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(), match() and subs() functions accept wildcards as placeholders for
114 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
148 non-commutative multiplication
182 All binary operators are left-associative, with the exception of
184 which are right-associative. The result of the assignment operator
186 is its right-hand side, so it's possible to assign multiple symbols in one
188 .BR "a = b = c = 2;" ).
190 Lists are used by the
194 functions. A list consists of an opening curly brace
196 a (possibly empty) comma-separated sequence of expressions, and a closing curly
200 A matrix consists of an opening square bracket
202 a non-empty comma-separated sequence of matrix rows, and a closing square bracket
204 Each matrix row consists of an opening square bracket
206 a non-empty comma-separated sequence of expressions, and a closing square bracket
208 If the rows of a matrix are not of the same length, the width of the matrix
209 becomes that of the longest row and shorter rows are filled up at the end
210 with elements of value zero.
212 A function call in ginsh has the form
214 .IB name ( arguments )
218 is a comma-separated sequence of expressions. ginsh provides a couple of built-in
219 functions and also "imports" all symbolic functions defined by GiNaC and additional
220 libraries. There is no way to define your own functions other than linking ginsh
221 against a library that defines symbolic GiNaC functions.
223 ginsh provides Tab-completion on function names: if you type the first part of
224 a function name, hitting Tab will complete the name if possible. If the part you
225 typed is not unique, hitting Tab again will display a list of matching functions.
226 Hitting Tab twice at the prompt will display the list of all available functions.
228 A list of the built-in functions follows. They nearly all work as the
229 respective GiNaC methods of the same name, so I will not describe them in
230 detail here. Please refer to the GiNaC documentation.
233 \" GINSH_FCN_HELP_START
234 .BI charpoly( matrix ", " symbol )
235 \- characteristic polynomial of a matrix
237 .BI coeff( expression ", " object ", " number )
238 \- extracts coefficient of object^number from a polynomial
240 .BI collect( expression ", " object-or-list )
241 \- collects coefficients of like powers (result in recursive form)
243 .BI collect_distributed( expression ", " list )
244 \- collects coefficients of like powers (result in distributed form)
246 .BI content( expression ", " symbol )
247 \- content part of a polynomial
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 and products of matrices
276 .BI expand( expression )
277 \- expands an expression
279 .BI gcd( expression ", " expression )
280 \- greatest common divisor
282 .BI has( expression ", " expression )
283 \- returns "1" if the first expression contains the second (which may contain wildcards) as a subexpression, "0" otherwise
285 .BI inverse( matrix )
286 \- inverse of a matrix
289 \- returns "1" if the relation is true, "0" otherwise (false or undecided)
291 .BI lcm( expression ", " expression )
292 \- least common multiple
294 .BI lcoeff( expression ", " object )
295 \- leading coefficient of a polynomial
297 .BI ldegree( expression ", " object )
298 \- low degree of a polynomial
300 .BI lsolve( equation-list ", " symbol-list )
301 \- solve system of linear equations
303 .BI match( expression ", " pattern )
304 \- check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
306 .BI nops( expression )
307 \- number of operands in expression
309 .BI normal( "expression [" ", " level] )
310 \- rational function normalization
312 .BI numer( expression )
313 \- numerator of a rational function
315 .BI numer_denom( expression )
316 \- numerator and denumerator of a rational function as a list
318 .BI op( expression ", " number )
319 \- extract operand from expression
321 .BI power( expr1 ", " expr2 )
322 \- exponentiation (equivalent to writing expr1^expr2)
324 .BI prem( expression ", " expression ", " symbol )
325 \- pseudo-remainder of polynomials
327 .BI primpart( expression ", " symbol )
328 \- primitive part of a polynomial
330 .BI quo( expression ", " expression ", " symbol )
331 \- quotient of polynomials
333 .BI rem( expression ", " expression ", " symbol )
334 \- remainder of polynomials
336 .BI series( expression ", " relation-or-symbol ", " order )
339 .BI sqrfree( "expression [" ", " symbol-list] )
340 \- square-free factorization of a polynomial
342 .BI sqrt( expression )
345 .BI subs( expression ", " relation-or-list )
347 .BI subs( expression ", " look-for-list ", " replace-by-list )
348 \- substitute subexpressions (you may use wildcards)
350 .BI tcoeff( expression ", " object )
351 \- trailing coefficient of a polynomial
353 .BI time( expression )
354 \- returns the time in seconds needed to evaluate the given expression
359 .BI transpose( matrix )
360 \- transpose of a matrix
362 .BI unassign( symbol )
363 \- unassign an assigned symbol
365 .BI unit( expression ", " symbol )
366 \- unit part of a polynomial
368 \" GINSH_FCN_HELP_END
380 ginsh can display a (short) help for a given topic (mostly about functions
381 and operators) by entering
389 will display a list of available help topics.
393 .BI print( expression );
395 will print a dump of GiNaC's internal representation for the given
397 This is useful for debugging and for learning about GiNaC internals.
401 .BI iprint( expression );
405 (which must evaluate to an integer) in decimal, octal, and hexadecimal representations.
407 Finally, the shell escape
410 .RI [ "command " [ arguments ]]
416 to the shell for execution. With this method, you can execute shell commands
417 from within ginsh without having to quit.
425 (x+1)^(\-2)*(\-2\-x+x^2)
427 (2*x\-1)*(x+1)^(\-2)\-2*(x+1)^(\-3)*(\-x+x^2\-2)
431 717897987691852588770249
433 717897987691852588770247/717897987691852588770250
437 0.999999999999999999999995821133292704384960990679
441 (x+1)^(\-2)*(\-x+x^2\-2)
442 > series(sin(x),x==0,6);
443 1*x+(\-1/6)*x^3+1/120*x^5+Order(x^6)
444 > lsolve({3*x+5*y == 7}, {x, y});
445 {x==\-5/3*y+7/3,y==y}
446 > lsolve({3*x+5*y == 7, \-2*x+10*y == \-5}, {x, y});
448 > M = [ [a, b], [c, d] ];
449 [[\-x+x^2\-2,(x+1)^2],[c,d]]
451 \-2*d\-2*x*c\-x^2*c\-x*d+x^2*d\-c
453 (\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
454 > solve quantum field theory;
455 parse error at quantum
460 .RI "parse error at " foo
461 You entered something which ginsh was unable to parse. Please check the syntax
462 of your input and try again.
464 .RI "argument " num " to " function " must be a " type
469 must be of a certain type (e.g. a symbol, or a list). The first argument has
470 number 0, the second argument number 1, etc.
475 Christian Bauer <Christian.Bauer@uni-mainz.de>
477 Alexander Frink <Alexander.Frink@uni-mainz.de>
479 Richard Kreckel <Richard.Kreckel@uni-mainz.de>
481 GiNaC Tutorial \- An open framework for symbolic computation within the
482 C++ programming language
484 CLN \- A Class Library for Numbers, Bruno Haible
486 Copyright \(co 1999-2001 Johannes Gutenberg Universit\(:at Mainz, Germany
488 This program is free software; you can redistribute it and/or modify
489 it under the terms of the GNU General Public License as published by
490 the Free Software Foundation; either version 2 of the License, or
491 (at your option) any later version.
493 This program is distributed in the hope that it will be useful,
494 but WITHOUT ANY WARRANTY; without even the implied warranty of
495 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
496 GNU General Public License for more details.
498 You should have received a copy of the GNU General Public License
499 along with this program; if not, write to the Free Software
500 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.