| 摘要 |
A computer implemented method ( 200 ) is described for determining the equivalence of two sets of simultaneous linear algebraic equations. Each of said equations is of a form: <?in-line-formulae description="In-line Formulae" end="lead"?>e<SUB>i1</SUB>x<SUB>1</SUB>+e<SUB>i2</SUB>x<SUB>2</SUB>+e<SUB>i3</SUB>x<SUB>3</SUB>+ . . . +e<SUB>ii</SUB>x<SUB>n</SUB>=b<SUB>i </SUB><?in-line-formulae description="In-line Formulae" end="tail"?> wherein x<SUB>j </SUB>are unknowns, e<SUB>ij </SUB>are coefficients and b<SUB>i </SUB>are quantities, and defining the relationship between the unknowns within the set. The coefficients and quantities are known algebraic expressions. The unknowns are iteratively eliminated ( 250 to 280 ) from each of the sets of simultaneous linear algebraic equations until each of said equations are in the form: <?in-line-formulae description="In-line Formulae" end="lead"?>(l<SUB>ii</SUB>)<SUB>k</SUB>x<SUB>i</SUB>=(r<SUB>i</SUB>)<SUB>k </SUB><?in-line-formulae description="In-line Formulae" end="tail"?> wherein l<SUB>ii </SUB>and r<SUB>i </SUB>are algebraic expressions, and k={1;2} indicate one of said sets that said equation is derived from. The products (l<SUB>ii</SUB>)<SUB>1</SUB>*(r<SUB>i</SUB>)<SUB>2 </SUB>and (l<SUB>ii</SUB>)<SUB>2</SUB>*(r<SUB>i</SUB>)<SUB>1 </SUB>are compared ( 300 ) for each of the unknowns. Only if the products match ( 310 ) for all the unknowns are the two sets of simultaneous linear algebraic equations equivalent ( 312 ). An apparatus ( 100 ) for performing the above method ( 200 ) is also provided.
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