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Over the ensuing centuries, Chinese, Indian, and Arab mathematicians extended the number of decimal places known through tedious calculations, rather than improvements on Archimedes' method.
After tedious calculations, we have the following lemma.
After tedious calculations, we end up with equation (21).21.
end{aligned} (3.12) After some tedious calculations, we derive (3.11).
Since these are tedious calculations, we restrict ourselves to some exemplary items.
To avoid some tedious calculations, we prove this theorem for a 2 × 2 matrices.
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(It is a little known fact that we at The Economist like nothing better than a nice, tedious calculation; many is the happy hour spent at our offices with a spreadsheet, a gaggle of journalists, and a fresh pot of tea).
The above example shows tedious calculation in candidate generation step.
The GHX boreholes were designed without any tedious calculation by using these graphs.
With the approach given in this paper, we can easily derive Lagrange multipliers without tedious calculation and new variational iteration formulae can be derived.
Following a tedious calculation, we have begin{aligned} operatorname{det}(mathbb{A})&=frac{1}{4}h^{4} bigl[a{b}^{2}cdot b+a^{2}b cdot a+b 1-ab cdotrho b+a+b 1-ab cdotrhob+a 1-ab cdotrho4}h^{4}b+a 1-ab cdotrhobigr) cdotbigl[rho(1-abigrbbigr].
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