1math::polynomials(n) Tcl Math Library math::polynomials(n)
2______________________________________________________________________________
6
8 math::polynomials - Polynomial functions
9
11 package require Tcl ?8.3?
12 package require math::polynomials ?1.0.1?
14 ::math::polynomials::polynomial coeffs
16 ::math::polynomials::polynCmd coeffs
18 ::math::polynomials::evalPolyn polynomial x
20 ::math::polynomials::addPolyn polyn1 polyn2
22 ::math::polynomials::subPolyn polyn1 polyn2
24 ::math::polynomials::multPolyn polyn1 polyn2
26 ::math::polynomials::divPolyn polyn1 polyn2
28 ::math::polynomials::remainderPolyn polyn1 polyn2
30 ::math::polynomials::derivPolyn polyn
32 ::math::polynomials::primitivePolyn polyn
34 ::math::polynomials::degreePolyn polyn
36 ::math::polynomials::coeffPolyn polyn index
38 ::math::polynomials::allCoeffsPolyn polyn
40_________________________________________________________________
42
44 This package deals with polynomial functions of one variable:
45 · the basic arithmetic operations are extended to polynomials
47 · computing the derivatives and primitives of these functions
49 · evaluation through a general procedure or via specific proce‐
51 dures)
52
54 The package defines the following public procedures:
55 ::math::polynomials::polynomial coeffs
57 Return an (encoded) list that defines the polynomial. A polyno‐
58 mial
59 f(x) = a + b.x + c.x**2 + d.x**3
61 can be defined via:
63 set f [::math::polynomials::polynomial [list $a $b $c $d]
65 list coeffs
68 Coefficients of the polynomial (in ascending order)
69 ::math::polynomials::polynCmd coeffs
72 Create a new procedure that evaluates the polynomial. The name
73 of the polynomial is automatically generated. Useful if you need
74 to evualuate the polynomial many times, as the procedure con‐
75 sists of a single [expr] command.
76 list coeffs
78 Coefficients of the polynomial (in ascending order) or
79 the polynomial definition returned by the polynomial com‐
80 mand.
81 ::math::polynomials::evalPolyn polynomial x
84 Evaluate the polynomial at x.
85 list polynomial
87 The polynomial's definition (as returned by the polyno‐
88 mial command). order)
89 float x
91 The coordinate at which to evaluate the polynomial
92 ::math::polynomials::addPolyn polyn1 polyn2
95 Return a new polynomial which is the sum of the two others.
96 list polyn1
98 The first polynomial operand
99 list polyn2
101 The second polynomial operand
102 ::math::polynomials::subPolyn polyn1 polyn2
105 Return a new polynomial which is the difference of the two oth‐
106 ers.
107 list polyn1
109 The first polynomial operand
110 list polyn2
112 The second polynomial operand
113 ::math::polynomials::multPolyn polyn1 polyn2
116 Return a new polynomial which is the product of the two others.
117 If one of the arguments is a scalar value, the other polynomial
118 is simply scaled.
119 list polyn1
121 The first polynomial operand or a scalar
122 list polyn2
124 The second polynomial operand or a scalar
125 ::math::polynomials::divPolyn polyn1 polyn2
128 Divide the first polynomial by the second polynomial and return
129 the result. The remainder is dropped
130 list polyn1
132 The first polynomial operand
133 list polyn2
135 The second polynomial operand
136 ::math::polynomials::remainderPolyn polyn1 polyn2
139 Divide the first polynomial by the second polynomial and return
140 the remainder.
141 list polyn1
143 The first polynomial operand
144 list polyn2
146 The second polynomial operand
147 ::math::polynomials::derivPolyn polyn
150 Differentiate the polynomial and return the result.
151 list polyn
153 The polynomial to be differentiated
154 ::math::polynomials::primitivePolyn polyn
157 Integrate the polynomial and return the result. The integration
158 constant is set to zero.
159 list polyn
161 The polynomial to be integrated
162 ::math::polynomials::degreePolyn polyn
165 Return the degree of the polynomial.
166 list polyn
168 The polynomial to be examined
169 ::math::polynomials::coeffPolyn polyn index
172 Return the coefficient of the term of the index'th degree of the
173 polynomial.
174 list polyn
176 The polynomial to be examined
177 int index
179 The degree of the term
180 ::math::polynomials::allCoeffsPolyn polyn
183 Return the coefficients of the polynomial (in ascending order).
184 list polyn
186 The polynomial in question
187
189 The implementation for evaluating the polynomials at some point uses
190 Horn's rule, which guarantees numerical stability and a minimum of
191 arithmetic operations. To recognise that a polynomial definition is
192 indeed a correct definition, it consists of a list of two elements: the
193 keyword "POLYNOMIAL" and the list of coefficients in descending order.
194 The latter makes it easier to implement Horner's rule.
195
197 This document, and the package it describes, will undoubtedly contain
198 bugs and other problems. Please report such in the category math ::
199 polynomials of the Tcllib SF Trackers [http://source‐
200 forge.net/tracker/?group_id=12883]. Please also report any ideas for
201 enhancements you may have for either package and/or documentation.
202
204 math, polynomial functions
205
207 Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
208math 1.0.1 math::polynomials(n)