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
62 can be defined via:
65 set f [::math::polynomials::polynomial [list $a $b $c $d]
68 list coeffs
71 Coefficients of the polynomial (in ascending order)
72 ::math::polynomials::polynCmd coeffs
75 Create a new procedure that evaluates the polynomial. The name
76 of the polynomial is automatically generated. Useful if you need
77 to evualuate the polynomial many times, as the procedure con‐
78 sists of a single [expr] command.
79 list coeffs
81 Coefficients of the polynomial (in ascending order) or
82 the polynomial definition returned by the polynomial com‐
83 mand.
84 ::math::polynomials::evalPolyn polynomial x
87 Evaluate the polynomial at x.
88 list polynomial
90 The polynomial's definition (as returned by the polyno‐
91 mial command). order)
92 float x
94 The coordinate at which to evaluate the polynomial
95 ::math::polynomials::addPolyn polyn1 polyn2
98 Return a new polynomial which is the sum of the two others.
99 list polyn1
101 The first polynomial operand
102 list polyn2
104 The second polynomial operand
105 ::math::polynomials::subPolyn polyn1 polyn2
108 Return a new polynomial which is the difference of the two oth‐
109 ers.
110 list polyn1
112 The first polynomial operand
113 list polyn2
115 The second polynomial operand
116 ::math::polynomials::multPolyn polyn1 polyn2
119 Return a new polynomial which is the product of the two others.
120 If one of the arguments is a scalar value, the other polynomial
121 is simply scaled.
122 list polyn1
124 The first polynomial operand or a scalar
125 list polyn2
127 The second polynomial operand or a scalar
128 ::math::polynomials::divPolyn polyn1 polyn2
131 Divide the first polynomial by the second polynomial and return
132 the result. The remainder is dropped
133 list polyn1
135 The first polynomial operand
136 list polyn2
138 The second polynomial operand
139 ::math::polynomials::remainderPolyn polyn1 polyn2
142 Divide the first polynomial by the second polynomial and return
143 the remainder.
144 list polyn1
146 The first polynomial operand
147 list polyn2
149 The second polynomial operand
150 ::math::polynomials::derivPolyn polyn
153 Differentiate the polynomial and return the result.
154 list polyn
156 The polynomial to be differentiated
157 ::math::polynomials::primitivePolyn polyn
160 Integrate the polynomial and return the result. The integration
161 constant is set to zero.
162 list polyn
164 The polynomial to be integrated
165 ::math::polynomials::degreePolyn polyn
168 Return the degree of the polynomial.
169 list polyn
171 The polynomial to be examined
172 ::math::polynomials::coeffPolyn polyn index
175 Return the coefficient of the term of the index'th degree of the
176 polynomial.
177 list polyn
179 The polynomial to be examined
180 int index
182 The degree of the term
183 ::math::polynomials::allCoeffsPolyn polyn
186 Return the coefficients of the polynomial (in ascending order).
187 list polyn
189 The polynomial in question
190
192 The implementation for evaluating the polynomials at some point uses
193 Horn's rule, which guarantees numerical stability and a minimum of
194 arithmetic operations. To recognise that a polynomial definition is
195 indeed a correct definition, it consists of a list of two elements: the
196 keyword "POLYNOMIAL" and the list of coefficients in descending order.
197 The latter makes it easier to implement Horner's rule.
198
200 This document, and the package it describes, will undoubtedly contain
201 bugs and other problems. Please report such in the category math ::
202 polynomials of the Tcllib Trackers
203 [http://core.tcl.tk/tcllib/reportlist]. Please also report any ideas
204 for enhancements you may have for either package and/or documentation.
205 When proposing code changes, please provide unified diffs, i.e the out‐
207 put of diff -u.
208 Note further that attachments are strongly preferred over inlined
210 patches. Attachments can be made by going to the Edit form of the
211 ticket immediately after its creation, and then using the left-most
212 button in the secondary navigation bar.
213
215 math, polynomial functions
216
218 Mathematics
219
221 Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
222tcllib 1.0.1 math::polynomials(n)