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FACTOR(‘(X^3-9*X)/(X^2-5*X+6)’ )=‘X*(X+3)/(X-2)’
The SIMP2 function
Function SIMP2, in the ARITHMETIC menu, takes as arguments two
numbers or polynomials, representing the numerator and denominator of a
rational fraction, and returns the simplified numerator and denominator.
For example:
SIMP2(‘X^3-1’,’X^2-4*X+3’) = {‘X^2+X+1’,‘X-3’}
The PROPFRAC function
The function PROPFRAC converts a rational fraction into a “proper”
fraction, i.e., an integer part added to a fractional part, if such
decomposition is possible. For example:
PROPFRAC(‘5/4’) = ‘1+1/4’
PROPFRAC(‘(x^2+1)/x^2’) = ‘1+1/x^2’
The PARTFRAC function
The function PARTFRAC decomposes a rational fraction into the partial
fractions that produce the original fraction. For example:
PARTFRAC(‘(2*X^6-14*X^5+29*X^4-37*X^3+41*X^2-16*X+5)/(X^5-
7*X^4+11*X^3-7*X^2+10*X)’) =
‘2*X+(1/2/(X-2)+5/(X-5)+1/2/X+X/(X^2+1))’
The FCOEF function
The function FCOEF, available through the ARITHMETIC/POLYNOMIAL
menu, is used to obtain a rational fraction, given the roots and poles of the
fraction.
The input for the function is a vector listing the roots followed by their
multiplicity (i.e., how many times a given root is repeated), and the poles
followed by their multiplicity represented as a negative number. For
example, if we want to create a fraction having roots 2 with multiplicity 1,
0 with multiplicity 3, and -5 with multiplicity 2, and poles 1 with multiplicity
2 and –3 with multiplicity 5, use:
NOTE: If a rational fraction is given as F(X) = N(X)/D(X), the roots of
the fraction result from solving the equation N(X) = 0, while the poles
result from solving the equation D(X) = 0.
SG49A.book Page 10 Friday, September 16, 2005 1:31 PM