Polynomial long division: Difference between revisions
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Let us suppose a polynomial is represented by a vector, <math>x</math> (i.e., an ordered collection of [[wp:Coefficient|coefficients]]) so that the <math>i</math><sup>th</sup> element keeps the coefficient of <math>x^i</math>, and the multiplication by a monomial is a ''shift'' of the vector's elements "towards right" (injecting zeros from left) followed by a multiplication of each element by the coefficient of the monomial. |
Let us suppose a polynomial is represented by a vector, <math>x</math> (i.e., an ordered collection of [[wp:Coefficient|coefficients]]) so that the <math>i</math><sup>th</sup> element keeps the coefficient of <math>x^i</math>, and the multiplication by a monomial is a ''shift'' of the vector's elements "towards right" (injecting zeros from left) followed by a multiplication of each element by the coefficient of the monomial. |
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Then a pseudocode for the polynomial long division could be: |
Then a pseudocode for the polynomial long division using the conventions described above could be: |
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degree('''P'''): |
degree('''P'''): |
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* Error handling (for allocations or for wrong inputs) is not mandatory. |
* Error handling (for allocations or for wrong inputs) is not mandatory. |
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* Conventions can be different; in particular, note that if the first coefficient in the vector is the highest power of x for the polynomial represented by the vector, then the algorithm becomes simpler and shifting can be avoided. |
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'''Example for clarification''' |
'''Example for clarification''' |
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