- added numer_denom()

[ginac.git] / ginsh / ginsh.1.in

diff --git a/ginsh/ginsh.1.in b/ginsh/ginsh.1.in
index d933c33556907f59d1f9e380726b26b82b211226..39ece405aa08c11a229ad97801d917d69a6bd158 100644 (file)
--- a/ginsh/ginsh.1.in
+++ b/ginsh/ginsh.1.in
@@ -109,6 +109,13 @@ There is also the special
 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(), 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
@@ -229,16 +236,19 @@ detail here. Please refer to the GiNaC documentation.
 .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 ", " object-or-list )
+\- collects coefficients of like powers (result in recursive form)
 .br
-.BI collect( expression ", " symbol )
-\- collects coefficients of like powers
+.BI collect_distributed( expression ", " list )
+\- collects coefficients of like powers (result in distributed form)
 .br
 .BI content( expression ", " symbol )
 \- content part of a polynomial
 .br
-.BI degree( expression ", " symbol )
+.BI degree( expression ", " object )
 \- degree of a polynomial
 .br
 .BI denom( expression )
@@ -269,7 +279,7 @@ detail here. Please refer to the GiNaC documentation.
 \- greatest common divisor
 .br
 .BI has( expression ", " expression )
-\- returns "1" if the first expression contains the second as a subexpression, "0" otherwise
+\- returns "1" if the first expression contains the second (which may contain wildcards) as a subexpression, "0" otherwise
 .br
 .BI inverse( matrix )
 \- inverse of a matrix
@@ -280,15 +290,18 @@ detail here. Please refer to the GiNaC documentation.
 .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 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
@@ -298,6 +311,9 @@ detail here. Please refer to the GiNaC documentation.
 .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
@@ -328,9 +344,9 @@ detail here. Please refer to the GiNaC documentation.
 .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 )
@@ -401,11 +417,11 @@ from within ginsh without having to quit.
 .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);
@@ -422,6 +438,8 @@ from within ginsh without having to quit.
 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]);