The MuPAD solver

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ToDo’s in the system solverStill a lot is to be added:To do:Replace square roots by new identifiers, and add the minimalpolynomials to the system.To do:Non-algebraic triangular systems.To do:Correct handling of parametrized equations using piecewise.The Open Computer Algebra System 6
Solving algebraic systemsLet a system {f 1 = 0, . . . , f n = 0} in the variables x 1 , . . . , x k be given.The solver proceeds as follows:• Compute a Groebner basis of the ideal I generated by the f i .• Factor: try to write the variety of I as a union of varieties (described as zero-setsof polynomial ideals); if this succeeds, find the zeroes of the ideals separately• Determine a triangular set, that is, polynomials g 1 , . . . , g k with g k only dependingon x k , g k−1 only depending on x k−1 and x k , etc.• Solve g k for x k , substitute the solutions into g k−1 , solve this for x k−1 , etc.The Open Computer Algebra System 7
Page 1 and 2: The MuPAD solverPart IIMuPAD semina
Page 3 and 4: The system solverCalled if:• the
Page 5: Subroutines of the system solverThe
Page 9 and 10: ExampleConsider the system2xy 2 −
Page 11 and 12: To do:We should use walk methods, b
Page 13 and 14: For each list, MuPAD now solves the
Page 15 and 16: Remark:At the moment, (systems of)
Page 17 and 18: NOTE THAT:This part of the solver h
Page 19 and 20: The corresponding equation has the
Page 21 and 22: Another example showing a few of th
Page 23 and 24: Hence we insert three points for x
Page 25 and 26: The handling of optionsThe function
Page 27 and 28: The meaning of the optionsMost opti
Page 29 and 30: Weaknesses and subjects to discussT

The MuPAD solver

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