X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?p=ginac.git;a=blobdiff_plain;f=ginsh%2Fginsh.1.in;h=a66c23e1295276511c077daf74fc7c5ff9275381;hp=d933c33556907f59d1f9e380726b26b82b211226;hb=44710f0b91c510114a4cf3eacc81b007ea294217;hpb=bf15b9a4a59c0eac7a8ab7f0a116bcdefd8689d2 diff --git a/ginsh/ginsh.1.in b/ginsh/ginsh.1.in index d933c335..a66c23e1 100644 --- 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(), 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 @@ -184,22 +191,20 @@ Lists are used by the .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. @@ -229,16 +234,22 @@ 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 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 ) @@ -262,14 +273,20 @@ detail here. Please refer to the GiNaC documentation. .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 @@ -280,15 +297,21 @@ 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 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 @@ -298,6 +321,9 @@ 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 +354,9 @@ 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 +427,11 @@ 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); @@ -422,12 +448,14 @@ from within ginsh without having to quit. 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);