly empty) comma-separated sequence of expressions, and a closing curly
197 A matrix consists of an opening square bracket
199 a non-empty comma-separated sequence of matrix rows, and a closing square bracket
201 Each matrix row consists of an opening square bracket
203 a non-empty comma-separated sequence of expressions, and a closing square bracket
205 If the rows of a matrix are not of the same length, the width of the matrix
206 becomes that of the longest row and shorter rows are filled up at the end
207 with elements of value zero.
209 A function call in ginsh has the form
211 .IB name ( arguments )
215 is a comma-separated sequence of expressions. ginsh provides a couple of built-in
216 functions and also "imports" all symbolic functions defined by GiNaC and additional
217 libraries. There is no way to define your own functions other than linking ginsh
218 against a library that defines symbolic GiNaC functions.
220 ginsh provides Tab-completion on function names: if you type the first part of
221 a function name, hitting Tab will complete the name if possible. If the part you
222 typed is not unique, hitting Tab again will display a list of matching functions.
223 Hitting Tab twice at the prompt will display the list of all available functions.
225 A list of the built-in functions follows. They nearly all work as the
226 respective GiNaC methods of the same name, so I will not describe them in
227 detail here. Please refer to the GiNaC documentation.
230 \" GINSH_FCN_HELP_START
231 .BI charpoly( matrix ", " symbol )
232 \- characteristic polynomial of a matrix
234 .BI coeff( expression ", " object ", " number )
235 \- extracts coefficient of object^number from a polynomial
237 .BI collect( expression ", " object-or-list )
238 \- collects coefficients of like powers (result in recursive form)
240 .BI collect_distributed( expression ", " list )
241 \- collects coefficients of like powers (result in distributed form)
243 .BI content( expression ", " symbol )
244 \- content part of a polynomial
246 .BI decomp_rational( expression ", " symbol )
247 \- decompose rational function into polynomial and proper rational function
249 .BI degree( expression ", " object )
250 \- degree of a polynomial
252 .BI denom( expression )
253 \- denominator of a rational function
255 .BI determinant( matrix )
256 \- determinant of a matrix
258 .BI diag( expression... )
259 \- constructs diagonal matrix
261 .BI diff( expression ", " "symbol [" ", " number] )
262 \- partial differentiation
264 .BI divide( expression ", " expression )
265 \- exact polynomial division
267 .BI eval( "expression [" ", " level] )
268 \- evaluates an expression, replacing symbols by their assigned value
270 .BI evalf( "expression [" ", " level] )
271 \- evaluates an expression to a floating point number
273 .BI evalm( expression )
274 \- evaluates sums, products and integer powers of matrices
276 .BI expand( expression )
277 \- expands an expression
279 .BI find( expression ", " pattern )
280 \- returns a list of all occurrences of a pattern in an expression
282 .BI gcd( expression ", " expression )
283 \- greatest common divisor
285 .BI has( expression ", " pattern )
286 \- returns "1" if the first expression contains the pattern as a subexpression, "0" otherwise
288 .BI inverse( matrix )
289 \- inverse of a matrix
292 \- returns "1" if the relation is true, "0" otherwise (false or undecided)
294 .BI lcm( expression ", " expression )
295 \- least common multiple
297 .BI lcoeff( expression ", " object )
298 \- leading coefficient of a polynomial
300 .BI ldegree( expression ", " object )
301 \- low degree of a polynomial
303 .BI lsolve( equation-list ", " symbol-list )
304 \- solve system of linear equations
306 .BI map( expression ", " pattern )
307 \- apply function to each operand; the function to be applied is specified as a pattern with the "$0" wildcard standing for the operands
309 .BI match( expression ", " pattern )
310 \- check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
312 .BI nops( expression )
313 \- number of operands in expression
315 .BI normal( "expression [" ", " level] )
316 \- rational function normalization
318 .BI numer( expression )
319 \- numerator of a rational function
321 .BI numer_denom( expression )
322 \- numerator and denumerator of a rational function as a list
324 .BI op( expression ", " number )
325 \- extract operand from expression
327 .BI power( expr1 ", " expr2 )
328 \- exponentiation (equivalent to writing expr1^expr2)
330 .BI prem( expression ", " expression ", " symbol )
331 \- pseudo-remainder of polynomials
333 .BI primpart( expression ", " symbol )
334 \- primitive part of a polynomial
336 .BI quo( expression ", " expression ", " symbol )
337 \- quotient of polynomials
339 .BI rem( expression ", " expression ", " symbol )
340 \- remainder of polynomials
342 .BI series( expression ", " relation-or-symbol ", " order )
345 .BI sprem( expression ", " expression ", " symbol )
346 \- sparse pseudo-remainder of polynomials
348 .BI sqrfree( "expression [" ", " symbol-list] )
349 \- square-free factorization of a polynomial
351 .BI sqrt( expression )
354 .BI subs( expression ", " relation-or-list )
356 .BI subs( expression ", " look-for-list ", " replace-by-list )
357 \- substitute subexpressions (you may use wildcards)
359 .BI tcoeff( expression ", " object )
360 \- trailing coefficient of a polynomial
362 .BI time( expression )
363 \- returns the time in seconds needed to evaluate the given expression
368 .BI transpose( matrix )
369 \- transpose of a matrix
371 .BI unassign( symbol )
372 \- unassign an assigned symbol
374 .BI unit( expression ", " symbol )
375 \- unit part of a polynomial
377 \" GINSH_FCN_HELP_END
389 ginsh can display a (short) help for a given topic (mostly about functions
390 and operators) by entering
398 will display a list of available help topics.
402 .BI print( expression );
404 will print a dump of GiNaC's internal representation for the given
406 This is useful for debugging and for learning about GiNaC internals.
410 .BI print_latex( expression );
412 prints a LaTeX representation of the given
417 .BI print_csrc( expression );
421 in a way that can be used in a C or C++ program (complex numbers are not
426 .BI iprint( expression );
430 (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.
432 Finally, the shell escape
435 .RI [ "command " [ arguments ]]
441 to the shell for execution. With this method, you can execute shell commands
442 from within ginsh without having to quit.
450 (x+1)^(\-2)*(\-2\-x+x^2)
452 (2*x\-1)*(x+1)^(\-2)\-2*(x+1)^(\-3)*(\-x+x^2\-2)
456 717897987691852588770249
458 717897987691852588770247/717897987691852588770250
462 0.999999999999999999999995821133292704384960990679
466 (x+1)^(\-2)*(\-x+x^2\-2)
467 > series(sin(x),x==0,6);
468 1*x+(\-1/6)*x^3+1/120*x^5+Order(x^6)
469 > lsolve({3*x+5*y == 7}, {x, y});
470 {x==\-5/3*y+7/3,y==y}
471 > lsolve({3*x+5*y == 7, \-2*x+10*y == \-5}, {x, y});
473 > M = [ [a, b], [c, d] ];
474 [[\-x+x^2\-2,(x+1)^2],[c,d]]
476 \-2*d\-2*x*c\-x^2*c\-x*d+x^2*d\-c
478 (\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
479 > solve quantum field theory;
480 parse error at quantum
485 .RI "parse error at " foo
486 You entered something which ginsh was unable to parse. Please check the syntax
487 of your input and try again.
489 .RI "argument " num " to " function " must be a " type
494 must be of a certain type (e.g. a symbol, or a list). The first argument has
495 number 0, the second argument number 1, etc.
500 Christian Bauer <Christian.Bauer@uni-mainz.de>
502 Alexander Frink <Alexander.Frink@uni-mainz.de>
504 Richard Kreckel <Richard.Kreckel@uni-mainz.de>
506 GiNaC Tutorial \- An open framework for symbolic computation within the
507 C++ programming language
509 CLN \- A Class Library for Numbers, Bruno Haible
511 Copyright \(co 1999-2002 Johannes Gutenberg Universit\(:at Mainz, Germany
513 This program is free software; you can redistribute it and/or modify
514 it under the terms of the GNU General Public License as published by
515 the Free Software Foundation; either version 2 of the License, or
516 (at your option) any later version.
518 This program is distributed in the hope that it will be useful,
519 but WITHOUT ANY WARRANTY; without even the implied warranty of
520 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
521 GNU General Public License for more details.
523 You should have received a copy of the GNU General Public License
524 along with this program; if not, write to the Free Software
525 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.