For more information refer to the simplifysiderels

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Unformatted text preview: dx > combine( expr ); combine: combine: combine: combine: combine: combine: combine: combine: combine: combine: combine: combine: combine: combine: combining combining combining combining combining combining combining combining combining combining combining combining combining combining with with with with with with with with with with with with with with respect respect respect respect respect respect respect respect respect respect respect respect respect respect to to to to to to to to to to to to to to linear linear linear cmbpwr power power power cmbplus cmbpwr power cmbpwr power power power x2 + 1 dx The expand command applies most of these transformation rules in the other direction. See this section, page 156. Factored Normal Form If an expression contains fractions, convert the expression into one large fraction, and cancel common factors in the numerator and denominator. The normal command performs this process, which often leads to simpler expressions. > normal( x + 1/x ); x2 + 1 x 166 • Chapter 6: Evaluation and Simplification > expr := x/(x+1) + 1/x + 1/(1+x); expr := > normal( expr ); x 1 1 ++ x+1 x x+1 x+1 x > expr := (x^2 - y^2) / (x-y)^3; expr := x2 − y 2 (x − y )3 > normal( expr ); x+y (x − y )2 > expr := (x - 1/x) / (x-2); 1 x expr := x−2 x− > normal( expr ); x2 − 1 x (x − 2) Use the second argument expanded if you want normal to expand the numerator and the denominator. > normal( expr, expanded ); x2 − 1 x2 − 2 x The normal command acts recursively over functions, sets, and lists. > normal( [ expr, exp(x+1/x) ] ); 6.1 Mathematical Manipulations • 167 [ x2 +1 x2 − 1 , e( x ) ] x (x − 2) > big_expr := sin( (x*(x+1)-x)/(x+2) )^2 > + cos( (x^2)/(-x-2) )^2; big _expr := sin( > normal( big_expr ); (x + 1) x − x 2 x2 ) + cos( )2 x+2 −x − 2 sin( x2 2 x2 2 ) + cos( ) x+2 x+2 Note from the previous example that normal does not simplify trigonometric expressions, only rational polynomial functions. A Special Case Normal may return an expression in expanded form that is not as simple as the factored form. > expr := (x^25-1) / (x-1); expr := > normal( expr ); x25 − 1 x−1 1 + x2 + x + x11 + x12 + x4 + x3 + x5 + x16 + x7 + x6 + x14 + x19 + x17 + x15 + x18 + x9 + x8 + x10 + x24 + x22 + x23 + x21 + x20 + x13 To cancel the common (x − 1) term from the numerator and the denominator without expanding the numerator, use factor. See this section, page 161. > factor(expr); (x4 + x3 + x2 + x + 1) (x20 + x15 + x10 + x5 + 1) 168 • Chapter 6: Evaluation and Simplification Simplifying Expressions The results of Maple simplification calculations can be very complicated. The simplify command tries to find a simpler expression by applying a list of manipulations. > expr := 4^(1/2) + 3; expr := > simplify( expr ); √ 4+3 5 > expr := cos(x)^5 + sin(x)^4 + 2*cos(x)^2 > - 2*sin(x)^2 - cos(2*x); expr := cos(x)5 + sin(x)4 + 2 cos(x)2 − 2 sin(x)2 − cos(2 x) &...
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This note was uploaded on 08/27/2012 for the course MATH 1100 taught by Professor Nil during the Spring '12 term at National University of Singapore.

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