For the past few years I have been working on an artificial intelligence
step-by-step equation solver for elementary algebra equations that solves
these equations using steps that a human would typically use. Here is an
example of what I have working so far:
In> LineForm(SolveSteps(MathParse("(8*x - 2 == -9 + 7*x)"), _x))
8*x - 2 == (-9) + 7*x The original equation.
(8*x - 2) - ((-9) + 7*x) == 0 Subtract (-9) + 7 * x from both
sides.
(8*x - 2) + (-1)*((-9) + 7*x) == 0 Undefine a binary '-' operator.
(8*x + (-1)*2) + (-1)*((-9) + 7*x) == 0 Undefine a binary '-'
operator.
(8*x + (-2)) + (-1)*((-9) + 7*x) == 0 Arithmetic.
(8*x + (-2)) + ((-1)*(-9) + (-1)*(7*x)) == 0 Move occurrences of
the unknown higher.
(8*x + (-2)) + (9 + (-1)*(7*x)) == 0 Arithmetic.
(8*x + (-2)) + (9 + ((-1)*7)*x) == 0 Change the association of *
operators.
(8*x + (-2)) + (9 + (-7)*x) == 0 Arithmetic.
((-2) + 8*x) + (9 + (-7)*x) == 0 Move a copy of the unknown to the
right.
((-2) + 8*x) + ((-7)*x + 9) == 0 Move a copy of the unknown to the
left.
(((-2) + 8*x) + (-7)*x) + 9 == 0 Change the association of +
operators.
((-2) + (8*x + (-7)*x)) + 9 == 0 Change the association of +
operators.
((-2) + (8 + (-7))*x) + 9 == 0 Eliminate one copy of the unknown.
(-2) + (8 + (-7))*x == 0 - 9 Subtract 9 from both sides.
(8 + (-7))*x == (0 - 9) - (-2) Subtract -2 from both sides.
x == ((0 - 9) - (-2))/(8 + (-7)) Divide both sides by 8 + (-7).
x == (-7) Arithmetic.
Is anybody interested in having step-by-step equation solving abilities
like this added to Sage?
Ted
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