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Fungrim entry: 73b76c

ab=ab\sqrt{a b} = \sqrt{a} \sqrt{b}
Assumptions:(aCandb[0,))or(bCanda[0,))\left(a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \left[0, \infty\right)\right) \,\mathbin{\operatorname{or}}\, \left(b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, a \in \left[0, \infty\right)\right)
Alternative assumptions:aCandbCandarg ⁣(a)+arg ⁣(b)(π,π]a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \arg\!\left(a\right) + \arg\!\left(b\right) \in \left(-\pi, \pi\right]
TeX:
\sqrt{a b} = \sqrt{a} \sqrt{b}

\left(a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \left[0, \infty\right)\right) \,\mathbin{\operatorname{or}}\, \left(b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, a \in \left[0, \infty\right)\right)

a \in \mathbb{C} \,\mathbin{\operatorname{and}}\, b \in \mathbb{C} \,\mathbin{\operatorname{and}}\, \arg\!\left(a\right) + \arg\!\left(b\right) \in \left(-\pi, \pi\right]
Definitions:
Fungrim symbol Notation Short description
Sqrtz\sqrt{z} Principal square root
CCC\mathbb{C} Complex numbers
ClosedOpenInterval[a,b)\left[a, b\right) Closed-open interval
Infinity\infty Positive infinity
Argarg ⁣(z)\arg\!\left(z\right) Complex argument
OpenClosedInterval(a,b]\left(a, b\right] Open-closed interval
ConstPiπ\pi The constant pi (3.14...)
Source code for this entry:
Entry(ID("73b76c"),
    Formula(Equal(Sqrt(Mul(a, b)), Mul(Sqrt(a), Sqrt(b)))),
    Variables(a, b),
    Assumptions(Or(And(Element(a, CC), Element(b, ClosedOpenInterval(0, Infinity))), And(Element(b, CC), Element(a, ClosedOpenInterval(0, Infinity)))), And(Element(a, CC), Element(b, CC), Element(Add(Arg(a), Arg(b)), OpenClosedInterval(Neg(ConstPi), ConstPi)))))

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

2019-08-21 11:44:15.926409 UTC