By Razvan A. Mezei

"An creation to SAGE Programming: With functions to SAGE Interacts for Numerical tools emphasizes the right way to enforce numerical equipment utilizing SAGE Math and SAGE Interacts and in addition addresses the basics of laptop programming, together with if statements, loops, capabilities, and interacts"--

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Compute A10 . ⎜ ⎟ ⎝ 1 2 0⎠ (64) Approximate the solutions of the equation (53) (54) (55) (56) (57) (58) (59) (60) (61) sin(x) = x2 . (65) Approximate the solutions of the equation cos(x) = x3 . (66) Approximate the solutions of the equation sin(x) cos(x) = x2 + 4x + 1. (67) Approximate the solutions of the equation x = x4 − x. 3 GRAPHS In this section, we see how Sage Math can produce the graph of a given function (in both 2D and 3D), and plot a given set of points. This feature is especially important in Numerical Analysis and we’ll use it throughout the remaining of the book.

For example, type is_ and then press the TAB key. You should obtain a list of available functions that start with is_. In this list, one can note functions such as is_even, is_power_of_two, is_prime, is_pseudoprime, and is_squarefree. 7 Working with Strings To output a value or a text, one can use the print statement. This function is especially useful if we need to output to the user multiple lines. Strings (see also p. 80) are text that are included between single or double quotes. When we output a string, Sage Math will print the text as is.

456023377174738 The same solve function (as seen above) can be used to solve for inequalities: solve(x^2-6>=8,x) [[x <= -sqrt(14)], [x >= sqrt(14)]] solve(x^2-6<0,x) [[x > -sqrt(6), x < sqrt(6)]] Note how solutions are enclosed in individual brackets as in [[x <= -sqrt (14)], sqrt(14)]]. This means that we have two distinct solutions: √ [x >= √ (−∞, − 14] and [ 14, ∞). In [[x > √ -sqrt(6), x < sqrt(6)]], we should read that the solution is √ the interval (− 6, 6). Note: As stated above, whenever we are using several variables, we need to declare them.