'\"
'\" Generated from file 'polynomials\&.man' by tcllib/doctools with format 'nroff'
'\" Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net>
'\"
.TH "math::polynomials" 3tcl 1\&.0\&.1 tcllib "Tcl Math Library"
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.BS
.SH NAME
math::polynomials \- Polynomial functions
.SH SYNOPSIS
package require \fBTcl  ?8\&.3?\fR
.sp
package require \fBmath::polynomials  ?1\&.0\&.1?\fR
.sp
\fB::math::polynomials::polynomial\fR \fIcoeffs\fR
.sp
\fB::math::polynomials::polynCmd\fR \fIcoeffs\fR
.sp
\fB::math::polynomials::evalPolyn\fR \fIpolynomial\fR \fIx\fR
.sp
\fB::math::polynomials::addPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
.sp
\fB::math::polynomials::subPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
.sp
\fB::math::polynomials::multPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
.sp
\fB::math::polynomials::divPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
.sp
\fB::math::polynomials::remainderPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
.sp
\fB::math::polynomials::derivPolyn\fR \fIpolyn\fR
.sp
\fB::math::polynomials::primitivePolyn\fR \fIpolyn\fR
.sp
\fB::math::polynomials::degreePolyn\fR \fIpolyn\fR
.sp
\fB::math::polynomials::coeffPolyn\fR \fIpolyn\fR \fIindex\fR
.sp
\fB::math::polynomials::allCoeffsPolyn\fR \fIpolyn\fR
.sp
.BE
.SH DESCRIPTION
.PP
This package deals with polynomial functions of one variable:
.IP \(bu
the basic arithmetic operations are extended to polynomials
.IP \(bu
computing the derivatives and primitives of these functions
.IP \(bu
evaluation through a general procedure or via specific procedures)
.PP
.SH PROCEDURES
The package defines the following public procedures:
.TP
\fB::math::polynomials::polynomial\fR \fIcoeffs\fR
Return an (encoded) list that defines the polynomial\&. A polynomial
.CS


   f(x) = a + b\&.x + c\&.x**2 + d\&.x**3

.CE
.IP
can be defined via:
.CS


   set f [::math::polynomials::polynomial [list $a $b $c $d]

.CE
.RS
.TP
list \fIcoeffs\fR
Coefficients of the polynomial (in ascending
order)
.RE
.sp
.TP
\fB::math::polynomials::polynCmd\fR \fIcoeffs\fR
Create a new procedure that evaluates the polynomial\&. The name of the
polynomial is automatically generated\&. Useful if you need to evualuate
the polynomial many times, as the procedure consists of a single
[expr] command\&.
.RS
.TP
list \fIcoeffs\fR
Coefficients of the polynomial (in ascending
order) or the polynomial definition returned by the \fIpolynomial\fR
command\&.
.RE
.sp
.TP
\fB::math::polynomials::evalPolyn\fR \fIpolynomial\fR \fIx\fR
Evaluate the polynomial at x\&.
.RS
.TP
list \fIpolynomial\fR
The polynomial's definition (as returned by
the polynomial command)\&.
order)
.TP
float \fIx\fR
The coordinate at which to evaluate the polynomial
.RE
.sp
.TP
\fB::math::polynomials::addPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
Return a new polynomial which is the sum of the two others\&.
.RS
.TP
list \fIpolyn1\fR
The first polynomial operand
.TP
list \fIpolyn2\fR
The second polynomial operand
.RE
.sp
.TP
\fB::math::polynomials::subPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
Return a new polynomial which is the difference of the two others\&.
.RS
.TP
list \fIpolyn1\fR
The first polynomial operand
.TP
list \fIpolyn2\fR
The second polynomial operand
.RE
.sp
.TP
\fB::math::polynomials::multPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
Return a new polynomial which is the product of the two others\&. If one
of the arguments is a scalar value, the other polynomial is simply
scaled\&.
.RS
.TP
list \fIpolyn1\fR
The first polynomial operand or a scalar
.TP
list \fIpolyn2\fR
The second polynomial operand or a scalar
.RE
.sp
.TP
\fB::math::polynomials::divPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
Divide the first polynomial by the second polynomial and return the
result\&. The remainder is dropped
.RS
.TP
list \fIpolyn1\fR
The first polynomial operand
.TP
list \fIpolyn2\fR
The second polynomial operand
.RE
.sp
.TP
\fB::math::polynomials::remainderPolyn\fR \fIpolyn1\fR \fIpolyn2\fR
Divide the first polynomial by the second polynomial and return the
remainder\&.
.RS
.TP
list \fIpolyn1\fR
The first polynomial operand
.TP
list \fIpolyn2\fR
The second polynomial operand
.RE
.sp
.TP
\fB::math::polynomials::derivPolyn\fR \fIpolyn\fR
Differentiate the polynomial and return the result\&.
.RS
.TP
list \fIpolyn\fR
The polynomial to be differentiated
.RE
.sp
.TP
\fB::math::polynomials::primitivePolyn\fR \fIpolyn\fR
Integrate the polynomial and return the result\&. The integration
constant is set to zero\&.
.RS
.TP
list \fIpolyn\fR
The polynomial to be integrated
.RE
.sp
.TP
\fB::math::polynomials::degreePolyn\fR \fIpolyn\fR
Return the degree of the polynomial\&.
.RS
.TP
list \fIpolyn\fR
The polynomial to be examined
.RE
.sp
.TP
\fB::math::polynomials::coeffPolyn\fR \fIpolyn\fR \fIindex\fR
Return the coefficient of the term of the index'th degree of the
polynomial\&.
.RS
.TP
list \fIpolyn\fR
The polynomial to be examined
.TP
int \fIindex\fR
The degree of the term
.RE
.sp
.TP
\fB::math::polynomials::allCoeffsPolyn\fR \fIpolyn\fR
Return the coefficients of the polynomial (in ascending order)\&.
.RS
.TP
list \fIpolyn\fR
The polynomial in question
.RE
.PP
.SH "REMARKS ON THE IMPLEMENTATION"
The implementation for evaluating the polynomials at some point uses
Horn's rule, which guarantees numerical stability and a minimum of
arithmetic operations\&.
To recognise that a polynomial definition is indeed a correct
definition, it consists of a list of two elements: the keyword
"POLYNOMIAL" and the list of coefficients in descending order\&. The
latter makes it easier to implement Horner's rule\&.
.SH "BUGS, IDEAS, FEEDBACK"
This document, and the package it describes, will undoubtedly contain
bugs and other problems\&.
Please report such in the category \fImath :: polynomials\fR of the
\fITcllib Trackers\fR [http://core\&.tcl\&.tk/tcllib/reportlist]\&.
Please also report any ideas for enhancements you may have for either
package and/or documentation\&.
.PP
When proposing code changes, please provide \fIunified diffs\fR,
i\&.e the output of \fBdiff -u\fR\&.
.PP
Note further that \fIattachments\fR are strongly preferred over
inlined patches\&. Attachments can be made by going to the \fBEdit\fR
form of the ticket immediately after its creation, and then using the
left-most button in the secondary navigation bar\&.
.SH KEYWORDS
math, polynomial functions
.SH CATEGORY
Mathematics
.SH COPYRIGHT
.nf
Copyright (c) 2004 Arjen Markus <arjenmarkus@users\&.sourceforge\&.net>

.fi