Automatically solving equations in finite fields

Division

• In any circuit or computer program for computing reciprocals in a mathematical system such as a finite field or ring or modular arithmetic system,
• where the reciprocal is built up as a linear combination of two or more working variables or registers that are initialized at the start of the computation, and where the building up is a sequence of operations chosen from
• shifting a variable,
• adding one variable to another,
• subtracting one variable from another,
• negating a variable,
• adding or subtracting a multiple of one variable to or from another,
• exchanging variables,
• permuting variables,
• or renaming variables;
• I claim the corresponding method or circuit for computing a quotient of two quantities, a numerator and a denominator, by initializing said working variables or registers, at the start of the computation, to different values, specifically, each working variable or register is initialized to a value equal to the product of the numerator times the corresponding initial value from the reciprocal circuit or program.