1math::polynomials(n)           Tcl Math Library           math::polynomials(n)
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5______________________________________________________________________________
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NAME

8       math::polynomials - Polynomial functions
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SYNOPSIS

11       package require Tcl  ?8.3?
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13       package require math::polynomials  ?1.0.1?
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15       ::math::polynomials::polynomial coeffs
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17       ::math::polynomials::polynCmd coeffs
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19       ::math::polynomials::evalPolyn polynomial x
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21       ::math::polynomials::addPolyn polyn1 polyn2
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23       ::math::polynomials::subPolyn polyn1 polyn2
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25       ::math::polynomials::multPolyn polyn1 polyn2
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27       ::math::polynomials::divPolyn polyn1 polyn2
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29       ::math::polynomials::remainderPolyn polyn1 polyn2
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31       ::math::polynomials::derivPolyn polyn
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33       ::math::polynomials::primitivePolyn polyn
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35       ::math::polynomials::degreePolyn polyn
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37       ::math::polynomials::coeffPolyn polyn index
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39       ::math::polynomials::allCoeffsPolyn polyn
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41_________________________________________________________________
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DESCRIPTION

44       This package deals with polynomial functions of one variable:
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46       ·      the basic arithmetic operations are extended to polynomials
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48       ·      computing the derivatives and primitives of these functions
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50       ·      evaluation  through  a  general procedure or via specific proce‐
51              dures)
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PROCEDURES

54       The package defines the following public procedures:
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56       ::math::polynomials::polynomial coeffs
57              Return an (encoded) list that defines the polynomial. A  polyno‐
58              mial
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60                 f(x) = a + b.x + c.x**2 + d.x**3
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62              can be defined via:
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64                 set f [::math::polynomials::polynomial [list $a $b $c $d]
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67              coeffs list Coefficients of the polynomial (in ascending
68                     order)
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71       ::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.
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77              coeffs list Coefficients of the polynomial (in ascending
78                     order) or the polynomial definition returned by the poly‐
79                     nomial command.
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82       ::math::polynomials::evalPolyn polynomial x
83              Evaluate the polynomial at x.
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85              polynomial list The polynomial's definition (as returned by
86                     the polynomial command).  order)
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88              x float The coordinate at which to evaluate the polynomial
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91       ::math::polynomials::addPolyn polyn1 polyn2
92              Return a new polynomial which is the sum of the two others.
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94              polyn1 list The first polynomial operand
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96              polyn2 list The second polynomial operand
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99       ::math::polynomials::subPolyn polyn1 polyn2
100              Return  a new polynomial which is the difference of the two oth‐
101              ers.
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103              polyn1 list The first polynomial operand
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105              polyn2 list The second polynomial operand
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108       ::math::polynomials::multPolyn polyn1 polyn2
109              Return a new polynomial which is the product of the two  others.
110              If  one of the arguments is a scalar value, the other polynomial
111              is simply scaled.
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113              polyn1 list The first polynomial operand or a scalar
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115              polyn2 list The second polynomial operand or a scalar
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118       ::math::polynomials::divPolyn polyn1 polyn2
119              Divide the first polynomial by the second polynomial and  return
120              the result. The remainder is dropped
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122              polyn1 list The first polynomial operand
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124              polyn2 list The second polynomial operand
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127       ::math::polynomials::remainderPolyn polyn1 polyn2
128              Divide  the first polynomial by the second polynomial and return
129              the remainder.
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131              polyn1 list The first polynomial operand
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133              polyn2 list The second polynomial operand
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136       ::math::polynomials::derivPolyn polyn
137              Differentiate the polynomial and return the result.
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139              polyn list The polynomial to be differentiated
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142       ::math::polynomials::primitivePolyn polyn
143              Integrate the polynomial and return the result. The  integration
144              constant is set to zero.
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146              polyn list The polynomial to be integrated
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149       ::math::polynomials::degreePolyn polyn
150              Return the degree of the polynomial.
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152              polyn list The polynomial to be examined
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155       ::math::polynomials::coeffPolyn polyn index
156              Return the coefficient of the term of the index'th degree of the
157              polynomial.
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159              polyn list The polynomial to be examined
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161              index int The degree of the term
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164       ::math::polynomials::allCoeffsPolyn polyn
165              Return the coefficients of the polynomial (in ascending order).
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167              polyn list The polynomial in question
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REMARKS ON THE IMPLEMENTATION

170       The implementation for evaluating the polynomials at  some  point  uses
171       Horn's  rule,  which  guarantees  numerical  stability and a minimum of
172       arithmetic operations.  To recognise that a  polynomial  definition  is
173       indeed a correct definition, it consists of a list of two elements: the
174       keyword "POLYNOMIAL" and the list of coefficients in descending  order.
175       The latter makes it easier to implement Horner's rule.
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KEYWORDS

178       math, polynomial functions
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181       Copyright (c) 2004 Arjen Markus <arjenmarkus@users.sourceforge.net>
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186math                                 1.0.1                math::polynomials(n)
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