1math::rationalfunctions(n) Math math::rationalfunctions(n)
2______________________________________________________________________________
6
8 math::rationalfunctions - Polynomial functions
9
11 package require Tcl ?8.4?
12 package require math::rationalfunctions ?1.0.1?
14 ::math::rationalfunctions::rationalFunction num den
16 ::math::rationalfunctions::ratioCmd num den
18 ::math::rationalfunctions::evalRatio rational x
20 ::math::rationalfunctions::addRatio ratio1 ratio2
22 ::math::rationalfunctions::subRatio ratio1 ratio2
24 ::math::rationalfunctions::multRatio ratio1 ratio2
26 ::math::rationalfunctions::divRatio ratio1 ratio2
28 ::math::rationalfunctions::derivPolyn ratio
30 ::math::rationalfunctions::coeffsNumerator ratio
32 ::math::rationalfunctions::coeffsDenominator ratio
34_________________________________________________________________
36
38 This package deals with rational functions of one variable:
39 · the basic arithmetic operations are extended to rational func‐
41 tions
42 · computing the derivatives of these functions
44 · evaluation through a general procedure or via specific proce‐
46 dures)
47
49 The package defines the following public procedures:
50 ::math::rationalfunctions::rationalFunction num den
52 Return an (encoded) list that defines the rational function. A
53 rational function
54 1 + x^3
56 f(x) = ------------
57 1 + 2x + x^2
58 can be defined via:
60 set f [::math::rationalfunctions::rationalFunction [list 1 0 0 1] [list 1 2 1]]
62 list num
65 Coefficients of the numerator of the rational function
66 (in ascending order)
67 list den
70 Coefficients of the denominator of the rational function
71 (in ascending order)
72 ::math::rationalfunctions::ratioCmd num den
75 Create a new procedure that evaluates the rational function. The
76 name of the function is automatically generated. Useful if you
77 need to evaluate the function many times, as the procedure con‐
78 sists of a single [expr] command.
79 list num
81 Coefficients of the numerator of the rational function
82 (in ascending order)
83 list den
86 Coefficients of the denominator of the rational function
87 (in ascending order)
88 ::math::rationalfunctions::evalRatio rational x
91 Evaluate the rational function at x.
92 list rational
94 The rational function's definition (as returned by the
95 rationalFunction command). order)
96 float x
98 The coordinate at which to evaluate the function
99 ::math::rationalfunctions::addRatio ratio1 ratio2
102 Return a new rational function which is the sum of the two oth‐
103 ers.
104 list ratio1
106 The first rational function operand
107 list ratio2
109 The second rational function operand
110 ::math::rationalfunctions::subRatio ratio1 ratio2
113 Return a new rational function which is the difference of the
114 two others.
115 list ratio1
117 The first rational function operand
118 list ratio2
120 The second rational function operand
121 ::math::rationalfunctions::multRatio ratio1 ratio2
124 Return a new rational function which is the product of the two
125 others. If one of the arguments is a scalar value, the other
126 rational function is simply scaled.
127 list ratio1
129 The first rational function operand or a scalar
130 list ratio2
132 The second rational function operand or a scalar
133 ::math::rationalfunctions::divRatio ratio1 ratio2
136 Divide the first rational function by the second rational func‐
137 tion and return the result. The remainder is dropped
138 list ratio1
140 The first rational function operand
141 list ratio2
143 The second rational function operand
144 ::math::rationalfunctions::derivPolyn ratio
147 Differentiate the rational function and return the result.
148 list ratio
150 The rational function to be differentiated
151 ::math::rationalfunctions::coeffsNumerator ratio
154 Return the coefficients of the numerator of the rational func‐
155 tion.
156 list ratio
158 The rational function to be examined
159 ::math::rationalfunctions::coeffsDenominator ratio
162 Return the coefficients of the denominator of the rational func‐
163 tion.
164 list ratio
166 The rational function to be examined
167
170 The implementation of the rational functions relies on the math::poly‐
171 nomials package. For further remarks see the documentation on that
172 package.
173
175 This document, and the package it describes, will undoubtedly contain
176 bugs and other problems. Please report such in the category math ::
177 rationalfunctions of the Tcllib SF Trackers [http://source‐
178 forge.net/tracker/?group_id=12883]. Please also report any ideas for
179 enhancements you may have for either package and/or documentation.
180
182 math, rational functions
183
185 Copyright (c) 2005 Arjen Markus <arjenmarkus@users.sourceforge.net>
186math 1.0.1 math::rationalfunctions(n)