28 lines
947 B
Text
28 lines
947 B
Text
module
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-- Tests for `grind` as solver for linear equations in an `IntModule` or `RatModule`.
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open Lean.Grind
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section IntModule
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variable (R : Type u) [IntModule R]
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-- In an `IntModule`, we should be able to handle relations
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-- this is harder, and less important, than being able to do this in `RatModule`.
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example (a b : R) (h : a + b = 0) : 3 * a - 7 * b = 9 * a + a := by grind
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example (a b c : R) (h : 2 * a + 2 * b = 4 * c) : 3 * a + c = 5 * c - b + (-b) + a := by grind
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end IntModule
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section RatModule
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variable (R : Type u) [IntModule R] [NoNatZeroDivisors R]
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example (a b : R) (h : a + b = 0) : 3 * a - 7 * b = 9 * a + a := by grind
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example (a b c : R) (h : 2 * a + 2 * b = 4 * c) : 3 * a + c = 5 * c - b + (-b) + a := by grind
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-- In a `RatModule` we can clear common divisors.
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example (a : R) (h : a + a = 0) : a = 0 := by grind
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example (a b c : R) (h : 2 * a + 2 * b = 4 * c) : 3 * a + c = 7 * c - 3 * b := by grind
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end RatModule
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