1 - ws 1 calculations and rounding.sagews

Writing simple arithmetic expressions and performing basic math operations

basic arithmetic operators are + add, - subtract, asterisk multiply, / divide. Multiplication is NEVER implied! You must use the asterisk.

Make heavy use of parentheses especially when creating fractions! If you want to compute $\frac{2X3}{5-4}$, enter this:

(2*3)/(5-4)

6

To do square roots, use the syntax, sqrt(). For higher roots, use fractional exponents

sqrt(16)

4

3^(1/4)

3^(1/4)

Can we get sage to write the last result using a radical sign? Answer: Any time we want to see a pretty answer, we use the show() command, by wrapping your entire calculation in parentheses. Take f'rinstance our last expression.

show(3^(1/4))

$\displaystyle 3^{\frac{1}{4}}$

no radical sign, but it still looks prettier.

I wonder what sage does if you ask it to do an even root if a negative number?

show(sqrt(-2))

$\displaystyle \sqrt{-2}$

simplify(sqrt(-2))

I*sqrt(2)

Sometimes you might want SAGE to round. Here's one way:

3^(1/4).n(digits=1)
3^(1/4).n(digits=2)
3^(1/4).n(digits=3)
3^(1/4).n(digits=4)
3^(1/4).n(digits=5)
3^(1/4).n(digits=25)

1.3 1.3 1.32 1.316 1.3161 1.316074012952492460819219

pi.n(digits=3)

Another way to approximate is the function, numerical_approx(). Use it like this:

show(numerical_approx(sqrt(2),digits=10))

$\displaystyle 1.414213562$

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