Fungrim home page

Fungrim entry: 4e5aad

(abanda=2d)    (v=sgn ⁣(b))   where (d,u,v)=xgcd ⁣(a,b)\left(\left|a\right| \ne \left|b\right| \,\mathbin{\operatorname{and}}\, \left|a\right| = \left|2 d\right|\right) \implies \left(v = \operatorname{sgn}\!\left(b\right)\right)\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)
Assumptions:aZ{0}andbZ{0}a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
\left(\left|a\right| \ne \left|b\right| \,\mathbin{\operatorname{and}}\, \left|a\right| = \left|2 d\right|\right) \implies \left(v = \operatorname{sgn}\!\left(b\right)\right)\; \text{ where } \left(d, u, v\right) = \operatorname{xgcd}\!\left(a, b\right)

a \in \mathbb{Z} \setminus \left\{0\right\} \,\mathbin{\operatorname{and}}\, b \in \mathbb{Z} \setminus \left\{0\right\}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Signsgn ⁣(z)\operatorname{sgn}\!\left(z\right) Sign function
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
ZZZ\mathbb{Z} Integers
Source code for this entry:
    Formula(Where(Implies(And(Unequal(Abs(a), Abs(b)), Equal(Abs(a), Abs(Mul(2, d)))), Equal(v, Sign(b))), Equal(Tuple(d, u, v), XGCD(a, b)))),
    Variables(a, b),
    Assumptions(And(Element(a, SetMinus(ZZ, Set(0))), Element(b, SetMinus(ZZ, Set(0))))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC