Jelly, (削除) 32 (削除ここまで) 31 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪṪƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.
Explanation
ḷ‘ɼ | Increment the register, then revert to the original left argument (i.e. b)
_ | b - a
’ | Subtract 1
;N} | Concatenate to -a
;1 | Concatenate to 1
Ær | Roots of polynomial with terms (b - a - 1, -a, 1)
ÆiṪṪƊ? | Does the last root havecan imaginary component?
\/} , | - If yes, do the following using the original arguments to this link:
1⁄2ßH} | - Call the current link recursively with the square root of the left argument and half the right argument
x®$ | - If not, repeat each term the number of times indicated by the register
ḟ0 | Filter out zeros
Jelly, (削除) 32 (削除ここまで) 31 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪṪƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.
Jelly, (削除) 32 (削除ここまで) 31 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪṪƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.
Explanation
ḷ‘ɼ | Increment the register, then revert to the original left argument (i.e. b)
_ | b - a
’ | Subtract 1
;N} | Concatenate to -a
;1 | Concatenate to 1
Ær | Roots of polynomial with terms (b - a - 1, -a, 1)
ÆiṪṪƊ? | Does the last root havecan imaginary component?
\/} , | - If yes, do the following using the original arguments to this link:
1⁄2ßH} | - Call the current link recursively with the square root of the left argument and half the right argument
x®$ | - If not, repeat each term the number of times indicated by the register
ḟ0 | Filter out zeros
Jelly, 32(削除) 32 (削除ここまで) 31 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪ€ẸƊx®$ÆiṪṪƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.
Jelly, 32 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪ€ẸƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.
Jelly, (削除) 32 (削除ここまで) 31 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪṪƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.
Jelly, 32 bytes
ḷ‘ɼ_’;N};1Ær1⁄2ßH}\/}x®$ÆiṪ€ẸƊ?,ḟ0
A full program taking two arguments, b and a in that order. Implements @xnor’s algorithm, so be sure to upvote that one too! Uses recursion to find real roots to a quadratic equation of the form \$x^2 - w x + (y - w - 1) = 0\$ where \$w = \frac{a}{2 ^ n}\$ and \$y = b ^ \frac{1}{2n} \$ for some non-negative integer \$n\$.