HP 50g manual SIMP2 function, Propfrac function, Partfrac function, Fcoef function

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.

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.

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:

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