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TagsInteger Equations Numbers Numerical Analysis Pi
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Page 1

command the brilliance of a thousand mathematicians

Learning Guide

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Page 2

Maple 8
Learning Guide

Based in part on the work of B. W. Char

c© 2002 by Waterloo Maple Inc.

Page 160

5.1 Mathematical Manipulations • 151

> rat_expr := (x^16 - y^16) / (x^8 - y^8);

rat_expr :=
x16 − y16

x8 − y8

> factor( rat_expr );

x8 + y8

> rat_expr := (x^16 - y^16) / (x^7 - y^7);

rat_expr :=
x16 − y16

x7 − y7

> factor(rat_expr);

(y + x) (x2 + y2) (x4 + y4) (x8 + y8)

x6 + y x5 + y2 x4 + y3 x3 + y4 x2 + y5 x+ y6

Specifying the Algebraic Number Field The factor command factors a
polynomial over the ring implied by the coefficients. The following poly-
nomial has integer coefficients, so the terms in the factored form have
integer coefficients.

> poly := x^5 - x^4 - x^3 + x^2 - 2*x + 2;

poly := x5 − x4 − x3 + x2 − 2x+ 2

> factor( poly );

(x− 1) (x2 − 2) (x2 + 1)

In this next example, the coefficients include

2. Note the differences

in the result.

> expand( sqrt(2)*poly );


2x5 −


2x4 −


2x3 +


2x2 − 2


2x+ 2


2

> factor( % );

Page 161

152 • Chapter 5: Evaluation and Simplißcation


2 (x2 + 1) (x+


2) (x−


2) (x− 1)

You can explicitly extend the coefficient field by giving a second ar-
gument to factor.

> poly := x^4 - 5*x^2 + 6;

poly := x4 − 5x2 + 6

> factor( poly );

(x2 − 2) (x2 − 3)

> factor( poly, sqrt(2) );

(x2 − 3) (x+

2) (x−


2)

> factor( poly, { sqrt(2), sqrt(3) } );

−(x+

2) (x−


2) (−x+


3) (x+


3)

You can also specify the extension by using RootOf. Here RootOf(x^2-2)
represents any solution to x2 − 2 = 0, that is either


2 or −


2.

> factor( poly, RootOf(x^2-2) );

(x2 − 3) (x+RootOf(_Z 2 − 2)) (x− RootOf(_Z 2 − 2))

For more information on performing calculations in an algebraic num-
ber field, refer to ?evala.

Factoring in Special Domains Use the Factor command to factor an
expression over the integers modulo p for some prime p. The syntax is
similar to that of the Expand command.

> Factor( x^2+3*x+3 ) mod 7;

(x+ 4) (x+ 6)

The Factor command also allows algebraic field extensions.

Page 319

310 • Index

unordered lists (sets), 22

value, 64, 67
variables

changing, 28
VariationalCalculus, 82
vector fields, 133
VectorCalculus, 82
vectors, 89

transpose of, 89
verboseproc, 194
verifying solutions, 45–47, 71
viewing array contents, 26
viewing coordinates, 97

wave equation, 261
whattype, 179
with, 76
Worksheet, 82
worksheets

saving, 278

XML, 283
XMLTools, 82

zip, 173

Page 320

command the brilliance of a thousand mathematicians

Advanced Programming Guide
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