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166 | 166 |
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167 | 167 | ; Fractions |
168 | 168 | (define-rules arithmetic |
169 | | - [sum-to-mult (+ a b) (* (+ 1 (/ b a)) a) #:unsound] ; unsound @ a = 0, b = 1 |
| 169 | + #;[sum-to-mult (+ a b) (* (+ 1 (/ b a)) a) #:unsound] ; unsound @ a = 0, b = 1 |
170 | 170 | [sum-to-mult-rev (* (+ 1 (/ b a)) a) (+ a b)] |
171 | | - [sub-to-mult (- a b) (* (- 1 (/ b a)) a) #:unsound] ; unsound @ a = 0, b = 1 |
| 171 | + #;[sub-to-mult (- a b) (* (- 1 (/ b a)) a) #:unsound] ; unsound @ a = 0, b = 1 |
172 | 172 | [sub-to-mult-rev (* (- 1 (/ b a)) a) (- a b)] |
173 | 173 | [add-to-fraction (+ c (/ b a)) (/ (+ (* c a) b) a)] |
174 | 174 | [add-to-fraction-rev (/ (+ (* c a) b) a) (+ c (/ b a))] |
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177 | 177 | [common-denominator (+ (/ a b) (/ c d)) (/ (+ (* a d) (* c b)) (* b d))]) |
178 | 178 |
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179 | 179 | (define-rules polynomials |
180 | | - [sqr-pow (pow a b) (* (pow a (/ b 2)) (pow a (/ b 2))) #:unsound] ; unsound @ a = -1, b = 1 |
| 180 | + #;[sqr-pow (pow a b) (* (pow a (/ b 2)) (pow a (/ b 2))) #:unsound] ; unsound @ a = -1, b = 1 |
181 | 181 | [flip-+ (+ a b) (sound-/ (- (* a a) (* b b)) (- a b) (+ a b))] |
182 | 182 | [flip-- (- a b) (sound-/ (- (* a a) (* b b)) (+ a b) (- a b))]) |
183 | 183 |
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359 | 359 | [pow-neg (pow a (neg b)) (sound-/ 1 (sound-pow a b 0) 0)]) |
360 | 360 |
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361 | 361 | (define-rules exponents |
362 | | - [pow-to-exp (pow a b) (exp (* (log a) b)) #:unsound] ; unsound @ a = -1, b = 1 |
363 | | - [pow-add (pow a (+ b c)) (* (pow a b) (pow a c)) #:unsound] ; unsound @ a = -1, b = c = 1/2 |
364 | | - [pow-sub (pow a (- b c)) (/ (pow a b) (pow a c)) #:unsound] ; unsound @ a = -1, b = c = 1/2 |
365 | | - [unpow-prod-down (pow (* b c) a) (* (pow b a) (pow c a)) #:unsound]) ; unsound @ a = 1/2, b = c = -1 |
| 362 | + #;[pow-to-exp (pow a b) (exp (* (log a) b)) #:unsound] ; unsound @ a = -1, b = 1 |
| 363 | + #;[pow-add (pow a (+ b c)) (* (pow a b) (pow a c)) #:unsound] ; unsound @ a = -1, b = c = 1/2 |
| 364 | + #;[pow-sub (pow a (- b c)) (/ (pow a b) (pow a c)) #:unsound] ; unsound @ a = -1, b = c = 1/2 |
| 365 | + #;[unpow-prod-down (pow (* b c) a) (* (pow b a) (pow c a)) #:unsound]) ; unsound @ a = 1/2, b = c = -1 |
366 | 366 |
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367 | 367 | ; Logarithms |
368 | 368 | (define-rules exponents |
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