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.
+.SS WILDCARDS
+The has(), find(), match() and subs() functions accept wildcards as placeholders
+for expressions. These have the syntax
+.RS
+.BI $ number
+.RE
+for example $0, $1 etc.
.SS LAST PRINTED EXPRESSIONS
ginsh provides the three special symbols
.RS
-", "" and """
+%, %% and %%%
.RE
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
.B *
multiplication
.TP
-.B %
-non-commutative multiplication
-.TP
.B /
division
.TP
.B subs
and
.B lsolve
-functions. A list consists of an opening square bracket
+functions. A list consists of an opening curly brace
+.RB ( { ),
+a (possibly empty) comma-separated sequence of expressions, and a closing curly
+brace
+.RB ( } ).
+.SS MATRICES
+A matrix consists of an opening square bracket
.RB ( [ ),
-a (possibly empty) comma-separated sequence of expressions, and a closing square
-bracket
+a non-empty comma-separated sequence of matrix rows, and a closing square bracket
+.RB ( ] ).
+Each matrix row consists of an opening square bracket
+.RB ( [ ),
+a non-empty comma-separated sequence of expressions, and a closing square bracket
.RB ( ] ).
-.SS MATRICES
-A matrix consists of an opening double square bracket
-.RB ( [[ ),
-a non-empty comma-separated sequence of matrix rows, and a closing double square
-bracket
-.RB ( ]] ).
-Each matrix row consists of an opening double square bracket
-.RB ( [[ ),
-a non-empty comma-separated sequence of expressions, and a closing double square
-bracket
-.RB ( ]] ).
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.
.BI charpoly( matrix ", " symbol )
\- characteristic polynomial of a matrix
.br
-.BI coeff( expression ", " symbol ", " number )
-\- extracts coefficient of symbol^number from a polynomial
+.BI coeff( expression ", " object ", " number )
+\- extracts coefficient of object^number from a polynomial
.br
-.BI collect( expression ", " symbol )
-\- collects coefficients of like powers
+.BI collect( expression ", " object-or-list )
+\- collects coefficients of like powers (result in recursive form)
+.br
+.BI collect_distributed( expression ", " list )
+\- collects coefficients of like powers (result in distributed form)
+.br
+.BI collect_common_factors( expression )
+\- collects common factors from the terms of sums
.br
.BI content( expression ", " symbol )
\- content part of a polynomial
.br
-.BI degree( expression ", " symbol )
+.BI decomp_rational( expression ", " symbol )
+\- decompose rational function into polynomial and proper rational function
+.br
+.BI degree( expression ", " object )
\- degree of a polynomial
.br
.BI denom( expression )
.BI evalf( "expression [" ", " level] )
\- evaluates an expression to a floating point number
.br
+.BI evalm( expression )
+\- evaluates sums, products and integer powers of matrices
+.br
.BI expand( expression )
\- expands an expression
.br
+.BI find( expression ", " pattern )
+\- returns a list of all occurrences of a pattern in an expression
+.br
.BI gcd( expression ", " expression )
\- greatest common divisor
.br
-.BI has( expression ", " expression )
-\- returns "1" if the first expression contains the second as a subexpression, "0" otherwise
+.BI has( expression ", " pattern )
+\- returns "1" if the first expression contains the pattern as a subexpression, "0" otherwise
.br
.BI inverse( matrix )
\- inverse of a matrix
.BI lcm( expression ", " expression )
\- least common multiple
.br
-.BI lcoeff( expression ", " symbol )
+.BI lcoeff( expression ", " object )
\- leading coefficient of a polynomial
.br
-.BI ldegree( expression ", " symbol )
+.BI ldegree( expression ", " object )
\- low degree of a polynomial
.br
.BI lsolve( equation-list ", " symbol-list )
\- solve system of linear equations
.br
+.BI 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
+.br
+.BI match( expression ", " pattern )
+\- check whether expression matches a pattern; returns a list of wildcard substitutions or "FAIL" if there is no match
+.br
.BI nops( expression )
\- number of operands in expression
.br
.BI numer( expression )
\- numerator of a rational function
.br
+.BI numer_denom( expression )
+\- numerator and denumerator of a rational function as a list
+.br
.BI op( expression ", " number )
\- extract operand from expression
.br
.BI series( expression ", " relation-or-symbol ", " order )
\- series expansion
.br
-.BI sqrfree( expression ", " symbol )
+.BI sprem( expression ", " expression ", " symbol )
+\- sparse pseudo-remainder of polynomials
+.br
+.BI sqrfree( "expression [" ", " symbol-list] )
\- square-free factorization of a polynomial
.br
.BI sqrt( expression )
.BI subs( expression ", " relation-or-list )
.br
.BI subs( expression ", " look-for-list ", " replace-by-list )
-\- substitute subexpressions
+\- substitute subexpressions (you may use wildcards)
.br
-.BI tcoeff( expression ", " symbol )
+.BI tcoeff( expression ", " object )
\- trailing coefficient of a polynomial
.br
.BI time( expression )
.PP
The command
.RS
+.BI print_latex( expression );
+.RE
+prints a LaTeX representation of the given
+.IR expression .
+.PP
+The command
+.RS
+.BI print_csrc( expression );
+.RE
+prints the given
+.I expression
+in a way that can be used in a C or C++ program.
+.PP
+The command
+.RS
.BI iprint( expression );
.RE
prints the given
.SH EXAMPLES
.nf
> a = x^2\-x\-2;
-\-x+x^2\-2
+\-2\-x+x^2
> b = (x+1)^2;
(x+1)^2
> s = a/b;
-(x+1)^(\-2)*(\-x+x^2\-2)
+(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);
> Digits = 40;
40
> evalf(s);
-0.999999999999999999999995821133292704384960990679L0
+0.999999999999999999999995821133292704384960990679
> unassign('x');
x
> s;
(x+1)^(\-2)*(\-x+x^2\-2)
-> 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]] ]]
+> 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);
+> collect(%, x);
(\-d\-2*c)*x+(d\-c)*x^2\-2*d\-c
> solve quantum field theory;
parse error at quantum
.PP
CLN \- A Class Library for Numbers, Bruno Haible
.SH COPYRIGHT
-Copyright \(co 1999-2000 Johannes Gutenberg Universit\(:at Mainz, Germany
+Copyright \(co 1999-2003 Johannes Gutenberg Universit\(:at 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
git://www.ginac.de / ginac.git / blobdiff