No.1 | 2*(3
- x/5)/3 - 4*(1 - x/3) - x/3 - 2*(x/2 - 1/4)/27 + 5/54 = ... |
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This simplification results in
large numerals in a small term (can you imagine, how much effort was
required for inventing such an
example -- just to enjoy the student upon successful simplification !). |
No.2 | ((x- 1)/(x+1) + 1) / ((x- 1)/(x+1) - (x+1)/(x- 1)) - 2 = ... |
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Like all the others on this
page, this double fraction results from the fact, that ':' is not
defined as the division-operator in Isabelle. The fraction
simplifies considerably, too |
No.3 | "(x^2 / (1 - x^2) + 1) / (x / (1 - x) + 1) * (1 + x)" = ... |
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Another double fraction, which
actually simplifies to 1 ! |
No.4 | (36 * b ^ 3 + 3 * a ^ 2 * b ^ 2 + 16 * a ^ 4 * b) / (9 * a ^ 4) = ... |
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This is much work without such
an improblable simplification. |
No.5 | (15*a^2 / x^3 - 5*b^4 / x^2 + 25*c^2 / x) * (x^3 / (5*a*b^3*c^3)) + 1 / c^3 * (b*x / a - 3*a / b^3) = ... |
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This is nice, again ! |
No.6 | (a/2 + b/3)*(b/3 - a/2) = ... |
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And this example probably
should be handled differently. |
No.7 | (a^2/9 + 2*a/(3*b) + 4/b^2)*(a/3 - 2/b) + 8/b^3 = ... |
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Again, there is a nicer
simplification, which does not conform to the normal-form created by
ISACs simplifier (which expands nominator and denominator). The topic
of 'normal-forms' is of great importance in symbolic computation ! |
No.8 | (x / (5*x + 4*y) - y / (5*x - 4*y) + 1) * (25*x^2 - 16*y^2) = ... |
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A challenge for beginners ! |
No.9 | (2*x^2 / (3*y) + x / y^2) * (4*x^4 / (9*y^2) + x^2 / y^4) * (2*x^2 / (3*y) - x / y^2) = ... |
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... and these are just a lot of
work, if done by hand ... |
No.10 | (4*x / (3*y) + 2*y / (3*x))^2 - (2*y / (3*x) - 2*x / y) * (2*y / (3*x) + 2*x / y) = ... |
No.11 | (15*a^4 / (a*x^3) - 5*a*((b^4 - 5*c^2*x) / x^2)) * (x^3 / (5*a*b^3*c^3)) + a / c^3 * (x*(b/a) - 3*b*(a/b^4)) = ... |